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.

Some notes:

- 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.