# Posts tagged hierarchical model

## NBA Foul Analysis with Item Response Theory

- 17 April 2022
- Category: intermediate, tutorial

This tutorial shows an application of Bayesian Item Response Theory [Fox, 2010] to NBA basketball foul calls data using PyMC. Based on Austin Rochford’s blogpost NBA Foul Calls and Bayesian Item Response Theory.

## A Primer on Bayesian Methods for Multilevel Modeling

- 27 February 2022
- Category: intermediate

Hierarchical or multilevel modeling is a generalization of regression modeling. *Multilevel models* are regression models in which the constituent model parameters are given **probability models**. This implies that model parameters are allowed to **vary by group**. Observational units are often naturally **clustered**. Clustering induces dependence between observations, despite random sampling of clusters and random sampling within clusters.

## Hierarchical Binomial Model: Rat Tumor Example

- 11 November 2021
- Category: intermediate

This short tutorial demonstrates how to use PyMC3 to do inference for the rat tumour example found in chapter 5 of *Bayesian Data Analysis 3rd Edition* [Gelman *et al.*, 2013]. Readers should already be familliar with the PyMC3 API.

## Hierarchical Partial Pooling

- 07 October 2021
- Category: intermediate

Suppose you are tasked with estimating baseball batting skills for several players. One such performance metric is batting average. Since players play a different number of games and bat in different positions in the order, each player has a different number of at-bats. However, you want to estimate the skill of all players, including those with a relatively small number of batting opportunities.

## GLM: Mini-batch ADVI on hierarchical regression model

- 23 September 2021
- Category: intermediate

Unlike Gaussian mixture models, (hierarchical) regression models have independent variables. These variables affect the likelihood function, but are not random variables. When using mini-batch, we should take care of that.