Bayesian MCMC (Markov Chain Monte Carlo) Gibbs Sampling

[John Zoey]

Dear all,

I'm working on my thesis paper and trying to replicate this author's process for MCMC Gibbs Sampling. I have read some tutorials as well as Stata's manuals, so I know how to use the GUI (typing "db bayesmh") to build posterior models, priors distribution, input data and such.

However, I still cannot get the gist of the process and the steps needed to replicate it. The attached photo (or you can find it at https://imgur.com/a/8jHpvo6) is the explanation of the author for this process. The main idea is that I want to identify the 2 states of the stock market (whether it is bull or bear) using equally weighted market returns. The transition probabilities of the 2 states follow First-order Markov Chain.

I'm especially quite vague about the part that "estimate the transition probabilities using conjugate beta priors, but use weak priors".

I need to know how to do this process step by step, if possible. Otherwise, any help/ clarification is much appreciated as well!

I'm using Stata 15 for Windows.

Many thanks!

[Scott Merryman]

You might take a look at -mswitch- with the varswitch option or slides 47-51 https://www.stata.com/meeting/chicag...go16_balov.pdf which shows the using -bayesmh- to estimate a similar model.

[John Zoey]

You might take a look at -mswitch- with the varswitch option or slides 47-51 https://www.stata.com/meeting/chicag...go16_balov.pdf which shows the using -bayesmh- to estimate a similar model.

Thank you for an extremely relevant and helpful reference. I find the example you provided is similar to my problems, but as I'm not really proficient in Stata I would like to ask you a few more questions:
1. Why in the estimation results (page 50) only contain p1, but not p2? or how do I extract p2 from the results? so that I can use both p1 and p2 to graph the chart above
2. If I understand this correctly, I would first run -mswitch- with switching variance, then use the stored results from the -mswitch- to run the -bayesmh-? Please correct me if I'm wrong!

[Scott Merryman]

1. I was mistaken. It appears that is just switching model rather than a Markov switching model.

2. No. I don't think is that straightforward