Some Challenges Trying to Overcome

I have come to a realisation recently a change my modelling approach is probably necessary:

Current approach and concerns

Principal components can be modelled using a suitable probability distribution function. In practice life companies may use complex distributions.

For the purposes of generating an initial analysis I was going to stick with a normal distribution for each principal component. The normal distribution would form structural assumption about the model i.e. the model used to calculate the likelihood.

Multivariate or not ?

A concern on my mind about this aspect:

• should we produce bayesian model for each principal component separately
• or should we use a multivariate normal likelihood

Intuition Problem

Either way, priors would need to express something about our uncertainty of the parameters of these 3 normal distributions and this leads to another concern, namely:

• PCA transforms data into a new vector space
• and so parameters of the distribution have no obvious intuitive meaning.

It is therefore challenging to convert a prior belief with intuitive meaning, e.g. the yield curve will have a parallel downward shift of 30bps with probability 30%, into an expression about the parameters of the distibutions.

Perhaps I need to change the way priors are expressed. But perhaps (also/instead) I need to change the way the model is structured