https://www.chenk.top/en/tags/mcmc/Recent content in MCMC on Chen Kai BlogHugoenFri, 30 Aug 2024 09:00:00 +0000https://www.chenk.top/en/probability-statistics/08-bayesian-thinking/Fri, 30 Aug 2024 09:00:00 +0000https://www.chenk.top/en/probability-statistics/08-bayesian-thinking/<p>Two statisticians walk into a bar. One says: &ldquo;The probability of rain tomorrow is 30%.&rdquo; The other replies: &ldquo;Probability is a long-run frequency. Since tomorrow only happens once, that statement is meaningless.&rdquo; The first one says: &ldquo;It quantifies my uncertainty about a unique event.&rdquo; They proceed to argue for the rest of the evening.</p> <p>This, roughly, is the Bayesian-frequentist debate. It&rsquo;s not about who&rsquo;s right — both frameworks are mathematically consistent. It&rsquo;s about what &ldquo;probability&rdquo; means and how that interpretation shapes the tools you use. Having worked through six articles of largely frequentist reasoning, we now develop the Bayesian perspective: parameters are random, data update our beliefs, and uncertainty is quantified through distributions rather than confidence intervals.</p>