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Fixed titles, math rendering, and links on some pages
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# Bayesian Statistics
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---
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title: Week 1
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showthedate: false
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math: true
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---
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## Rules of Probability
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---
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title: Week 2
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showthedate: false
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math: true
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---
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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.
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## 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."
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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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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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---
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title: Week 3
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showthedate: false
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math: true
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---
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How do we choose a prior?
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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.
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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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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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---
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title: Week 4
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showthedate: false
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math: true
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---
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## Exponential Data
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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.
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