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Continuous mixture models: (a) If y |θ∼Poisson (θ), and θ∼Gamma(α, β), then the marginal (prior predictive) distribution of y is negative binomial with parameters αand β(or p=β/(1 β) ). Use the formulas (2.7) and (2.8) to derive the mean and variance of the negative binomial. (b) In the normal model with unknown location and scale (μ, σ^2), the noninformative prior density, p(μ, σ^2) ∝1 / σ^2, results in a normal-inverse- χ^2 posterior distribution for (μ, σ^2). Marginally then √(n)(μ-y̅) / s ha
Continuous mixture models: (a) If y |θ∼Poisson (θ), and θ∼Gamma(α, …
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