# Posts tagged regression

## Multivariate Gaussian Random Walk

This notebook shows how to fit a correlated time series using multivariate Gaussian random walks (GRWs). In particular, we perform a Bayesian regression of the time series data against a model dependent on GRWs.

## Rolling Regression

Pairs trading is a famous technique in algorithmic trading that plays two stocks against each other.

## Modeling Heteroscedasticity with BART

In this notebook we show how to use BART to model heteroscedasticity as described in Section 4.1 of `pymc-bart`’s paper . We use the `marketing` data set provided by the R package `datarium` . The idea is to model a marketing channel contribution to sales as a function of budget.

## Quantile Regression with BART

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.

## GLM: Robust Linear Regression

Duplicate implicit target name: “glm: robust linear regression”.

## GLM: Poisson Regression

This is a minimal reproducible example of Poisson regression to predict counts using dummy data.

## Difference in differences

This notebook provides a brief overview of the difference in differences approach to causal inference, and shows a working example of how to conduct this type of analysis under the Bayesian framework, using PyMC. While the notebooks provides a high level overview of the approach, I recommend consulting two excellent textbooks on causal inference. Both The Effect and Causal Inference: The Mixtape have chapters devoted to difference in differences.

## Bayesian regression with truncated or censored data

The notebook provides an example of how to conduct linear regression when your outcome variable is either censored or truncated.

## Counterfactual inference: calculating excess deaths due to COVID-19

Causal reasoning and counterfactual thinking are really interesting but complex topics! Nevertheless, we can make headway into understanding the ideas through relatively simple examples. This notebook focuses on the concepts and the practical implementation of Bayesian causal reasoning using PyMC.

## Splines

Often, the model we want to fit is not a perfect line between some \(x\) and \(y\). Instead, the parameters of the model are expected to vary over \(x\). There are multiple ways to handle this situation, one of which is to fit a spline. Spline fit is effectively a sum of multiple individual curves (piecewise polynomials), each fit to a different section of \(x\), that are tied together at their boundaries, often called knots.

## Regression discontinuity design analysis

Quasi experiments involve experimental interventions and quantitative measures. However, quasi-experiments do not involve random assignment of units (e.g. cells, people, companies, schools, states) to test or control groups. This inability to conduct random assignment poses problems when making causal claims as it makes it harder to argue that any difference between a control and test group are because of an intervention and not because of a confounding factor.

## Simpson’s paradox and mixed models

This notebook covers:

## Bayesian mediation analysis

This notebook covers Bayesian mediation analysis. This is useful when we want to explore possible mediating pathways between a predictor and an outcome variable.

## Lasso regression with block updating

Sometimes, it is very useful to update a set of parameters together. For example, variables that are highly correlated are often good to update together. In PyMC block updating is simple. This will be demonstrated using the parameter `step` of `pymc.sample`.

## Bayesian Additive Regression Trees: Introduction

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: