--- aliases: [] --- #mathematic #probability # [[Epistemic status]] #shower-thought #to-digest # Changelog ```dataview TABLE WITHOUT ID file.mtime AS "Last Modified" FROM [[#]] SORT file.mtime DESC LIMIT 3 ``` # Related - [[Bayesian network]] - [[Bayesian inference]] # TODO > [!TODO] TODO > some code example for fun # Bayes theorem [[Judea Pearl]] says, "The heart of **Bayesian** inference lies in the celebrated inversion formula, $ P(H \mid e)=\frac{P(e \mid H) P(H)}{P(e)} $ which states that the belief we accord a hypothesis H upon obtaining evidence e can be computed by multiplying our previous belief $P(H)$ by the likelihood $P(e | H)$ that $e$ will materialize if $H$ is true. This $P(He)$ is sometimes called the **posterior probability** (or simply **posterior**), and $P(H)$ is called the **prior probability** (or **prior**). " ![[5A8CF97D-7774-4393-B1B8-0E313146D408.jpeg]] ~ [[Marcus Hutter]] ## Common mistake - ignoring the dependency between variables (see video below) ![[Screenshot 2022-07-19 at 12.09.15.png]] <iframe width="560" height="315" src="https://www.youtube.com/embed/HZGCoVF3YvM" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe> <iframe width="560" height="315" src="https://www.youtube.com/embed/U_85TaXbeIo" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>