Posts tagged regression

Splines in PyMC3

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. The spline is effectively multiple individual lines, each fit to a different section of \(x\), that are tied together at their boundaries, often called knots.

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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.

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Simpson’s paradox and mixed models

This notebook covers:

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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.

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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.

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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.

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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:

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GLM: Robust Regression using Custom Likelihood for Outlier Classification

Using PyMC3 for Robust Regression with Outlier Detection using the Hogg 2010 Signal vs Noise method.

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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.

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Rolling Regression

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

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