Given 2 distributions and which are independent estimates of the distribution , this be estimated with the inverse-variance method from:
Under which conditions is this a good aproach? For example, for which types of distributions? These questions might be relevant for determining:
- A posterior distribution based on distributions for the prior and estimate.
- A distribution which combines estimates of different theories.
- The inverse-variance method minimises the variance of a weighted mean of and .
- Calculating and according to the above formula would result in a mean and variance equal to those derived in this analysis from Dario Amodei, which explains how to combine and following a Bayesian approach if these follow normal distributions.
Thanks for the reply!
I also think the above formula does not formally apply to non-normal distributions, but I was wondering whether it was a good enough approximation.
Is there a simple way of applying the Bayes Rule to two arrays X1 and X2 of Monte Carlo samples? I believe this is analagous to considering that all elements of X1 and X2 are equiprobable.