bayesian-statistics.ipynb

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    "# Statistical comparison using Bayesian Statistics\n",
    "___\n",
    "\n",
    "## Motivation\n",
    "\n",
    "Bayesian Statistics is the new prefered way of comparing results in Machine Learning, it has many advantages over the traditional frequentist approach.\n",
    "\n",
    "## Background\n",
    "\n",
    "Bayesian Statistics is based on [Bayes' Theorem](https://en.wikipedia.org/wiki/Bayes%27_theorem) and we have that the posterior is proportional to the prior times the likelihood:\n",
    "\n",
    "$\\text{posterior} \\propto \\text{prior} * \\text{likelihood} $\n",
    "\n",
    "the prior being the initial belief about the population and the likelihood the probability of occurrence of each sample in the population.\n",
    "\n",
    "After calculating the posterior, it holds our entire belief about the population and we can use it to answer questions probabilistically.\n",
    "\n",
    "## Assumptions\n",
    "\n",
    "Below we consider the set of live results of a single account as a single population.\n",
    "\n",
    "Also, it is assumed that accounts did not change models in the past 30 rounds because we cannot know this from other people's accounts.\n",
    "\n",
    "## Evaluating a single account\n",
    "\n",
    "The mean of a population is lower than zero?\n",
    "This is a null hypothesis that we can evaluate using Bayesian Statistics.\n",
    "\n",
    "And we can use the posterior to answer the following related question:\n",
    "What's the probability of the mean of a population being greater than zero?\n",
    "\n",
    "### How many live results should we use to evaluate an account?\n",
    "\n",
    "The [convergence plot below](#Plots) tries to answer this question.\n",
    "The plot is read backwards, as we consider an increasing number of points from the most recent results, the mean converges to a value and the 98% high density interval (HDI) converges to a small region.\n",
    "\n",
    "From this plot we select the number of rounds and we ask, can we reject the null hypothesis?\n",
    "- For arbitrage:\n",
    "  - considering 10 rounds, we cannot because zero is inside the HDI;\n",
    "  - considering 20 rounds, we can reject the null hypothesis.\n",
    "- For benben11:\n",
    "  - considering just 6 rounds, we can already reject the null hypothehis.\n",
    "- For jrb:\n",
    "  - even with 30 rounds, we cannot reject the null hypothesis.\n",
    "  \n",
    "When we can reject the null hypothesis, we also know that the probability of the mean of the population being grater than zero is greater than 99%!\n",
    "This is because we are performing a two-sided test.\n",
    "To calculate the 98% HDI, there's 1% above and below it... so when the HDI is above zero, more than 99% of the posterior probability is above zero.\n",
    "\n",
    "### How an account performance evolves after each round?\n",
    "\n",
    "The [timeseries plot below](#Plots) tries to answer this question.\n",
    "After selecting an appropriate number of rounds from the convergence plot, we can see in the timeseries plot how the posterior mean and HDI evolve at each round.\n",
    "\n",
    "Using 20 rounds as the official leaderboard, we note that:\n",
    "- For arbitrage, the HDI has been above zero only in the latest 11 rounds;\n",
    "- For benben11, the latest 10 rounds gave a huge boost to the HDI;\n",
    "- For hiryuu, the HDI has been steady above zero for the latest 20 rounds;\n",
    "- For jrb, the HDI has not been above zero for the latest 30 rounds;\n",
    "- For themicon, the HDI was well above zero for most rounds but it has lowered in the latest 5 rounds.\n",
    "\n",
    "## Comparing multiple accounts\n",
    "\n",
    "Is the difference of the mean of two populations equal to zero?\n",
    "This is a null hypothesis that cannot be evaluated using Bayesian Statistics because the probability of occurrence of a single particular value is, by definition, zero.\n",
    "\n",
    "Yet, we can use the posterior to answer the following related question:\n",
    "What's the probability of the mean of a population being greater than the mean of another population?\n",
    "\n",
    "It is helpful to define a region where we consider two populations as being equivalent, the region of practical equivalence (ROPE).\n",
    "\n",
    "Below, we consider that two populations with the difference of their means lower than 0.0025 as being equivalent and ignore this region, we are interested in the probability of a population being better than another.\n",
    "\n",
    "Still, comparing just two populations is very limited, so we use the posterior to calculate the probabilities of each population being better and worse than every other population, building a matrix of probabilities, and then we simply take the means and rank the populations.\n",
    "\n",
    "We end up with a mean probability of each population being better than all the others.\n",
    "\n",
    "We show some examples of rankings:\n",
    "- [Some popular accounts](#Some-popular-accounts);\n",
    "- [The top 20 accounts](#Top-20-accounts);\n",
    "- [Nasdaqjockey's accounts](#nasdaqjockey's-accounts), showing that this ranking strategy would work well with [their method to select diagnostic metrics](https://forum.numer.ai/t/does-good-model-diagnostics-correlate-with-tournament-performance/).\n",
    "\n",
    "## Conclusion\n",
    "\n",
    "These are statistical tests about the mean of the populations, meaning that an account can still suffer serious burns in upcoming rounds but we get from the results some hints that help us evaluate how many rounds to consider and how to compare models before deciding to replace underperforming models and how to allocate stakes.\n",
    "\n",
    "## Links\n",
    "\n",
    "- [Statistical comparison of models using grid search](https://scikit-learn.org/stable/auto_examples/model_selection/plot_grid_search_stats.html)\n",
    "- [Time for a Change:  a Tutorial for Comparing Multiple Classifiers Through Bayesian Analysis](https://www.jmlr.org/papers/volume18/16-305/16-305.pdf)\n",
    "- [Bayesian Estimation Supersedes the T-Test](https://docs.pymc.io/notebooks/BEST.html)\n",
    "- [Introduction to Bayesian Stastistics](https://www.amazon.com/Introduction-Bayesian-Statistics-William-Bolstad/dp/1118091566)"
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i < css_urls.length; i++) {\n      var url = css_urls[i];\n      const element = document.createElement(\"link\");\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.rel = \"stylesheet\";\n      element.type = \"text/css\";\n      element.href = url;\n      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n      document.body.appendChild(element);\n    }\n\n    const hashes = {\"https://cdn.bokeh.org/bokeh/release/bokeh-2.2.3.min.js\": \"T2yuo9Oe71Cz/I4X9Ac5+gpEa5a8PpJCDlqKYO0CfAuEszu1JrXLl8YugMqYe3sM\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.2.3.min.js\": \"98GDGJ0kOMCUMUePhksaQ/GYgB3+NH9h996V88sh3aOiUNX3N+fLXAtry6xctSZ6\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.2.3.min.js\": \"89bArO+nlbP3sgakeHjCo1JYxYR5wufVgA3IbUvDY+K7w4zyxJqssu7wVnfeKCq8\"};\n\n    for (var i = 0; i < js_urls.length; i++) {\n      var url = js_urls[i];\n      var element = document.createElement('script');\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.async = false;\n      element.src = url;\n      if (url in hashes) {\n        element.crossOrigin = \"anonymous\";\n        element.integrity = \"sha384-\" + hashes[url];\n      }\n      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      document.head.appendChild(element);\n    }\n  };\n\n  function inject_raw_css(css) {\n    const element = document.createElement(\"style\");\n    element.appendChild(document.createTextNode(css));\n    document.body.appendChild(element);\n  }\n\n  \n  var js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-2.2.3.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.2.3.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.2.3.min.js\"];\n  var css_urls = [];\n  \n\n  var inline_js = [\n    function(Bokeh) {\n      Bokeh.set_log_level(\"info\");\n    },\n    function(Bokeh) {\n    \n    \n    }\n  ];\n\n  function run_inline_js() {\n    \n    if (root.Bokeh !== undefined || force === true) {\n      \n    for (var i = 0; i < inline_js.length; i++) {\n      inline_js[i].call(root, root.Bokeh);\n    }\n    if (force === true) {\n        display_loaded();\n      }} else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(run_inline_js, 100);\n    } else if (!root._bokeh_failed_load) {\n      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n      root._bokeh_failed_load = true;\n    } else if (force !== true) {\n      var cell = $(document.getElementById(\"1001\")).parents('.cell').data().cell;\n      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n    }\n\n  }\n\n  if (root._bokeh_is_loading === 0) {\n    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n    run_inline_js();\n  } else {\n    load_libs(css_urls, js_urls, function() {\n      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n      run_inline_js();\n    });\n  }\n}(window));"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import arviz as az\n",
    "import numpy as np\n",
    "import pymc3 as pm\n",
    "import pandas as pd\n",
    "\n",
    "from scipy import stats\n",
    "from numerapi import NumerAPI\n",
    "from tqdm.notebook import tqdm\n",
    "\n",
    "from bokeh.io import output_notebook, show\n",
    "from bokeh.models import Span\n",
    "from bokeh.plotting import figure\n",
    "\n",
    "output_notebook()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import logging\n",
    "\n",
    "logging.getLogger('pymc3').setLevel(logging.CRITICAL)\n",
    "logging.getLogger('filelock').setLevel(logging.WARNING)\n",
    "logging.getLogger('numexpr.utils').setLevel(logging.WARNING)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "napi = NumerAPI()\n",
    "\n",
    "\n",
    "def get_metrics(username):\n",
    "    try:\n",
    "        df = pd.DataFrame(napi.daily_submissions_performances(username))\n",
    "    except:\n",
    "        return None\n",
    "\n",
    "    results = []\n",
    "    for name, group in df.groupby('roundNumber'):\n",
    "        values = group.drop(['correlationWithMetamodel', 'fnc'], axis=1).dropna()\n",
    "        if values.shape[0] > 0:\n",
    "            values = values.sort_values('date').tail(1).to_dict('records')[0]\n",
    "            results.append({\n",
    "                'round': name,\n",
    "                'corr': values['correlation'],\n",
    "                'mmc': values['mmc'],\n",
    "                'corr+mmc': values['correlation'] + values['mmc'],\n",
    "            })\n",
    "    return pd.DataFrame(results)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_summary_mean(observed, hdi_prob=0.98):\n",
    "     with pm.Model():\n",
    "        prior_mean = pm.Normal('mean', mu=0, sigma=1)\n",
    "        prior_std = pm.HalfNormal('std', sigma=0.4 / 6)\n",
    "        likelihood = pm.Normal('likelihood', mu=prior_mean, sigma=prior_std, observed=observed)\n",
    "\n",
    "        trace = pm.sample(2000, return_inferencedata=True, progressbar=False)\n",
    "        return az.summary(trace, hdi_prob=hdi_prob).T['mean'].to_dict()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_convergence(metrics, metric_name='corr+mmc', n_rounds=30):\n",
    "    stats = []\n",
    "    for n in tqdm(list(range(1, n_rounds+1)), leave=False):\n",
    "        df = metrics.tail(n)\n",
    "\n",
    "        if len(df) < n:\n",
    "            continue\n",
    "\n",
    "        idx = df['round'].values[0]\n",
    "        observed = df[metric_name].values\n",
    "        summary = get_summary_mean(observed)\n",
    "        stats.append({\n",
    "            'round': idx,\n",
    "            'mean': summary['mean'],\n",
    "            'lower': summary['hdi_1%'],\n",
    "            'higher': summary['hdi_99%'],\n",
    "        })\n",
    "\n",
    "    stats = pd.DataFrame(stats)\n",
    "    return metrics.merge(stats, on='round')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "def get_timeseries(metrics, metric_name='corr+mmc', n_rounds=30, n_points=20):\n",
    "    stats = []\n",
    "    for n in tqdm(list(range(n_rounds)), leave=False):\n",
    "        df = metrics.head(len(metrics) - n)\n",
    "        df = df.tail(n_points)\n",
    "\n",
    "        if len(df) < 1:\n",
    "            continue\n",
    "\n",
    "        idx = df['round'].values[-1]\n",
    "        observed = df[metric_name].values\n",
    "        summary = get_summary_mean(observed)\n",
    "        stats.append({\n",
    "            'round': idx,\n",
    "            'mean': summary['mean'],\n",
    "            'lower': summary['hdi_1%'],\n",
    "            'higher': summary['hdi_99%'],\n",
    "        })\n",
    "\n",
    "    stats = pd.DataFrame(stats)\n",
    "    return metrics.merge(stats, on='round')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_series(data, title='', metric_name='corr+mmc'):\n",
    "    plt = figure(width=900, height=300, y_range=(-0.26, 0.26), title=title)\n",
    "\n",
    "    plt.varea(data['round'], data['lower'], data['higher'], color='gray', alpha=0.1, legend_label='hdi')\n",
    "\n",
    "    plt.line(data['round'], data['mean'], color='green', line_width=1, legend_label='mean')\n",
    "\n",
    "    plt.line(data['round'], data[metric_name], color='blue', line_width=1, legend_label='metric')\n",
    "    plt.circle(data['round'], data[metric_name], color='blue', line_width=1, legend_label='metric')\n",
    "\n",
    "    if len(data) > 19:\n",
    "        plt.add_layout(Span(location=data['round'].max() - 19,\n",
    "                            dimension='height',\n",
    "                            line_color='gray',\n",
    "                            line_dash='dashed'))\n",
    "\n",
    "    if len(data) > 4:\n",
    "        plt.add_layout(Span(location=data['round'].max() - 3,\n",
    "                            dimension='height',\n",
    "                            line_color='gray',\n",
    "                            line_dash='dashed'))\n",
    "\n",
    "    plt.legend.location = 'bottom_left'\n",
    "    plt.legend.click_policy = 'hide'\n",
    "    return plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f700de6e3d154d71a14f3468f92575a7",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(HTML(value=''), FloatProgress(value=0.0, max=10.0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "accounts = [\n",
    "    'arbitrage',\n",
    "    'benben11',\n",
    "    'hiryuu',\n",
    "    'integration_test_7',\n",
    "    'jrb',\n",
    "    'nasdaqjockey',\n",
    "    'niam',\n",
    "    'sorios',\n",
    "    'themicon',\n",
    "    'uuazed',\n",
    "]\n",
    "\n",
    "results = {n: get_metrics(n) for n in tqdm(accounts)}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
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       "version_minor": 0
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      ]
     },
     "metadata": {},
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    },
    {
     "data": {
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     "metadata": {},
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    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "convergences = {k: get_convergence(v) for k, v in tqdm(results.items())}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
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   "outputs": [
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      "\n"
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    }
   ],
   "source": [
    "timeseries = {k: get_timeseries(v) for k, v in tqdm(results.items())}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "  <div class=\"bk-root\" id=\"e8d09826-d049-48e7-a238-be2030340bd2\" data-root-id=\"1002\"></div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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       "(function(root) {\n",
       "  function embed_document(root) {\n",
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       "  var render_items = [{\"docid\":\"38ed6878-798f-443d-bb70-3debeb994395\",\"root_ids\":[\"1002\"],\"roots\":{\"1002\":\"e8d09826-d049-48e7-a238-be2030340bd2\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else {\n",
       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
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       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
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       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
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       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
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       "  var render_items = [{\"docid\":\"08217cc5-36a4-46cb-8b2b-d92bc3c90a85\",\"root_ids\":[\"1390\"],\"roots\":{\"1390\":\"772f558f-edf7-4575-ac35-33fc523147e7\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else {\n",
       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
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       "\n",
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       "\n",
       "\n",
       "\n",
       "\n",
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       "  function embed_document(root) {\n",
       "    \n",
       "  var docs_json = 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:{\"data_source\":{\"id\":\"1638\"},\"glyph\":{\"id\":\"1639\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"1640\"},\"selection_glyph\":null,\"view\":{\"id\":\"1642\"}},\"id\":\"1641\",\"type\":\"GlyphRenderer\"},{\"attributes\":{},\"id\":\"1628\",\"type\":\"ResetTool\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.1},\"fill_color\":{\"value\":\"blue\"},\"line_alpha\":{\"value\":0.1},\"line_color\":{\"value\":\"blue\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1689\",\"type\":\"Circle\"},{\"attributes\":{\"click_policy\":\"hide\",\"items\":[{\"id\":\"1652\"},{\"id\":\"1668\"},{\"id\":\"1686\"}],\"location\":\"bottom_left\"},\"id\":\"1651\",\"type\":\"Legend\"},{\"attributes\":{\"end\":0.26,\"start\":-0.26},\"id\":\"1610\",\"type\":\"Range1d\"},{\"attributes\":{\"dimension\":\"height\",\"line_color\":\"gray\",\"line_dash\":[6],\"location\":234},\"id\":\"1706\",\"type\":\"Span\"},{\"attributes\":{\"data_source\":{\"id\":\"1653\"},\"glyph\":{\"id\":\"1654\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"1655\"},\"selection_glyph\":null,\"view\":{\"id\":\"1657\"}},\"id\":\"1656\",\"type\":\"GlyphRenderer\"},{\"attributes\":{},\"id\":\"1617\",\"type\":\"BasicTicker\"},{\"attributes\":{\"label\":{\"value\":\"metric\"},\"renderers\":[{\"id\":\"1672\"},{\"id\":\"1690\"}]},\"id\":\"1686\",\"type\":\"LegendItem\"},{\"attributes\":{\"data\":{\"x\":[223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253],\"y1\":{\"__ndarray__\":\"O99PjZdugr+4HoXrUbiOv7pJDAIrh5a/eekmMQisnL8ZBFYOLbKdv/p+arx0k5i/mpmZmZmZmb+amZmZmZmZv/p+arx0k5i/eekmMQisnL85tMh2vp+avxkEVg4tsp2/2c73U+Olm7/ZzvdT46Wbvzm0yHa+n5q/2/l+arx0k7956SYxCKyMv3sUrkfheoS/eekmMQisfL/8qfHSTWJgv/yp8dJNYnA/eekmMQisjD/6fmq8dJOYP+xRuB6F66E/7FG4HoXroT8730+Nl26iP9v5fmq8dKM/2/l+arx0oz8bL90kBoGlP8uhRbbz/aQ/\",\"dtype\":\"float64\",\"order\":\"little\",\"shape\":[30]},\"y2\":{\"__ndarray__\":\"001iEFg5tD+4HoXrUbiuP7pJDAIrh6Y/7FG4HoXroT956SYxCKycP/yp8dJNYqA/i2zn+6nxoj9MN4lBYOWgPxkEVg4tsp0/2c73U+Olmz956SYxCKycP1pkO99PjZc/GQRWDi2ynT/ZzvdT46WbP3npJjEIrJw/TDeJQWDloD8730+Nl26iP8uhRbbz/aQ/WmQ730+Npz+q8dJNYhCoP3npJjEIrKw//Knx0k1isD8730+Nl26yP9v5fmq8dLM/g8DKoUW2sz/TTWIQWDm0P3sUrkfherQ/arx0kxgEtj8K16NwPQq3P2IQWDm0yLY/\",\"dtype\":\"float64\",\"order\":\"little\",\"shape\":[30]}},\"selected\":{\"id\":\"1650\"},\"selection_policy\":{\"id\":\"1649\"}},\"id\":\"1638\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"green\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1655\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"1621\",\"type\":\"BasicTicker\"},{\"attributes\":{\"source\":{\"id\":\"1638\"}},\"id\":\"1642\",\"type\":\"CDSView\"},{\"attributes\":{\"fill_alpha\":0.1,\"x\":{\"field\":\"x\"},\"y1\":{\"field\":\"y1\"},\"y2\":{\"field\":\"y2\"}},\"id\":\"1639\",\"type\":\"VArea\"},{\"attributes\":{},\"id\":\"1685\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"1704\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"axis\":{\"id\":\"1620\"},\"dimension\":1,\"ticker\":null},\"id\":\"1623\",\"type\":\"Grid\"},{\"attributes\":{\"data_source\":{\"id\":\"1687\"},\"glyph\":{\"id\":\"1688\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"1689\"},\"selection_glyph\":null,\"view\":{\"id\":\"1691\"}},\"id\":\"1690\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"line_color\":\"green\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1654\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"1649\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"1624\",\"type\":\"PanTool\"},{\"attributes\":{\"source\":{\"id\":\"1669\"}},\"id\":\"1673\",\"type\":\"CDSView\"},{\"attributes\":{\"label\":{\"value\":\"hdi\"},\"renderers\":[{\"id\":\"1641\"}]},\"id\":\"1652\",\"type\":\"LegendItem\"},{\"attributes\":{\"source\":{\"id\":\"1653\"}},\"id\":\"1657\",\"type\":\"CDSView\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"blue\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1671\",\"type\":\"Line\"},{\"attributes\":{\"text\":\"Timeseries 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       "  var render_items = [{\"docid\":\"606eb5e7-3b12-4008-9d62-1aef2bc15831\",\"root_ids\":[\"1605\"],\"roots\":{\"1605\":\"aae6f246-9cd6-4d2b-9c19-69832c782766\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else {\n",
       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
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     "output_type": "display_data"
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     "data": {
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       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "  <div class=\"bk-root\" id=\"cd3d0d67-18b9-488c-ba2a-aa181f502025\" data-root-id=\"1834\"></div>\n"
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       "(function(root) {\n",
       "  function embed_document(root) {\n",
       "    \n",
       "  var docs_json = 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       "  var render_items = [{\"docid\":\"7c303068-e125-482a-b593-0500a4159df8\",\"root_ids\":[\"1834\"],\"roots\":{\"1834\":\"cd3d0d67-18b9-488c-ba2a-aa181f502025\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
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       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
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       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
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       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
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       "  var docs_json = 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integration_test_7\"},\"id\":\"2335\",\"type\":\"Title\"},{\"attributes\":{\"formatter\":{\"id\":\"2375\"},\"ticker\":{\"id\":\"2350\"}},\"id\":\"2349\",\"type\":\"LinearAxis\"},{\"attributes\":{},\"id\":\"2346\",\"type\":\"BasicTicker\"},{\"attributes\":{\"source\":{\"id\":\"2367\"}},\"id\":\"2371\",\"type\":\"CDSView\"},{\"attributes\":{\"label\":{\"value\":\"hdi\"},\"renderers\":[{\"id\":\"2370\"}]},\"id\":\"2381\",\"type\":\"LegendItem\"},{\"attributes\":{\"axis\":{\"id\":\"2345\"},\"ticker\":null},\"id\":\"2348\",\"type\":\"Grid\"},{\"attributes\":{},\"id\":\"2378\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"2353\",\"type\":\"PanTool\"},{\"attributes\":{\"line_color\":\"green\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"2383\",\"type\":\"Line\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"blue\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"2400\",\"type\":\"Line\"},{\"attributes\":{\"source\":{\"id\":\"2416\"}},\"id\":\"2420\",\"type\":\"CDSView\"},{\"attributes\":{\"end\":0.26,\"start\":-0.26},\"id\":\"2339\",\"type\":\"Range1d\"},{\"attributes\":{},\"id\":\"2396\",\"type\":\"Selection\"},{\"attributes\":{\"data_source\":{\"id\":\"2382\"},\"glyph\":{\"id\":\"2383\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"2384\"},\"selection_glyph\":null,\"view\":{\"id\":\"2386\"}},\"id\":\"2385\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"active_drag\":\"auto\",\"active_inspect\":\"auto\",\"active_multi\":null,\"active_scroll\":\"auto\",\"active_tap\":\"auto\",\"tools\":[{\"id\":\"2353\"},{\"id\":\"2354\"},{\"id\":\"2355\"},{\"id\":\"2356\"},{\"id\":\"2357\"},{\"id\":\"2358\"}]},\"id\":\"2360\",\"type\":\"Toolbar\"},{\"attributes\":{\"fill_alpha\":0.1,\"x\":{\"field\":\"x\"},\"y1\":{\"field\":\"y1\"},\"y2\":{\"field\":\"y2\"}},\"id\":\"2369\",\"type\":\"VArea\"},{\"attributes\":{},\"id\":\"2433\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"2350\",\"type\":\"BasicTicker\"},{\"attributes\":{\"click_policy\":\"hide\",\"items\":[{\"id\":\"2381\"},{\"id\":\"2397\"},{\"id\":\"2415\"}],\"location\":\"bottom_left\"},\"id\":\"2380\",\"type\":\"Legend\"},{\"attributes\":{},\"id\":\"2395\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"axis\":{\"id\":\"2349\"},\"dimension\":1,\"ticker\":null},\"id\":\"2352\",\"type\":\"Grid\"},{\"attributes\":{\"data_source\":{\"id\":\"2367\"},\"glyph\":{\"id\":\"2368\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"2369\"},\"selection_glyph\":null,\"view\":{\"id\":\"2371\"}},\"id\":\"2370\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"bottom_units\":\"screen\",\"fill_alpha\":0.5,\"fill_color\":\"lightgrey\",\"left_units\":\"screen\",\"level\":\"overlay\",\"line_alpha\":1.0,\"line_color\":\"black\",\"line_dash\":[4,4],\"line_width\":2,\"right_units\":\"screen\",\"top_units\":\"screen\"},\"id\":\"2359\",\"type\":\"BoxAnnotation\"},{\"attributes\":{\"data_source\":{\"id\":\"2416\"},\"glyph\":{\"id\":\"2417\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"2418\"},\"selection_glyph\":null,\"view\":{\"id\":\"2420\"}},\"id\":\"2419\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"data\":{\"x\":[224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253],\"y\":{\"__ndarray__\":\"nLY7ViQCk79jINPfK+2Lvxe4Sqpf1Ig//FwZGly0oD+Dvyq81WGwPx12+Gyp3rc/4My1W5HPqT95p7+ulC+dP2MofVApnIS/JPhtJ/9Zpr9aITZSNginv3Yc2ssWHZI/kqZrx0/WkD/+No3kCw+qP4XG9awDRq8/ycVCO4NKrT/hLqjPGDSiP55saBCm2qE/TnIgb9qukz+HrLwFhTV0v4Ewd3Fdb7A/+RE4dvQusT9RoKzMMjuwP+BFtq7xVKo/4fFNUMT7lz+sW+cotRVWv9wLevaJU3U//VgY3IhKlz+xFXF5LGdkP0N+ulS/zJa/\",\"dtype\":\"float64\",\"order\":\"little\",\"shape\":[30]}},\"selected\":{\"id\":\"2414\"},\"selection_policy\":{\"id\":\"2413\"}},\"id\":\"2398\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"data\":{\"x\":[224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253],\"y\":{\"__ndarray__\":\"+n5qvHSTmD+amZmZmZmZP9nO91PjpZs/2c73U+Olmz/ZzvdT46WbPzm0yHa+n5o/WmQ730+Nlz+6SQwCK4eWPxsv3SQGgZU/WmQ730+Nlz85tMh2vp+aP7gehetRuJ4/uB6F61G4nj9YObTIdr6fP7gehetRuJ4/eekmMQisnD85tMh2vp+aP5qZmZmZmZk/+n5qvHSTmD+amZmZmZmZP9nO91PjpZs/WmQ730+Nlz8730+Nl26SP7pJDAIrh4Y/exSuR+F6dD/8qfHSTWJQP/yp8dJNYmA//Knx0k1iYD+6SQwCK4eGvxsv3SQGgZW/\",\"dtype\":\"float64\",\"order\":\"little\",\"shape\":[30]}},\"selected\":{\"id\":\"2396\"},\"selection_policy\":{\"id\":\"2395\"}},\"id\":\"2382\",\"type\":\"ColumnDataSource\"}],\"root_ids\":[\"2334\"]},\"title\":\"Bokeh Application\",\"version\":\"2.2.3\"}};\n",
       "  var render_items = [{\"docid\":\"37b13908-7451-47e7-9e3e-1da472cbcc64\",\"root_ids\":[\"2334\"],\"roots\":{\"2334\":\"ac5f68fe-754c-4dd8-84d4-ebb14cdb3fef\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else {\n",
       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "2334"
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "  <div class=\"bk-root\" id=\"5673126f-d7cf-466d-a6f2-74f89b32eda3\" data-root-id=\"2605\"></div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
       "  function embed_document(root) {\n",
       "    \n",
       "  var docs_json = 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Application\",\"version\":\"2.2.3\"}};\n",
       "  var render_items = [{\"docid\":\"3a5eea1f-042a-4fc3-8559-e725d3571210\",\"root_ids\":[\"2605\"],\"roots\":{\"2605\":\"5673126f-d7cf-466d-a6f2-74f89b32eda3\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else {\n",
       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "2605"
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "  <div class=\"bk-root\" id=\"419f21d7-eb81-4d32-8c2d-6ff9fcc1d50c\" data-root-id=\"2890\"></div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
       "  function embed_document(root) {\n",
       "    \n",
       "  var docs_json = 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       "  var render_items = [{\"docid\":\"b3455967-d0a3-4c33-9004-a3c42a44e23a\",\"root_ids\":[\"2890\"],\"roots\":{\"2890\":\"419f21d7-eb81-4d32-8c2d-6ff9fcc1d50c\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else {\n",
       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
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       "    \n",
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       "  var render_items = [{\"docid\":\"6499ed93-d7fc-4b04-8ed2-44a848681d78\",\"root_ids\":[\"3189\"],\"roots\":{\"3189\":\"97f8ea98-7353-44e7-9654-c803618cf3a1\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else {\n",
       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
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       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
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       "(function(root) {\n",
       "  function embed_document(root) {\n",
       "    \n",
       "  var docs_json = 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- nasdaqjockey\"},\"id\":\"3503\",\"type\":\"Title\"},{\"attributes\":{\"line_color\":\"blue\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"3567\",\"type\":\"Line\"},{\"attributes\":{\"dimension\":\"height\",\"line_color\":\"gray\",\"line_dash\":[6],\"location\":250},\"id\":\"3604\",\"type\":\"Span\"},{\"attributes\":{\"label\":{\"value\":\"metric\"},\"renderers\":[{\"id\":\"3569\"},{\"id\":\"3587\"}]},\"id\":\"3583\",\"type\":\"LegendItem\"},{\"attributes\":{\"source\":{\"id\":\"3550\"}},\"id\":\"3554\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"3563\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.1},\"fill_color\":{\"value\":\"blue\"},\"line_alpha\":{\"value\":0.1},\"line_color\":{\"value\":\"blue\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"3586\",\"type\":\"Circle\"},{\"attributes\":{},\"id\":\"3543\",\"type\":\"BasicTickFormatter\"}],\"root_ids\":[\"3502\"]},\"title\":\"Bokeh Application\",\"version\":\"2.2.3\"}};\n",
       "  var render_items = [{\"docid\":\"472dace1-67a6-4ab9-aa1e-d171080c8a51\",\"root_ids\":[\"3502\"],\"roots\":{\"3502\":\"6a771e4e-1983-4f1f-bf60-1d56761322d4\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else {\n",
       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "3502"
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "  <div class=\"bk-root\" id=\"b7cc9e42-478a-411b-a5fd-d6f7fc34b2e0\" data-root-id=\"3829\"></div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
       "  function embed_document(root) {\n",
       "    \n",
       "  var docs_json = 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       "  var render_items = [{\"docid\":\"c1d68ac8-c2ce-48c0-ae0a-86773ef1f9e9\",\"root_ids\":[\"3829\"],\"roots\":{\"3829\":\"b7cc9e42-478a-411b-a5fd-d6f7fc34b2e0\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
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       "    var attempts = 0;\n",
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       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
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       "\n",
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       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
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       "  var render_items = [{\"docid\":\"6ade6cac-6004-487b-83d2-2fecf921c493\",\"root_ids\":[\"4525\"],\"roots\":{\"4525\":\"a500b8f1-a015-4e75-aca2-1f5ccbd82df4\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else {\n",
       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
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     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
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     "output_type": "display_data"
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    {
     "data": {
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       "\n",
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       "\n",
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     "output_type": "display_data"
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       "  function embed_document(root) {\n",
       "    \n",
       "  var docs_json = 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       "  var render_items = [{\"docid\":\"bbfc7fba-d02f-4e0a-a188-be66e7f530c8\",\"root_ids\":[\"4894\"],\"roots\":{\"4894\":\"85756f04-924d-400b-9786-2f9330f8295e\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else {\n",
       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "4894"
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     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "  <div class=\"bk-root\" id=\"2e1bde30-ecf0-4e79-b990-f675fdb2b48c\" data-root-id=\"5277\"></div>\n"
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     "metadata": {},
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       "  function embed_document(root) {\n",
       "    \n",
       "  var docs_json = 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       "  var render_items = [{\"docid\":\"750523ca-7d76-4895-80fc-bd5880da3aac\",\"root_ids\":[\"5277\"],\"roots\":{\"5277\":\"2e1bde30-ecf0-4e79-b990-f675fdb2b48c\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else {\n",
       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
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       "  var render_items = [{\"docid\":\"b45805b7-c8ca-46f4-aa7e-171c83583c29\",\"root_ids\":[\"5674\"],\"roots\":{\"5674\":\"99791d34-a248-43be-b490-a0db86ff3830\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else {\n",
       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
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       "  var render_items = [{\"docid\":\"11909596-3799-444f-915d-afa825ff3b25\",\"root_ids\":[\"6085\"],\"roots\":{\"6085\":\"9d864450-eba3-4344-9a93-1caeb1c466a2\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else {\n",
       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
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       "\n",
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       "    \n",
       "  var docs_json = 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       "  var render_items = [{\"docid\":\"d510fc3c-e749-4ad8-b3a9-0913ea4c9d31\",\"root_ids\":[\"6510\"],\"roots\":{\"6510\":\"33db8398-dbbf-4f50-8dbb-7c26aa126411\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else {\n",
       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
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       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "  <div class=\"bk-root\" id=\"fe1dfed7-c584-454c-bdf8-c43b27de2883\" data-root-id=\"6949\"></div>\n"
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       "  function embed_document(root) {\n",
       "    \n",
       "  var docs_json = 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Application\",\"version\":\"2.2.3\"}};\n",
       "  var render_items = [{\"docid\":\"619fdd7c-e74d-4bad-98e1-86bf2a4f8678\",\"root_ids\":[\"6949\"],\"roots\":{\"6949\":\"fe1dfed7-c584-454c-bdf8-c43b27de2883\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else {\n",
       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "6949"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for name in accounts:\n",
    "    if name in convergences and name in timeseries:\n",
    "        show(plot_series(convergences[name], title=f'Convergence - {name}'))\n",
    "        show(plot_series(timeseries[name], title=f'Timeseries - {name}'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_summary_diff(observed, hdi_prob=0.94):\n",
    "    with pm.Model():\n",
    "        prior_mean_0 = pm.Normal('mean0', mu=0, sigma=1)\n",
    "        prior_std_0 = pm.HalfNormal('std0', sigma=0.4 / 6)\n",
    "        likelihood_0 = pm.Normal('likelihood0', mu=prior_mean_0, sigma=prior_std_0, observed=observed[0])\n",
    "        \n",
    "        prior_mean_1 = pm.Normal('mean1', mu=0, sigma=1)\n",
    "        prior_std_1 = pm.HalfNormal('std1', sigma=0.4 / 6)\n",
    "        likelihood_1 = pm.Normal('likelihood1', mu=prior_mean_1, sigma=prior_std_1, observed=observed[1])\n",
    "\n",
    "        mean_diff = pm.Deterministic('mean_diff', prior_mean_0 - prior_mean_1)\n",
    "        std_diff = pm.Deterministic('std_diff', prior_std_0 - prior_std_1)\n",
    "        effect_size = pm.Deterministic('effect_size',\n",
    "                                       mean_diff / np.sqrt((prior_std_0 ** 2 + prior_std_1 ** 2) / 2))\n",
    "\n",
    "        trace = pm.sample(2000, return_inferencedata=True, progressbar=False)\n",
    "        return az.summary(trace, hdi_prob=hdi_prob).T['mean_diff'].to_dict()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compare(series, n_rounds=20, prob=0.94, rope_prob=0.0025):\n",
    "    summary = get_summary_diff([\n",
    "        series[0].tail(n_rounds).values,\n",
    "        series[1].tail(n_rounds).values\n",
    "    ], hdi_prob=prob)\n",
    "    posterior = stats.norm(loc=summary['mean'], scale=summary['sd'])\n",
    "    lower = posterior.cdf(-rope_prob)\n",
    "    higher = posterior.cdf(rope_prob)\n",
    "    return 1-higher, lower"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_probs(results, accounts, metric_name='corr+mmc', **kwargs):\n",
    "    n_accounts = len(accounts)\n",
    "    data = np.full((n_accounts, n_accounts), np.nan)\n",
    "    for i in tqdm(list(range(n_accounts))):\n",
    "        for j in range(i+1, n_accounts):\n",
    "            better, worse = compare([results[accounts[i]][metric_name], results[accounts[j]][metric_name]], **kwargs)\n",
    "            data[i, j] = better\n",
    "            data[j, i] = worse\n",
    "    return pd.DataFrame(data, columns=accounts, index=accounts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f80422124445495faf974151220c17ad",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(HTML(value=''), FloatProgress(value=0.0, max=10.0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "accounts = [\n",
    "    'arbitrage',\n",
    "    'benben11',\n",
    "    'hiryuu',\n",
    "    'integration_test_7',\n",
    "    'jrb',\n",
    "    'nasdaqjockey',\n",
    "    'niam',\n",
    "    'sorios',\n",
    "    'themicon',\n",
    "    'uuazed',\n",
    "]\n",
    "\n",
    "results = {n: get_metrics(n) for n in tqdm(accounts)}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ff90c31eb1234ab7b731ade7a4a71be2",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(HTML(value=''), FloatProgress(value=0.0, max=10.0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "probs = get_probs(results, accounts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>arbitrage</th>\n",
       "      <th>benben11</th>\n",
       "      <th>hiryuu</th>\n",
       "      <th>integration_test_7</th>\n",
       "      <th>jrb</th>\n",
       "      <th>nasdaqjockey</th>\n",
       "      <th>niam</th>\n",
       "      <th>sorios</th>\n",
       "      <th>themicon</th>\n",
       "      <th>uuazed</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>arbitrage</th>\n",
       "      <td>NaN</td>\n",
       "      <td>3.159335e-03</td>\n",
       "      <td>3.508822e-04</td>\n",
       "      <td>0.636831</td>\n",
       "      <td>0.997906</td>\n",
       "      <td>0.999596</td>\n",
       "      <td>0.967843</td>\n",
       "      <td>0.522152</td>\n",
       "      <td>0.752323</td>\n",
       "      <td>0.232460</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>benben11</th>\n",
       "      <td>0.990516</td>\n",
       "      <td>NaN</td>\n",
       "      <td>5.497382e-01</td>\n",
       "      <td>0.997505</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.999949</td>\n",
       "      <td>0.997378</td>\n",
       "      <td>0.999081</td>\n",
       "      <td>0.953382</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>hiryuu</th>\n",
       "      <td>0.997697</td>\n",
       "      <td>2.940241e-01</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.999423</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.999816</td>\n",
       "      <td>0.999975</td>\n",
       "      <td>0.953698</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>integration_test_7</th>\n",
       "      <td>0.197663</td>\n",
       "      <td>7.057045e-04</td>\n",
       "      <td>8.841729e-05</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.987035</td>\n",
       "      <td>0.995975</td>\n",
       "      <td>0.852094</td>\n",
       "      <td>0.270563</td>\n",
       "      <td>0.554233</td>\n",
       "      <td>0.098236</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>jrb</th>\n",
       "      <td>0.000453</td>\n",
       "      <td>4.492143e-08</td>\n",
       "      <td>2.876854e-11</td>\n",
       "      <td>0.003661</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.480061</td>\n",
       "      <td>0.079404</td>\n",
       "      <td>0.000099</td>\n",
       "      <td>0.007996</td>\n",
       "      <td>0.000144</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>nasdaqjockey</th>\n",
       "      <td>0.000059</td>\n",
       "      <td>2.929088e-08</td>\n",
       "      <td>7.403041e-14</td>\n",
       "      <td>0.000816</td>\n",
       "      <td>0.326355</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.040059</td>\n",
       "      <td>0.000063</td>\n",
       "      <td>0.002186</td>\n",
       "      <td>0.000075</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>niam</th>\n",
       "      <td>0.009387</td>\n",
       "      <td>9.807413e-06</td>\n",
       "      <td>5.256983e-09</td>\n",
       "      <td>0.066807</td>\n",
       "      <td>0.830096</td>\n",
       "      <td>0.894350</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.015130</td>\n",
       "      <td>0.109860</td>\n",
       "      <td>0.005516</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sorios</th>\n",
       "      <td>0.270563</td>\n",
       "      <td>6.675333e-04</td>\n",
       "      <td>1.410220e-05</td>\n",
       "      <td>0.522152</td>\n",
       "      <td>0.999229</td>\n",
       "      <td>0.999477</td>\n",
       "      <td>0.946422</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.691462</td>\n",
       "      <td>0.127902</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>themicon</th>\n",
       "      <td>0.127902</td>\n",
       "      <td>2.326291e-04</td>\n",
       "      <td>2.002612e-06</td>\n",
       "      <td>0.277291</td>\n",
       "      <td>0.974682</td>\n",
       "      <td>0.990613</td>\n",
       "      <td>0.780158</td>\n",
       "      <td>0.145586</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.052081</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>uuazed</th>\n",
       "      <td>0.635386</td>\n",
       "      <td>2.088953e-02</td>\n",
       "      <td>1.632489e-02</td>\n",
       "      <td>0.809213</td>\n",
       "      <td>0.999332</td>\n",
       "      <td>0.999631</td>\n",
       "      <td>0.983207</td>\n",
       "      <td>0.752323</td>\n",
       "      <td>0.886540</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    arbitrage      benben11        hiryuu  integration_test_7  \\\n",
       "arbitrage                 NaN  3.159335e-03  3.508822e-04            0.636831   \n",
       "benben11             0.990516           NaN  5.497382e-01            0.997505   \n",
       "hiryuu               0.997697  2.940241e-01           NaN            0.999423   \n",
       "integration_test_7   0.197663  7.057045e-04  8.841729e-05                 NaN   \n",
       "jrb                  0.000453  4.492143e-08  2.876854e-11            0.003661   \n",
       "nasdaqjockey         0.000059  2.929088e-08  7.403041e-14            0.000816   \n",
       "niam                 0.009387  9.807413e-06  5.256983e-09            0.066807   \n",
       "sorios               0.270563  6.675333e-04  1.410220e-05            0.522152   \n",
       "themicon             0.127902  2.326291e-04  2.002612e-06            0.277291   \n",
       "uuazed               0.635386  2.088953e-02  1.632489e-02            0.809213   \n",
       "\n",
       "                         jrb  nasdaqjockey      niam    sorios  themicon  \\\n",
       "arbitrage           0.997906      0.999596  0.967843  0.522152  0.752323   \n",
       "benben11            1.000000      1.000000  0.999949  0.997378  0.999081   \n",
       "hiryuu              1.000000      1.000000  1.000000  0.999816  0.999975   \n",
       "integration_test_7  0.987035      0.995975  0.852094  0.270563  0.554233   \n",
       "jrb                      NaN      0.480061  0.079404  0.000099  0.007996   \n",
       "nasdaqjockey        0.326355           NaN  0.040059  0.000063  0.002186   \n",
       "niam                0.830096      0.894350       NaN  0.015130  0.109860   \n",
       "sorios              0.999229      0.999477  0.946422       NaN  0.691462   \n",
       "themicon            0.974682      0.990613  0.780158  0.145586       NaN   \n",
       "uuazed              0.999332      0.999631  0.983207  0.752323  0.886540   \n",
       "\n",
       "                      uuazed  \n",
       "arbitrage           0.232460  \n",
       "benben11            0.953382  \n",
       "hiryuu              0.953698  \n",
       "integration_test_7  0.098236  \n",
       "jrb                 0.000144  \n",
       "nasdaqjockey        0.000075  \n",
       "niam                0.005516  \n",
       "sorios              0.127902  \n",
       "themicon            0.052081  \n",
       "uuazed                   NaN  "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "probs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Some popular accounts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>rank</th>\n",
       "      <th>mean_prob</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>benben11</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.943061</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>hiryuu</th>\n",
       "      <td>2.0</td>\n",
       "      <td>0.916070</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>uuazed</th>\n",
       "      <td>3.0</td>\n",
       "      <td>0.678094</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>arbitrage</th>\n",
       "      <td>4.0</td>\n",
       "      <td>0.568069</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sorios</th>\n",
       "      <td>5.0</td>\n",
       "      <td>0.506432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>integration_test_7</th>\n",
       "      <td>6.0</td>\n",
       "      <td>0.439621</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>themicon</th>\n",
       "      <td>7.0</td>\n",
       "      <td>0.372061</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>niam</th>\n",
       "      <td>8.0</td>\n",
       "      <td>0.214573</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>jrb</th>\n",
       "      <td>9.0</td>\n",
       "      <td>0.063535</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>nasdaqjockey</th>\n",
       "      <td>10.0</td>\n",
       "      <td>0.041068</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    rank  mean_prob\n",
       "benben11             1.0   0.943061\n",
       "hiryuu               2.0   0.916070\n",
       "uuazed               3.0   0.678094\n",
       "arbitrage            4.0   0.568069\n",
       "sorios               5.0   0.506432\n",
       "integration_test_7   6.0   0.439621\n",
       "themicon             7.0   0.372061\n",
       "niam                 8.0   0.214573\n",
       "jrb                  9.0   0.063535\n",
       "nasdaqjockey        10.0   0.041068"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "probs.mean(axis=1).rank(ascending=False).sort_values().to_frame('rank').join(\n",
    "    probs.mean(axis=1).to_frame('mean_prob'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "daf8cf6d2f504dc383b6562bda2714de",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(HTML(value=''), FloatProgress(value=0.0, max=20.0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "accounts = [x['username'] for x in napi.get_leaderboard(20)]\n",
    "\n",
    "results = {n: get_metrics(n) for n in tqdm(accounts)}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "05b7cf9ad4ca465eaae1781b10486343",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(HTML(value=''), FloatProgress(value=0.0, max=20.0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "probs = get_probs(results, accounts, 'corr')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Top 20 accounts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>rank</th>\n",
       "      <th>mean_prob</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>quantyquant</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.651241</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>benben11</th>\n",
       "      <td>2.0</td>\n",
       "      <td>0.646935</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>hb_falcon</th>\n",
       "      <td>3.0</td>\n",
       "      <td>0.638706</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>hiryuu</th>\n",
       "      <td>4.0</td>\n",
       "      <td>0.497765</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>labrat</th>\n",
       "      <td>5.0</td>\n",
       "      <td>0.489565</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>uuazed6</th>\n",
       "      <td>6.0</td>\n",
       "      <td>0.480233</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>neuralnetwork3</th>\n",
       "      <td>7.0</td>\n",
       "      <td>0.475968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>uuazed5</th>\n",
       "      <td>8.0</td>\n",
       "      <td>0.457606</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>anna13</th>\n",
       "      <td>9.0</td>\n",
       "      <td>0.437460</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>junyou</th>\n",
       "      <td>10.0</td>\n",
       "      <td>0.377131</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>quantaquetzalcoatlus</th>\n",
       "      <td>11.0</td>\n",
       "      <td>0.367260</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ezekiel_47_v12</th>\n",
       "      <td>12.0</td>\n",
       "      <td>0.345929</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>uuazed4</th>\n",
       "      <td>13.0</td>\n",
       "      <td>0.344450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>uuazed12</th>\n",
       "      <td>14.0</td>\n",
       "      <td>0.311241</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>hiyou</th>\n",
       "      <td>15.0</td>\n",
       "      <td>0.309449</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>kond</th>\n",
       "      <td>16.0</td>\n",
       "      <td>0.290668</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>linearato</th>\n",
       "      <td>17.0</td>\n",
       "      <td>0.278464</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>algotime</th>\n",
       "      <td>18.0</td>\n",
       "      <td>0.273605</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>algoinvestment</th>\n",
       "      <td>19.0</td>\n",
       "      <td>0.253617</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>victoria</th>\n",
       "      <td>20.0</td>\n",
       "      <td>0.164778</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                      rank  mean_prob\n",
       "quantyquant            1.0   0.651241\n",
       "benben11               2.0   0.646935\n",
       "hb_falcon              3.0   0.638706\n",
       "hiryuu                 4.0   0.497765\n",
       "labrat                 5.0   0.489565\n",
       "uuazed6                6.0   0.480233\n",
       "neuralnetwork3         7.0   0.475968\n",
       "uuazed5                8.0   0.457606\n",
       "anna13                 9.0   0.437460\n",
       "junyou                10.0   0.377131\n",
       "quantaquetzalcoatlus  11.0   0.367260\n",
       "ezekiel_47_v12        12.0   0.345929\n",
       "uuazed4               13.0   0.344450\n",
       "uuazed12              14.0   0.311241\n",
       "hiyou                 15.0   0.309449\n",
       "kond                  16.0   0.290668\n",
       "linearato             17.0   0.278464\n",
       "algotime              18.0   0.273605\n",
       "algoinvestment        19.0   0.253617\n",
       "victoria              20.0   0.164778"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "probs.mean(axis=1).rank(ascending=False).sort_values().to_frame('rank').join(\n",
    "    probs.mean(axis=1).to_frame('mean_prob'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "adf889d77d304acb9bec624334a274c2",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(HTML(value=''), FloatProgress(value=0.0, max=15.0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "accounts = [\n",
    "    'evolvz',\n",
    "    'zbrain',\n",
    "    'nasdaqjockey',\n",
    "    'nasdaqjockey1',\n",
    "    'nasdaqjockey2',\n",
    "    'nasdaqjockey3',\n",
    "    'nasdaqjockey4',\n",
    "    'nasdaqjockey5',\n",
    "    'nasdaqjockey6',\n",
    "    'nasdaqjockey7',\n",
    "    'nasdaqjockey8',\n",
    "    'nasdaqjockey9',\n",
    "    'nasdaqjockey10',\n",
    "    'nasdaqjockey11',\n",
    "    'nasdaqjockey12',\n",
    "]\n",
    "\n",
    "results = {n: get_metrics(n) for n in tqdm(accounts)}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a62f86f5123246699d10d6f3d755bf12",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(HTML(value=''), FloatProgress(value=0.0, max=15.0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "probs = get_probs(results, accounts, 'corr', n_rounds=13)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# nasdaqjockey's accounts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>rank</th>\n",
       "      <th>mean_prob</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>nasdaqjockey4</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.832989</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>nasdaqjockey3</th>\n",
       "      <td>2.0</td>\n",
       "      <td>0.693676</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>nasdaqjockey9</th>\n",
       "      <td>3.0</td>\n",
       "      <td>0.652473</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>nasdaqjockey12</th>\n",
       "      <td>4.0</td>\n",
       "      <td>0.520772</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>evolvz</th>\n",
       "      <td>5.0</td>\n",
       "      <td>0.462582</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>nasdaqjockey1</th>\n",
       "      <td>6.0</td>\n",
       "      <td>0.459245</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>nasdaqjockey7</th>\n",
       "      <td>7.0</td>\n",
       "      <td>0.410780</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>nasdaqjockey10</th>\n",
       "      <td>8.0</td>\n",
       "      <td>0.337432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>nasdaqjockey5</th>\n",
       "      <td>9.0</td>\n",
       "      <td>0.322857</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>nasdaqjockey11</th>\n",
       "      <td>10.0</td>\n",
       "      <td>0.299672</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>nasdaqjockey2</th>\n",
       "      <td>11.0</td>\n",
       "      <td>0.273403</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>nasdaqjockey8</th>\n",
       "      <td>12.0</td>\n",
       "      <td>0.191604</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>nasdaqjockey</th>\n",
       "      <td>13.0</td>\n",
       "      <td>0.173835</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>nasdaqjockey6</th>\n",
       "      <td>14.0</td>\n",
       "      <td>0.112489</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>zbrain</th>\n",
       "      <td>15.0</td>\n",
       "      <td>0.098287</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                rank  mean_prob\n",
       "nasdaqjockey4    1.0   0.832989\n",
       "nasdaqjockey3    2.0   0.693676\n",
       "nasdaqjockey9    3.0   0.652473\n",
       "nasdaqjockey12   4.0   0.520772\n",
       "evolvz           5.0   0.462582\n",
       "nasdaqjockey1    6.0   0.459245\n",
       "nasdaqjockey7    7.0   0.410780\n",
       "nasdaqjockey10   8.0   0.337432\n",
       "nasdaqjockey5    9.0   0.322857\n",
       "nasdaqjockey11  10.0   0.299672\n",
       "nasdaqjockey2   11.0   0.273403\n",
       "nasdaqjockey8   12.0   0.191604\n",
       "nasdaqjockey    13.0   0.173835\n",
       "nasdaqjockey6   14.0   0.112489\n",
       "zbrain          15.0   0.098287"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "probs.mean(axis=1).rank(ascending=False).sort_values().to_frame('rank').join(\n",
    "    probs.mean(axis=1).to_frame('mean_prob'))"
   ]
  }
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