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Bayesian Distribution of Sample Mean

prior parameters

-5

0.2

observed parameters

2.4

2.1

This Demonstration provides Bayesian estimates of the posterior distribution of the mean

and the standard deviation

of a normally distributed random variable

. These posterior distributions are based upon observing

independent observations of the random variable

that have sample mean

and sample distribution

. Prior knowledge about statistical parameters is an important part of Bayesian statistics. In this case, it is initially assumed that the unknown mean

is uniformly distributed on the interval

<μ<

and that the unknown standard deviation

is distributed with a Jeffrey's prior distribution on the interval

<σ<

. Bayes's theorem provides a convenient way of incorporating the prior information and the observed information into a posterior probabilistic characterization of the unknown parameters

and

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