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Suppose that we have vectors of random variables [ v, w] = [ v 1, v 2, …, v I , w 1, …, w J ] in \(\Re ^{(I+J)}\) . Denote as the joint density function: f v, w , which obeys: f v, w ( v, w) ≥ 0 and \(\int ^{\infty }_{-\infty }\ldots \int ^{\infty }_{-\infty } f_{\mathbf {v,w}}(v,w) dv_1\ldots dv_I dw_1\ldots dw_I=1\) .

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Marginal Probability: Its Use in Bayesian Statistics as the Evidence of Models and Bayes Factors

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  • 发表日期：

    2025年

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  • Luis Raúl Pericchi

摘要

Suppose that we have vectors of random variables [ v, w] = [ v 1, v 2, …, v I , w 1, …, w J ] in \(\Re ^{(I+J)}\) . Denote as the joint density function: f v, w , which obeys: f v, w ( v, w) ≥ 0 and \(\int ^{\infty }_{-\infty }\ldots \int ^{\infty }_{-\infty } f_{\mathbf {v,w}}(v,w) dv_1\ldots dv_I dw_1\ldots dw_I=1\) .