Question

A sample of n undergradute students is selected. The data recorded for the i-th student is (xi,yi) where xi is their weight in kilograms and yi=1(0）according to whether they are male (female). Provide a subjective Bayesian model justifying all of your distributional assumptions.

Answer 1

We can think of the whole problem in the following way.

For a male, the distribution of weight is Normally distributed which is in frequentist approach.

Similarly, for a female, the distribution of weight is Normally distributed which is again in frequentist approach.

Now, if we assume a distribution on the proportion of males in the class, then that will have a Bernoulli distribution.

Now, we know that Bernoulli distribution has a success probability p. So, if we assume a Beta distribution on that prior p, say Beta(1/2,1/2) then the whole structure will be of a Bayesian distribution.