Series: Bayesian Statistics

BDA Week 9: Large Sample Theory for the Posterior

As Richard McElreath says in his fantastic Statistics course, Frequentist statistics is more a framework to evaluate estimators than a framework for deriving them. Therefore, we can use frequentist tools to evaluate the…

BDA Week 8: Bayesian Decision Analysis

Many if not most statistical analyses are performed for the ultimate goal of decision making. Bayesian Statistics has the advantage of…

BDA week 7: LOO and its diagnostics

Once Stan’s implementation of HMC has run its magic, we finally have samples from the posterior distribution \(\pi (\theta | y))\). We can then run posterior predictive checks and hopefully our samples looks plausible under our posterior.…

BDA Week 6: MCMC in High Dimensions, Hamiltonian Monte Carlo

Bayesian Data Analysis: Week 5 -> Metropolis

Bayesian Data Analysis (Gelman, Vehtari et. alter) is equals part a great introduction and THE reference for advanced Bayesian Statistics. Luckily, it’s …

Bayesian Data Analysis: Week 4 -> Importance Sampling

Bayesian Data Analysis (Gelman, Vehtari et. alter) is equals part a great introduction and THE reference for advanced Bayesian Statistics. Luckily, it’s …

Bayesian Data Analysis: Week 3-> Exercises

Bayesian Data Analysis (Gelman, Vehtari et. alter) is equals part a great introduction and THE reference for advanced Bayesian Statistics. Luckily, it’s …

Bayesian Data Analysis: Week 3 -> Fitting a Gaussian probability model

Bayesian Data Analysis (Gelman, Vehtari et. alter) is equals part a great introduction and THE reference for advanced Bayesian Statistics. Luckily, it’s …

Bayesian Data Analysis: Week 2

Bayesian Data Analysis (Gelman, Vehtari et. alter) is equals part a great introduction and THE reference for advanced Bayesian Statistics. Luckily, it’s …

Statistical Rethinking Week 10

This is the final week of the best Statistics course out there. It showed the benefits of being ruthless with conditional…

Statistical Rethinking: Week 9

Week 9 was all about fitting models with multivariate distributions in them. For example, a multivariate likelihood helps us use an instrumental variable to estimate the…

Bayesian Instrumental Variable Regression

Statistical Rethinking is a fabulous course on Bayesian…

Understanding Pooling across Intercepts and Slopes

Statistical Rethinking is a fabulous course on Bayesian Statistics (and much more). By following simulations in the book, I recently tried to understand why pooling is the process and…

Statistical Rethinking Week 8

This week was our first introduction to Multilevel models. Models where we…

Simulating into understanding Multilevel Models

Pooling is the process and shrinkning is the result

Statistical Rethinking: Week 7

This week paid off. All the hard work of understanding link functions, HMC flavored Monte-Carlo, and GLM allowed to study more complex models. To keep…

Statistical Rethinking: Week 6

The week was a whirlwind tour of:

Statistical Rethinking Week 5 -> HMC samples

After a quick tour around interactions, this week was a quick introduction to MCMC samplers and how they are the engine that powers current Bayesian…

Statistical Rethinking: Week 5 -> Interactions

Statistical Rethinking: Week 4

This week was a…

Statistical Rethinking: Week 3

Week 3 gave the most interesting discussion of multiple regression. Why isn’t it enough with univariate regression? It allows us to disentagle two types of mistakes:

Statistical Rethinking: Week 2

Week 2 has gotten us to start exploring linear regression from a bayesian perspective. I found it the most interesting to propagate uncertainty through the model.

Statistical Rethinking: Week 1

Week 1 tries to go as deep as possible in the intuition and the mechanics of a very simple model. As always with McElreath, he goes on with both clarity and erudition.