Explore BrainMass
Share

Explore BrainMass

    Setting up likelihood function and finding MLE

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Consider the following data from 50 Bernoulli Trials

    Let theta be the probability of the observing a one for any single trial.
    a) Find the likelihood of any sequence of s trials containing y ones.
    b) If the prior on theta is uniform such that p(theta)=1, find an expression for the posterior distribution for theta after 10 trials. What is the maximum likelihood estimator of theta?
    c) Find an expression of the posterior after another 30 trials. In what sense has the prior been updated?

    See attached for data

    © BrainMass Inc. brainmass.com October 10, 2019, 7:24 am ad1c9bdddf
    https://brainmass.com/math/probability/setting-up-likelihood-function-finding-mle-580495

    Attachments

    Solution Preview

    a) Find the likelihood of any sequence of s trials containing y ones.
    The likelihood based on the bernoulli distribution is p(y|θ)=θy(1-θ)s-y

    b) If the prior on theta is uniform such that p(theta)=1, find an expression for the posterior ...

    Solution Summary

    The solution gives detailed steps on setting up likelihood function, finding MLE and then discussing properties. It involves finding the likelihood of any sequence of s trials, finding maximum likelihood estimator of theta, and finding the expression of a posterior.

    $2.19