Posts by Osvaldo Martin
Model Averaging
- 16 August 2024
When confronted with more than one model we have several options. One of them is to perform model selection as exemplified by the PyMC examples Model comparison and the GLM: Model Selection, usually is a good idea to also include posterior predictive checks in order to decide which model to keep. Discarding all models except one is equivalent to affirm that, among the evaluated models, one is correct (under some criteria) with probability 1 and the rest are incorrect. In most cases this will be an overstatment that ignores the uncertainty we have in our models. This is somewhat similar to computing the full posterior and then just keeping 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.
Categorical regression
- 16 May 2024
In this example, we will model outcomes with more than two categories.
Quantile Regression with BART
- 25 January 2023
Usually when doing regression we model the conditional mean of some distribution. Common cases are a Normal distribution for continuous unbounded responses, a Poisson distribution for count data, etc.
Bayes Factors and Marginal Likelihood
- 10 January 2023
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.
Bayesian Additive Regression Trees: Introduction
- 21 December 2021
Bayesian additive regression trees (BART) is a non-parametric regression approach. If we have some covariates \(X\) and we want to use them to model \(Y\), a BART model (omitting the priors) can be represented as: