论文检索

论有效的点预测系统AI 解读

Summary Assume that a forecaster observes a sequence of random variables and issues predictions according to a point prediction systems, i.e. a rule which, at every time t, issues a point prediction for the next observation at time t+1. We introduce the concept of efficiency of a point prediction system, for the case that the joint distribution of the sequence of observations is known to belong to a parametric family, and performance is assessed by the long run sum of…

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Jeffreys 先验下联立方程模型有限信息分析的后验分布AI 解读

This paper studies the use of the Jeffreys prior in Bayesian analysis of the simultaneous equations model (SEM). Exact representations are obtained for the posterior density of the structural coefficient β in canonical SEMs with two endogenous variables. For the general case with m endogenous variables and an unknown covariance matrix, the Laplace approximation is used to derive an analytic formula for the same posterior density. Both the exact and the approximate formulas…

有限总体的加权多项式模型与加权抽样方案AI 解读

This paper outlines a theoretical framework for finite population models with unequal sample probabilities, along with sampling schemes for drawing random samples from these models. We first present four exact weighted sampling schemes that can be used for any finite population model to satisfy such requirements as ordered/ unordered samples, with/without replacement, and fixed/nonfixed sample size. We then introduce a new class of finite population models called weighted…

区域判定问题AI 解读

In the problem of regions, we wish to know which one of a discrete set of possibilities applies to a continuous parameter vector. This problem arises in the following way: we compute a descriptive statistic from a set of data, notice an interesting feature and wish to assign a confidence level to that feature. For example, we compute a density estimate and notice that the estimate is bimodal. What confidence can we assign to bimodality? A natural way to measure confidence is…

计量经济学中先验密度比类的稳健性AI 解读

This article provides a generic, very fast method for computing exact density-ratio class bounds on posterior expectations, given the output of a posterior simulator. It illustrates application of the method in an econometric model of typical complexity. In this model, the exact bounds for expectations of some functions of interest are well approximated by the established asymptotic approximation but others are not. Software for the computations is publicly available in a…

Isserlis 矩阵及其在不可分解高斯图模型中的应用AI 解读

The operations of matrix completion and Isserlis matrix construction arise in the statistical analysis of graphical Gaussian models, in both the Bayesian and frequentist approaches. In this paper we study the properties of the Isserlis matrix of the completion, , of a positive definite matrix and propose an edge set indexing notation which highlights the symmetry existing between and its Isserlis matrix. In this way well-known properties of can be exploited to give an easy…

基于马尔可夫链蒙特卡洛与彩色连续三角剖分模型的贝叶斯图像分析AI 解读

Summary It is now possible to carry out Bayesian image segmentation from a continuum parametric model with an unknown number of regions. However, few suitable parametric models exist. We set out to model processes which have realizations that are naturally described by coloured planar triangulations. Triangulations are already used, to represent image structure in machine vision, and in finite element analysis, for domain decomposition. However, no normalizable parametric…

多元贝叶斯变量选择与预测AI 解读

Summary The multivariate regression model is considered with p regressors. A latent vector with p binary entries serves to identify one of two types of regression coefficients: those close to 0 and those not. Specializing our general distributional setting to the linear model with Gaussian errors and using natural conjugate prior distributions, we derive the marginal posterior distribution of the binary latent vector. Fast algorithms aid its direct computation, and in high…

固定行边际总数的 k×l 列联表同质性非参数贝叶斯分析AI 解读

In this work I postulate a nonparametric Bayesian model for data that can be accommodated in a contingency table with fixed right margin totals. This data structure usually arises when comparing different groups regarding classification probabilities for a number of categories. I assume that cell count vectors for each group are conditionally independent, with multinomial distribution given vectors of classification probabilities. In turn, these vectors of probabilities are…

使用狄利克雷过程先验的贝叶斯多重比较AI 解读

We consider the problem of multiple comparisons from a Bayesian viewpoint. The family of Dirichlet process priors is applied in the form of baseline prior/likelihood combinations to obtain posterior probabilities for various hypotheses of equality among population means. The baseline prior/likelihood combinations considered here are beta/binomial and normal/inverted gamma with equal variances on treatment means. The prior probabilities of the hypotheses depend directly on…

通过再生实现自适应马尔可夫链蒙特卡洛AI 解读

Markov chain Monte Carlo (MCMC) is used for evaluating expectations of functions of interest under a target distribution π. This is done by calculating averages over the sample path of a Markov chain having π as its stationary distribution. For computational efficiency, the Markov chain should be rapidly mixing. This sometimes can be achieved only by careful design of the transition kernel of the chain, on the basis of a detailed preliminary exploratory analysis of π. An…

计算机化自适应测试中异常作答者的贝叶斯识别AI 解读

We consider the problem of identifying examinees with aberrant response patterns in a computerized adaptive test (CAT). The vector Y of responses of an examinee from a CAT is a multivariate response vector. Multivariate observations may be outlying in many different directions, and we characterize specific directions as corresponding to outliers with different interpretations. We develop a class of outlier statistics to identify different types of outliers based on a control…

拒绝控制与序贯重要性抽样AI 解读

We discuss ways of combining rejection sampling and importance sampling methods in Monte Carlo computations and demonstrate their usefulness in updating dynamic systems. Specifically, we propose the rejection controlled sequential importance sampling (RC-SIS) algorithm, which is designed to simultaneously reduce Monte Carlo variation and retain independent samples in sequential importance sampling. The proposed method is demonstrated by three examples taken from…

计量经济学与统计学中的贝叶斯分析：Zellner 的观点与论文AI 解读

Part 1 Introduction. Part 2 Overview of Bayesian analysis. Part 3 Bayesian priors, models and information processing. Part 4 Bayesian methods. Part 5 Bayesian forecasting.

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统计证据：似然范式AI 解读

The First Principle Introduction The Law of Likelihood Three Questions Towards Verification Relativity of Evidence Strength of Evidence Counterexamples Testing Simple Hypotheses Composite Hypotheses Another Counterexample Irrelevance of the Sample Space The Likelihood Principle Evidence and Uncertainty Summary Exercises Neyman-Pearson Theory Introduction Neyman-Pearson Statistical Theory Evidential Interpretation of Results of Neyman-Pearson Decision Procedures…

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计算机自适应测试中异常作答者的贝叶斯识别AI 解读

We consider the problem of identifying examinees with aberrant response patterns in a computerized adaptive test (CAT). The vector Y of responses of an examinee from a CAT is a multivariate response vector. Multivariate observations may be outlying in many different directions, and we characterize specific directions as corresponding to outliers with different interpretations. We develop a class of outlier statistics to identify different types of outliers based on a control…

通过再生实现自适应马尔可夫链蒙特卡洛AI 解读

Markov chain Monte Carlo (MCMC) is used for evaluating expectations of functions of interest under a target distribution π. This is done by calculating averages over the sample path of a Markov chain having π as its stationary distribution. For computational efficiency, the Markov chain should be rapidly mixing. This sometimes can be achieved only by careful design of the transition kernel of the chain, on the basis of a detailed preliminary exploratory analysis of π. An…

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利用无限维指数族的贝叶斯拟合优度检验AI 解读

We develop a nonparametric Bayes factor for testing the fit of a parametric model. We begin with a nominal parametric family which we then embed into an infinite-dimensional exponential family. The new model then has a parametric and nonparametric component. We give the log density of the nonparametric component a Gaussian process prior. An asymptotic consistency requirement puts a restriction on the form of the prior, leaving us with a single hyperparameter for which we…

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