Posts tagged
Confirmatory Factor Analysis and Structural Equation Models in Psychometrics
- 04 September 2024
“Evidently, the notions of relevance and dependence are far more basic to human reasoning than the numerical values attached to probability judgments…the language used for representing probabilistic information should allow assertions about dependency relationships to be expressed qualitatively, directly, and explicitly” - Pearl in Probabilistic Reasoning in Intelligent Systems Pearl [1985]
Time Series Models Derived From a Generative Graph
- 04 July 2024
In this notebook, we show how to model and fit a time series model starting from a generative graph. In particular, we explain how to use scan to loop efficiently inside a PyMC model.
Baby Births Modelling with HSGPs
- 04 January 2024
This notebook provides an example of using the Hilbert Space Gaussian Process (HSGP) technique, introduced in [Solin and Särkkä, 2020], in the context of time series modeling. This technique has proven successful in speeding up models with Gaussian process components.
GLM: Negative Binomial Regression
- 04 September 2023
This notebook uses libraries that are not PyMC dependencies and therefore need to be installed specifically to run this notebook. Open the dropdown below for extra guidance.
Regression Models with Ordered Categorical Outcomes
- 04 April 2023
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
- 31 July 2022
Example of simple Gaussian Process fit, adapted from Stan’s example-models repository.
General API quickstart
- 31 May 2022
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
- 04 March 2022
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
- 04 February 2022
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
- 08 January 2022
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.
Bayesian Estimation Supersedes the T-Test
- 07 January 2022
Non-consecutive header level increase; H1 to H3 [myst.header]
Marginalized Gaussian Mixture Model
- 18 September 2021
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.
Dirichlet process mixtures for density estimation
- 16 September 2021
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 \(\Omega\),