Point estimate from multiple sampling distributions

capy_bara

Dear all, I hope someone can help me.

I have two experimental groups, A (n=5) and B (n=8) containing biological samples. The samples are used to estimate my parameter of interest, θ. I do this with Markov-chain Monte-Carlo, which gives me a posterior distribution of θ for each of my samples. The distributions look approximately normal but are skewed a bit to the right. All values for θ are positive.
I wonder how I can now report single estimates (and confidence intervals) for θ in groups A and B, respectively.

Averaging the means of each distribution in one group gives me very different results than averaging the medians of all distributions. I also tried combining all distributions from one group and then taking the mean or the median. How can I find out which is the best way to summarize all distributions within one group to get a single point estimate?

I hope my problem is clear, I would appreciate any help.
Many thanks in advance,
capy_bara

mfb

For each sample in A and B, you get a distribution of (possible) θ, and you want a single number and confidence interval for θ in A and B?

Convolution, if nothing simpler works. This allows to get your point estimate and confidence level in a natural way.