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A Monte Carlo method for an objective Bayesian procedure. (English) Zbl 0719.65098
Often a statistical model is described by the likelihood function L(θ,Y) for a given set of data Y and an unknown parameter vector θ. In the case of an ill-conditioned situation the function lnL(θ,Y)-Q(θ,τ) is introduced, where Q represents a set of penalties and τ is the vector of respective weights for the penalties. Consider the prior distribution π (θ /τ) with π(θ/τ)=exp{-Q(θ,τ)}/exp{-Q(θ,τ)}dθ· Then Λ(τ;Y)=L(θ,Y)π(θ,τ)dθ is the Bayesian likelihood of τ, and is useful to obtain the optimal hyper-parameter τ which maximizes Λ or its logarithm. A Monte Carlo integration method is described and is used to determine Λ (,Y) and some numerical examples are discussed.

65C99Probabilistic methods, simulation and stochastic differential equations (numerical analysis)
62F15Bayesian inference
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