# Bayesian Statistics

## Foreword

Started 06/06/2024

So, as you may know if you’re taking a gander at my website is I do molecular bio and AI.

Rationality is about knowing which facts are relevant, not knowing the facts.

Statistical inference is the logical framework whichwe can use to trial our beliefs about the noisy world against data. We formalise our beliefs in models of probability. The models are probabilistic bc we are ignorant of many of the interacting parts of a system, meaning we cannot say with certainty whether something will, or not, occur.

- $\lnot$ is used as
`not`

in probability, e.g. $\lnot 10$ `|`

means*given*in probability, e.g. $Pr(1,1| \text{ rigged casino })$

Bayes’ theorem is the rule or theorem that allows us to find the causation behind the effect

$Pr(\text{effect}|\text{cause}) \xrightarrow{\text{bayes' theorem}} Pr(\text{cause}|\text{effet})$Which can be written as

$Pr(\text{cause}|\text{effet}) = \dfrac{Pr(\text{cause}|\text{effect}) \cdot Pr(\text{cause})}{Pr(\text{effect})}$