Question 1. Take a moment to convince yourself that the exponential and gamma distributions are exponential...
Question 2 a. Show that, for the exponential model with gamma prior, the posterior Π(9121m) under n observations can be computed as the posterior given a single observation xn using the prior q(の는 1101r1:n-1). Give the formula for the parameters (an,ßn) of the posterior ll(θ|X1:n, α0,Ao) as a function of (an-1, Bn-1). b. Visualize the gradual change of shape of the posterior II(01:n, ao, Bo) with increasing n: . Generate n 256 exponentially distributed samples with parameter θ-1. . Use...
(al This question asks you to consider a Bayesian approach to inference about λ, the mortality rate in an exponential model for survival time. In order to take a Bayesian . Show that the gamma distribution is a conjugate prior distribution for the distribution is also Gamma, with parameters that depend on a, P, n,y. approach, we specify a prior distribution for A which is gamma distribution exponential model, ie. if we specify that λ~Gamma (α, β) a priori, then...