Bayesian analysis

Gist

General guide on how to do Bayesian analysis.

Using the Bayes formula we know that:

P r (A | B) = Pr (B | A) Pr (A)

which for our observed data $y$ and model parameter $θ$ can be rewritten as:

Pr(\theta|y) = Pr(y|\theta) Pr(\theta)$$ However, analytical expressions are impossible a lot of times so we need to be able to simulate from the posterior distribution through methods likeMarkov Chain Monte Carlo. ## Methodology -Hierarchal Bayesian Modeling## Pro's 1. No need to correct forMultiplicitylike Frequentist methods. ## Workflows This is the suggested workflow for modeling disease transmission usingModel - SIRwith Stan. But I think this workflow is generalizable to other analyses [^1] ![Pasted image 20260801221100.png](/img/user/Images/Pasted%20image%2020260801221100.png) 1. **Criticize model before looking at data - **Prior predictive check:** We want priors that allow for every reasonable configuration of the data but exclude patently absurd scenarios, per our domain expertise. 2. [^1]: [Grinsztajn, Léo, et al. "Bayesian workflow for disease transmission modeling in Stan." _Statistics in medicine_ 40.27 (2021): 6209-6234.](https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.9164)