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<!DOCTYPE html>
<html>
<head>
<title>Statistical Inference Overview</title>
<meta charset="utf-8">
<meta name="description" content="Statistical Inference Overview">
<meta name="author" content="Jeffrey Leek">
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<hgroup class="auto-fadein">
<h1>Statistical Inference Overview</h1>
<h2></h2>
<p>Jeffrey Leek<br/>Johns Hopkins Bloomberg School of Public Health</p>
</hgroup>
<article></article>
</slide>
<!-- SLIDES -->
<slide class="" id="slide-1" style="background:;">
<hgroup>
<h2>Statistical Inference Content</h2>
</hgroup>
<article data-timings="">
<ul>
<li>Basic probability</li>
<li>Likelihood</li>
<li>Common distributions</li>
<li>Asymptotics</li>
<li>Confidence intervals</li>
<li>Hypothesis tests</li>
<li>Power</li>
<li>Bootstrapping</li>
<li>Non-parametric tests</li>
<li>Basic bayesian statistics</li>
</ul>
</article>
<!-- Presenter Notes -->
</slide>
<slide class="" id="slide-2" style="background:;">
<hgroup>
<h2>Example</h2>
</hgroup>
<article data-timings="">
<p>Suppose that the proportion of help calls that get addressed in
a random day by a help line is given by
\[
f(x) = \left\{\begin{array}{ll}
2 x & \mbox{ for } 1 > x > 0 \\
0 & \mbox{ otherwise}
\end{array} \right.
\]</p>
<p>Is this a mathematically valid density?</p>
</article>
<!-- Presenter Notes -->
</slide>
<slide class="" id="slide-3" style="background:;">
<hgroup>
<h2>The normal distribution</h2>
</hgroup>
<article data-timings="">
<ul>
<li>A random variable is said to follow a <strong>normal</strong> or <strong>Gaussian</strong> distribution with mean \(\mu\) and variance \(\sigma^2\) if the associated density is
\[
(2\pi \sigma^2)^{-1/2}e^{-(x - \mu)^2/2\sigma^2}
\]
If \(X\) a random variable with this density then \(E[X] = \mu\) and \(Var(X) = \sigma^2\)</li>
<li>We write \(X\sim \mbox{N}(\mu, \sigma^2)\)</li>
<li>When \(\mu = 0\) and \(\sigma = 1\) the resulting distribution is called <strong>the standard normal distribution</strong></li>
<li>The standard normal density function is labeled \(\phi\)</li>
<li>Standard normal RVs are often labeled \(Z\)</li>
</ul>
</article>
<!-- Presenter Notes -->
</slide>
<slide class="" id="slide-4" style="background:;">
<hgroup>
<h2>Example bootstrap code</h2>
</hgroup>
<article data-timings="">
<pre><code class="r">B <- 1000
n <- length(gmVol)
resamples <- matrix(sample(gmVol,
n * B,
replace = TRUE),
B, n)
medians <- apply(resamples, 1, median)
sd(medians)
[1] 3.148706
quantile(medians, c(.025, .975))
2.5% 97.5%
582.6384 595.3553
</code></pre>
</article>
<!-- Presenter Notes -->
</slide>
<slide class="backdrop"></slide>
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<ul>
<li>
<a href="#" target="_self" rel='tooltip'
data-slide=1 title='Statistical Inference Content'>
1
</a>
</li>
<li>
<a href="#" target="_self" rel='tooltip'
data-slide=2 title='Example'>
2
</a>
</li>
<li>
<a href="#" target="_self" rel='tooltip'
data-slide=3 title='The normal distribution'>
3
</a>
</li>
<li>
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data-slide=4 title='Example bootstrap code'>
4
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</li>
</ul>
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