Mathematics Homework Help. Mathematics
Derive the posterior distribution of if a Beta distribution Be(; ) is used as the
prior, where ; > 0. [3 MARKS]
(b) An intuitive way to interpret the information contained in the Beta prior for is
that the information is equivalent to that in an observation from a distribution
of the same form as that above, but possibly with a dierent value of r. What is
the value of this notional observation and what is the corresponding value of r?
Specify the values using and . [2 MARKS]
(c) Is the Beta distribution a conjugate prior? Explain. [2 MARKS]
(d) Derive Jereys’ prior for . [5 MARKS]
(e) Is the Jereys’ prior proper? Explain. [2 MARKS]
(f) Is it ne to use the Jereys’ prior above for inference? Explain. [2 MARKS]
(g) Derive the posterior predictive distribution p(~yjy) for new observation ~y given that
the Beta prior Be(; ) is used
