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Update README.md
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arnauqb authored Sep 25, 2023
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Expand Up @@ -9,7 +9,7 @@ Here we include multiple examples showcasing the utility of Blackbirds to perfor
The random walk process we considered is given by

$$
x(t+1) = x(t) + 2\epsilon -1, \;\;\; \epsilon \sim \mathrm{Bernoulli}(p)
x(t+1) = x(t) + 2\epsilon -1, \epsilon \sim \mathrm{Bernoulli}(p)
$$

and the inference exercise consists on inferring the value of $p$ from an observed time-series $\{x(t)\}_t$. In `smd/01-random_walk.ipynb` we recover $p$ by just employing gradient descent to minimize the L2 distance between the simulated and the observed time-series. A Bayesian approach using generalized variational inference (GVI) is shown in `variational_inference/01-random_walk.ipynb`. In this case we consider the candidate family to approximate the generalised posterior as a family of normal distributions where we vary the mean $\mu$ and standard deviation $\sigma$.
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