# Bayesian Statistics

## On Curbing Your Measurement Error: From Classical Corrections to Generative Models

Introduction In this post, we will explore how measurement error arising from imprecise parameter estimation can be corrected for. Specifically, we will explore the case where our goal is to estimate the correlation between a self-report and behavioral measure–a common situation throughout the social and behavioral sciences. For example, as someone who studies impulsivity and externalizing psychopathology, I am often interested in whether self-reports of trait impulsivity (e.g., the Barratt Impulsiveness Scale) correlate with performance on tasks designed to measure impulsive behavior (e.

## Thinking generatively: Why do we use atheoretical statistical models to test substantive psychological theories?

The Reliability Paradox Defining Reliability In 2017, Hedge, Powell, and Sumner (2017) conducted a study to determine the reliability of a variety of of behavioral tasks. Reliability has many different meanings throughout the psychological literature, but what Hedge et al. were interested in was how well a behavioral measure consistently ranks individuals. In other words, when I have people perform a task and then measure their performance, does the measure that I use to summarize their behavior show high test-retest reliability?

## On the equivalency between frequentist Ridge (and LASSO) regression and hierarchial Bayesian regression

Introduction In this post, we will explore frequentist and Bayesian analogues of regularized/penalized linear regression models (e.g., LASSO [L1 penalty], Ridge regression [L2 penalty]), which are an extention of traditional linear regression models of the form: [y = \beta_{0}+X\beta + \epsilon\tag{1}] where (\epsilon) is the error, which is normally distributed as: [\epsilon \sim \mathcal{N}(0, \sigma)\tag{2}] Unlike these traditional linear regression models, regularized linear regression models produce biased estimates for the (\beta) weights.