# Examples overview

This section contains a set of examples for Bayesian Inference with `ReactiveMP`

package in various probabilistic models.

More examples can be found in `demo/`

folder at GitHub repository.

- Linear regression: An example of linear regression Bayesian inference.
- [Assessing Peoples Skills]: The demo is inspired by the example from Chapter 2 of Bishop's Model-Based Machine Learning book.

We are going to perform an exact inference to assess the skills of a student given the results of the test.

- Gaussian Linear Dynamical System: An example of inference procedure for Gaussian Linear Dynamical System with multivariate noisy observations using Belief Propagation (Sum Product) algorithm. Reference: Simo Sarkka, Bayesian Filtering and Smoothing.
- Hidden Markov Model: An example of structured variational Bayesian inference in Hidden Markov Model with unknown transition and observational matrices.
- Hierarchical Gaussian Filter: An example of online inference procedure for Hierarchical Gaussian Filter with univariate noisy observations using Variational Message Passing algorithm. Reference: Ismail Senoz, Online Message Passing-based Inference in the Hierarchical Gaussian Filter.
- Autoregressive Model: An example of variational Bayesian Inference on full graph for Autoregressive model. Reference: Albert Podusenko, Message Passing-Based Inference for Time-Varying Autoregressive Models.
- Invertible Neural Networks: An example of variational Bayesian Inference with invertible neural networks. Reference: Bart van Erp, Hybrid Inference with Invertible Neural Networks in Factor Graphs (accepted).
- Univariate Gaussian Mixture: This example implements variational Bayesian inference in a univariate Gaussian mixture model with mean-field assumption.
- Multivariate Gaussian Mixture: This example implements variational Bayesian inference in a multivariate Gaussian mixture model with mean-field assumption.
- Gamma Mixture: This example implements one of the experiments outlined in https://biaslab.github.io/publication/mp-based-inference-in-gmm/ .
- Custom nonlinear node: This example shows how to build an arbitrary factor node for non-linear function using sample list approximation.
- Missing data: This examples show how to extend basic functionality of ReactiveMP to support missing data points.
- Expectation Propagation (Probit): In this demo we illustrate EP in the context of state-estimation in a linear state-space model that combines a Gaussian state-evolution model with a discrete observation model.