# Posts tagged

## Regression Models with Ordered Categorical Outcomes

Like many areas of statistics the language of survey data comes with an overloaded vocabulary. When discussing survey design you will often hear about the contrast between design based and model based approaches to (i) sampling strategies and (ii) statistical inference on the associated data. We won’t wade into the details about different sample strategies such as: simple random sampling, cluster random sampling or stratified random sampling using population weighting schemes. The literature on each of these is vast, but in this notebook we’ll talk about when any why it’s useful to apply model driven statistical inference to Likert scaled survey response data and other kinds of ordered categorical data.

## Gaussian Processes using numpy kernel

Example of simple Gaussian Process fit, adapted from Stan’s example-models repository.

## GLM: Negative Binomial Regression

This notebook closely follows the GLM Poisson regression example by Jonathan Sedar (which is in turn inspired by a project by Ian Osvald) except the data here is negative binomially distributed instead of Poisson distributed.

## General API quickstart

Models in PyMC are centered around the Model class. It has references to all random variables (RVs) and computes the model logp and its gradients. Usually, you would instantiate it as part of a with context:

## Bayesian moderation analysis

This notebook covers Bayesian moderation analysis. This is appropriate when we believe that one predictor variable (the moderator) may influence the linear relationship between another predictor variable and an outcome. Here we look at an example where we look at the relationship between hours of training and muscle mass, where it may be that age (the moderating variable) affects this relationship.

## Binomial regression

This notebook covers the logic behind Binomial regression, a specific instance of Generalized Linear Modelling. The example is kept very simple, with a single predictor variable.

## Dirichlet mixtures of multinomials

This example notebook demonstrates the use of a Dirichlet mixture of multinomials (a.k.a Dirichlet-multinomial or DM) to model categorical count data. Models like this one are important in a variety of areas, including natural language processing, ecology, bioinformatics, and more.

## Using a “black box” likelihood function (numpy)

This notebook in part of a set of two twin notebooks that perform the exact same task, this one uses numpy whereas this other one uses Cython

## Marginalized Gaussian Mixture Model

Gaussian mixtures are a flexible class of models for data that exhibits subpopulation heterogeneity. A toy example of such a data set is shown below.

The Dirichlet process is a flexible probability distribution over the space of distributions. Most generally, a probability distribution, $$P$$, on a set $$\Omega$$ is a [measure](https://en.wikipedia.org/wiki/Measure_(mathematics%29) that assigns measure one to the entire space ($$P(\Omega) = 1$$). A Dirichlet process $$P \sim \textrm{DP}(\alpha, P_0)$$ is a measure that has the property that, for every finite disjoint partition $$S_1, \ldots, S_n$$ of $$\Omega$$,