## Let's Bayesian thinking --- ## Bayesian Methods for Hackers ch1-2 - Present: Dragon Chen - Date: 09/18 --- ## Intro - Title: Bayesian Methods for Hackers - Github: [這](https://github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers)(qsirch 上也有 pdf)  ---- - You are a **skilled programmer**, but bugs still slip into your code. - After a particularly difficult implementation of an algorithm, you decide to **test your code** on a trivial example. ---- - It passes. You test the code on a harder problem. - It passes once again. And it passes the next, even more difficult, test too! - You are **starting to believe** that there may be no bugs in this code. . . ---- ## You already are thinking Bayesian! Bayesian inference is simply **updating your beliefs** after considering new **evidence** --- ## Bayesian Worldview ---- - Bayesian worldview interprets probability as measure of believability in an event <span><!-- .element: class="fragment" -->==How confident we are in an event occurring==</span> ---- ### versus Frequentists - Frequentist assume probability is the long-run frequency of events - *Probability of plane accidents* under a frequentist philosophy is interpreted as the *long-term frequency of plane accidents* ---- ### Belief - Bayesians interpret a probability as the measure of belief, or confidence, in an event occurring. - An individual assigns belief of p(probability) to an event - The definition leaves room for conflicting **beliefs between individuals** ---- ### Different Belief - Different individuals have different beliefs of events occurring because they possess different information about the world. - The existence of different beliefs does not imply that anyone is wrong. --- ## Procedure ### Coin Example - I flip a coin. We assume the coin is fair, that the probability of heads is 0.5. Assume, then, that I peek at the coin. Now I know for certain what the result is. - Now what is your belief that the coin is heads? ---- - Assume the coin is fair, prob is 0.5 - We denote our belief about event A as P(A) - We call this quantity the **prior probability** "When the facts change, I change my mind. What do you do, sir?", John Maynard Keynes ---- - Bayesian updates his/her beliefs after seeing evidence - We denote our updated belief as P(A|X) - Prob of A given the evidence X - We call the updated belief the **posterior probability** ---- - If you flip 1/3/5 coins keep showing head-up, do you still believe the coin is fair? ----  ---- The posterior probabilities are represented by the curves, and our uncertainty is proportional to the <font color="red">width of the curve</font>. ---- - We did not **completely discard the prior belief** after seeing new evidence X, but we **re-weighted the prior** to incorporate the **new evidence** --- ## Else Detail - N → ∞, our Bayesian results (often) align with frequentist results - For small N, inference is much more unstable --- ## Some Detail of PyMC  ----  ----  --- ### Thank you for listening! :dragon: