Let (given , or conditioning on) be i.i.d. where the variance is known. The sample mean is the sufficient statistic for , such that Then so the posterior distribution is The same as previous examples, we are setting the posterior distribution as where Therefore as know from the general theorem, the posterior distribution using the sufficient statistic yields the same result as the one using the entire likelihood in example 2. 4. Frequentist Properties of Bayesian Estimators. Given a random sample from a Normal population with mean and variance 4. Please (a) Derive a sufficient statistic for. (b) Derive the maximum likelihood estimator (MLE) of. (c) Assuming the prior ofDerive the the Bayes estimator of. (d) Which of the two estimators (the Bayes estimator and the MLE) are better? Why?
Let (given , or conditioning on) be i.i.d. where the variance is known. The sample mean is the sufficient statistic for , such that Then so the posterior distribution is The same as previous examples, we are setting the posterior distribution as where Therefore as know from the general theorem, the posterior distribution using the sufficient statistic yields the same result as the one using the entire likelihood in example 2. 4. Frequentist Properties of Bayesian Estimators. Given a random sample from a Normal population with mean and variance 4. Please (a) Derive a sufficient statistic for. (b) Derive the maximum likelihood estimator (MLE) of. (c) Assuming the prior ofDerive the the Bayes estimator of. (d) Which of the two estimators (the Bayes estimator and the MLE) are better? Why?
Bayesian_Normal.docx