Fixed titles, math rendering, and links on some pages

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Brandon Rozek 2021-07-26 09:13:20 -04:00
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# Bayesian Statistics
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title: Week 1
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## Rules of Probability

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title: Week 2
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Under the frequentest paradigm, you view the data as a random sample from some larger, potentially hypothetical population. We can then make probability statements i.e, long-run frequency statements based on this larger population.
## Coin Flip Example (Central Limit Theorem)
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Frequentest confidence intervals have the interpretation that "If you were to repeat many times the process of collecting data and computing a 95% confidence interval, then on average about 95% of those intervals would contain the true parameter value; however, once you observe data and compute an interval the true value is either in the interval or it is not, but you can't tell which."
Bayesian credible intervals have the interpretation that "Your posterior probability that the parameter is in a 95% credible interval is 95%."
Bayesian credible intervals have the interpretation that "Your posterior probability that the parameter is in a 95% credible interval is 95%."

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---
title: Week 3
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How do we choose a prior?
Our prior needs to represent our personal perspective, beliefs, and our uncertainties.
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2. In Bayesian Statistics, a vague prior refers to one that's relatively flat across much of the space. For a Gamma prior we can choose $\Gamma(\epsilon, \epsilon)$ where $\epsilon$ is small and strictly positive.
This would create a distribution with a mean of 1 and a huge standard deviation across the whole space. Hence the posterior will be largely driven by the data and very little by the prior.
This would create a distribution with a mean of 1 and a huge standard deviation across the whole space. Hence the posterior will be largely driven by the data and very little by the prior.

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---
title: Week 4
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## Exponential Data
Suppose you're waiting for a bus that you think comes on average once every 10 minutes, but you're not sure exactly how often it comes.