What is the posterior in-sample vs the posterior out-of-sample?

Question

I'm watching this video on Bayesian modelling for the stock market by Thomas Wiecki, Thomas has a slide with two posterior distribution over the mean parameter in his stock return model. Around 18:26 we see this slide:

The phrase “in-sample” and “out-of-sample” in regard to a posterior distribution, both in regard to the same latent variable, confuses me.

If one wants to look at the latent variables, the way I understand it, one can:

• Look at the prior of a latent variable, which is designed by the user.
• Look at the posterior of a latent variable, which one can obtain after observing some data.

At no point in the Bayesian workflow does an “out-of-sample” vs “in-sample posterior” come up, just posterior vs prior.

Question: What does “in-sample posterior” vs “out-of-sample posterior” mean?

Answer 1

This is explained earlier in the talk, from around 3:12 (link).

Quantopian users train financial models on historical data ("in-sample period"), and test them on new data ("out-of-sample period"). Due to overfitting, the models usually do better on the in-sample data.

The speaker's job is to evaluate how well these financial models perform, by considering both their in-sample and out-of-sample performance. He fits a model to evaluate the performance data generated by the users' models. This is where the terminology gets confusing!