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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…

基于种群的可逆跳跃马尔可夫链蒙特卡洛AI 解读

In this paper we present an extension of population-based Markov chain Monte Carlo (MCMC) to the trans-dimensional case. One of the main challenges in MCMC-based inference is that of simulating from high and trans-dimensional target measures. In such cases, MCMC methods may not adequately traverse the support of the target; the simulation results will be unreliable. We develop population methods to deal with such problems, and give a result proving the uniform ergodicity of…

最近邻分类模型中的似然推断AI 解读

Traditionally the neighbourhood size k in the k‐nearest‐neighbour algorithm is either fixed at the first nearest neighbour or is selected on the basis of a crossvalidation study. In this paper we present an alternative approach that develops the k‐nearest‐neighbour algorithm using likelihood‐based inference. Our method takes the form of a generalised linear regression on a set of k‐nearest‐neighbour autocovariates. By defining the k‐nearest‐neighbour algorithm in this way we…

多元线性样条的贝叶斯回归AI 解读

Summary We present a Bayesian analysis of a piecewise linear model constructed by using basis functions which generalizes the univariate linear spline to higher dimensions. Prior distributions are adopted on both the number and the locations of the splines, which leads to a model averaging approach to prediction with predictive distributions that take into account model uncertainty. Conditioning on the data produces a Bayes local linear model with distributions on both…