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信念分布更新的一般框架AI 解读

Summary We propose a framework for general Bayesian inference. We argue that a valid update of a prior belief distribution to a posterior can be made for parameters which are connected to observations through a loss function rather than the traditional likelihood function, which is recovered as a special case. Modern application areas make it increasingly challenging for Bayesians to attempt to model the true data-generating mechanism. For instance, when the object of…

单调性的非参数贝叶斯检验AI 解读

This paper adopts a nonparametric Bayesian approach to testing whether a function is monotone. Two new families of tests are constructed. The first uses constrained smoothing splines with a hierarchical stochastic-process prior that explicitly controls the prior probability of monotonicity. The second uses regression splines together with two proposals for the prior over the regression coefficients. Via simulation, the finite-sample performance of the tests is shown to…

离散参数空间先验概率质量函数的客观构造方法AI 解读

C. Villa & S. G. WalkerC. Villa is Lecturer, School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, UK (E-mail: cv88@kent.ac.uk). S. G. Walker is Professor, Department of Statistics and Data Sciences, and Division of Statistics and Scientific Computation, University of Texas at Austin, TX 78712 (E-mail: s.g.walker@math.utexas.edu).Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/r/jasa.We…

物种抽样模型：物种数量的一致性AI 解读

This paper considers species sampling models using constructions that arise from Bayesian nonparametric prior distributions. A discrete random measure, used to generate a species sampling model, can have either a countable infinite number of atoms, which has been the emphasis in the recent literature, or a finite number of atoms K, while allowing K to be assigned a prior probability distribution on the positive integers. It is the latter class of model we consider here, due…