Is that needed badly? If so write a dissertation on the topic.. David Booth

There are quite a few Bayesian process monitoring methods. They tend to be complicated and none have really caught on. Steve Rigdon wrote a process monitoring paper in which MCMC methods were used. I think it was in the Journal of Quality Technology.

See Article A Bayesian Approach to Diagnostics for Multivariate Control Charts

I would recommend writing a review paper on Bayesian process monitoring. One seems needed.

Is there a relatively simple, effective Bayesian approach? I don’t know. I’ve never worked on this topic. I can’t offer much advice.

I think the main reason is related to their complexity. For example, I tried hard to reach the result of the following paper:

Article On Monitoring of Linear Profiles using Bayesian Methods

but I was not able. Although better results than conventional monitoring methods may be acquired, Bayesian methods lead to several complexity.

Best regards.

Hello, until now there is no useful method to calculate exactly Bayesian posterior distribution except variational inference. Monte Carlo algorithms(score function estimator, pathwise derivative estimator and characteristic function estimator) are popular @to estimate variational inference. However, these estimators still have high variance and not accuracy. And problems contains samples, layers make these methods worse. Thanks and hope i answer your question