# What does non-ergodicity mean for Bayesian statistics?

As said in the title, what would non-ergodicity mean for Bayesian satistics, and if the process being investigated is non-ergodic, how would Bayesian methods tackle this process - would it be different from ergodic case or not?

So in classical(frequentist) statistic, if the world investigated is stochastic process, in many cases it needs to be ergodic process or needs to converted to ergodic process. I am somehow new to Bayesian statistics, but I know that MCMC method has ergodic theorem. Now, the question is, this is how we can estimate parameters. If so, does this solve many problems related to non-ergodic stochastic process?

• Do you mean "ergodic" in the sense of the MCMC methods used to tackle Bayesian problems or something related to a particular stochastic process in the real world? Can you give a particular example of what you are talking about? – guy Jun 12 '14 at 19:02
• It's a wonder you don't have this figured out yet, considering your name. – gregory_britten Jun 12 '14 at 19:40
• So in classical(frequentist) statistic, if the world investigated is stochastic process, in many cases it needs to be ergodic process or needs to converted to ergodic process. I am somehow new to Bayesian statistics, but I know that MCMC method has ergodic theorem. Now, the question is, this is how we can estimate parameters. If so, does this solve many problems related to non-ergodic stochastic process? – ergodic bayesian Jun 13 '14 at 5:21
• Do you know what MCMC is / aims to do / why it works? The ergodicity of MCMC is related to the chain of samples produced by the MCMC method, not to any ergodicity of the model whose parameters we are estimating. Do you have in mind some specific model that you are interested in? – Juho Kokkala Jun 13 '14 at 12:28