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Point estimate from multiple sampling distributions

by capy_bara
Tags: distributions, estimate, multiple, point, sampling
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capy_bara
#1
Nov20-12, 08:04 AM
P: 1
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
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mfb
#2
Nov20-12, 08:29 AM
Mentor
P: 11,580
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?

How can I find out which is the best way to summarize all distributions within one group to get a single point estimate?
Convolution, if nothing simpler works. This allows to get your point estimate and confidence level in a natural way.


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