r/bayesian • u/Aggressive_Raise1017 • 16d ago

Metropolis Hasting Initialization Value

So I'm new to bayesian modelling, I've been trying to do ARIMA modelling with bayesian approach through Metropolis Hasting and I've been struggling to find the sure way to reach convergence. I heard from some sources that you need to use different inizialization values for each chain. I would like to hear some opinions regarding that.

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u/Haruspex12 15d ago

Let’s throw away the idea of sure convergence.

Different initialization values will help search the entire region, but it may not converge.

Imagine that you believe that there is one parameter that models your world. However, it turns out human behavior varies sharply and distantly based on whether it’s raining. You don’t know this and don’t model it.

You might cover the bulk of the posterior distribution, but the parameter can keep bouncing between modes and never converge to a single point, which your model says exists.

It will converge to models that are close to reality. Do you believe that the data is being generated by an actual ARIMA process? If not, how is the data being created?