# Posts tagged model comparison

## Bayes Factors and Marginal Likelihood

- 10 January 2023
- explanation, beginner

The “Bayesian way” to compare models is to compute the *marginal likelihood* of each model \(p(y \mid M_k)\), *i.e.* the probability of the observed data \(y\) given the \(M_k\) model. This quantity, the marginal likelihood, is just the normalizing constant of Bayes’ theorem. We can see this if we write Bayes’ theorem and make explicit the fact that all inferences are model-dependant.

## Model Averaging

- 08 August 2022
- intermediate

When confronted with more than one model we have several options. One of them is to perform model selection, using for example a given Information Criterion as exemplified the PyMC examples Model comparison and the GLM: Model Selection. Model selection is appealing for its simplicity, but we are discarding information about the uncertainty in our models. This is somehow similar to computing the full posterior and then just keep a point-estimate like the posterior mean; we may become overconfident of what we really know. You can also browse the blog/tag/model-comparison tag to find related posts.

## GLM: Model Selection

- 08 January 2022
- intermediate

A fairly minimal reproducible example of Model Selection using WAIC, and LOO as currently implemented in PyMC3.

## Bayesian Estimation Supersedes the T-Test

- 07 January 2022
- beginner

Non-consecutive header level increase; H1 to H3 [myst.header]