Big list of Markov chain Monte Carlo (MCMC) applications

I became quite obsessed with Markov chain Monte Carlo Methods lately. It is said that MCMC methods form the most frequently used class of algorithms in computer science. However when I was searching for a comprehensive list of MCMC applications across different domains to my surprise I have found none. So I’d like to ask you to help fill in the public Google Sheet called Big list of Markov chain Monte Carlo (MCMC) applications the columns of the list being:

1. Particular quantity estimated, system simulated, sampled. (mandatory)

2. General class of quantity, system sampled. (mandatory)

3. Reference to paper or link. (strongly recommended or optional for commercial examples)

4. MCMC variant used. (optional)

5. Software implementation. (optional)

I provided a couple of examples so I think it is quite straightforward once you have an example to add. Also added the request on Quora.