2 Layers of Assumptions

If we are modelling principal components using a normal distribution, that is the distribution used to calculate the likelihood. In a way the form of distribution for the likelihood is also an assumption. So bayesian inference has two layers of assumptions: structural (likelihood) and prior (uncertainty about parameters) In summary, the likelihood reflects modelling assumptions, while the prior reflects parameter uncertainty within that model.

Practical Application of Posterior Distribution

Posterior distribution is updated belief of unknown quantity after seeing data.
We therefore draw from the posterior distribution to get simulated component scores, and transform back.

and use those values for the mean... perhaps... but what should use for the variance and other parameters. this insight is just one set of values... one assigns probability to the prior... but is it appropriate to have a fixed curve in mind.... no it isnt... this would be impossible as it allows no variety.

why use bayesian PCA

... the posterior probabilities are proportional to the prior probabilities and the likelihoods.
..

what the marginal likelihood in this context

the marginal likelihood is the probability you would have observed the data whether prior / hypothesis is true or not.... mmmmm.....

Mathematical Definition of Orthogonality

Concerns re the shape of the solution

which component of the model do we fit to a distribution

In PCA, we typically fit a probability distribution function to the principal component scores, which represent the data's projections onto the principal components.

Example Prior Desires

The types of priors one might want to express: * a 30% probability of a parallel downward shift in the yield curve
* each principal component has a normal distribution

meaningful insight into parameters of the distribution

determining parameter values of interest

• take yield curve
• perform a transformation
• derive component scores
• use component scores for mean of each principal component
• determine paramters accordingly

my concern here is that we are not saying anything about the variance or other characteristics, just one curve that is of interest.

do the parameters of the distribution have intuitive meeting

No

Dataset Considerations

why use spot rates instead of forward rates

there a several options for choice of datasets, swap rates being one alternative. spot rates chosen only because one of available options.

Not Relevant to Analysis

Arbitrage Considerations

Consistency with market prices is gained insofar that the starting yield curve is 'today`s' yield curve. It stops there. Nothing further to consider in this respect.