Thanks for all this information. I will definitely find some quality time this weekend with a big pot of coffee and dive into it.
I agree that choosing 20 series is arbitrary but I haven’t reached that point yet. I am constructing what type of model I want in my head and then trying to find the best tools before I finalize a building plan. I came across PCA and Dynamic Factor models and the idea of using weights appealed to me so I started getting more familiar with it in python by building a simple model. Then I came across Bayesian and how it was superior to frequentist ideas and it sounded promising so I started working with pymc to get a feel for it. It led me to the idea of combing PCA and Bayesian but because of my knowledge gap in statistics I couldn’t be sure if I was correct in my thinking which led me here. But if you’re saying that I don’t need to use PCA, that Bayesian alone can provide me with a model that matches the plans I have in my head then I will definitely be sympathetic to that idea.
You said that I can apply Laplace priors to the effect size/beta coefficients. I’m still trying to understand this better in the overall context of building a Bayes model. Going back to my simplified model of using three economic indicators and forgetting PCA for a minute, would that mean creating a Laplace prior for the beta coefficient and then the size variable (k) is 3? And then if GDP values are the observed data I would need to construct an appropriate model for the mean applying this prior variable? Is this the general idea?