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Point estimate from multiple sampling distributions

  1. Nov 20, 2012 #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,
  2. jcsd
  3. Nov 20, 2012 #2


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    2017 Award

    Staff: Mentor

    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.
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