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周期性状态转换模型的贝叶斯推断AI 解读

We present a general class of nonlinear time-series Markov regime-switching models for seasonal data which may exhibit periodic features in the hidden Markov process as well as in the laws of motion in each of the regimes. This class of models allows for non-trivial dependencies between seasonal, cyclical and long-term patterns in the data. To overcome the computational burden we adopt a Bayesian approach to estimation and inference. This paper contains two empirical…

We begin by showing how piecewise linear bounds may be devised, which bound both above and below any concave log-density in general dimensions. We then show how these bounds may be used to gain an upper bound to the volume in the tails outside the convex hull of the sample path in order to assess how well the sampler has explored the target distribution. This method can be used as a stand-alone diagnostic to determine when the sampler output provides a reliable basis for…

辛普森悖论与贝叶斯因子AI 解读

Summary A counter-example presented by Lindley to Aitkin’s posterior Bayes factor is examined. The paradoxical feature of the counter-example is found to be a simple case of Simpson’s paradox.

贝叶斯自助法与可交换抽球方案族的扩展AI 解读

Summary A Bayesian bootstrap for a finite population with censored observations is introduced. It is shown to reduce to the finite population Bayesian bootstrap if there is no censoring and to reduce to the censored data Bayesian bootstrap for a large population. A class of general urn schemes for simulating exchangeable sequences of variables is introduced which is connected to the bootstrap method.

存在不可忽略无应答的分类调查数据模型推断AI 解读

Summary We consider non-response models for a single categorical response with categorical covariates whose values are always observed. We present Bayesian methods for ignorable models and a particular non-ignorable model, and we argue that standard methods of model comparison are inappropriate for comparing ignorable and non-ignorable models. Uncertainty about ignorability of non-response is incorporated by introducing parameters describing the extent of non-ignorability…

推广用于区域行业间就业预测的贝叶斯向量自回归方法AI 解读

The Bayesian vector autoregression (BVAR) employment-forecast approach is generalized using data for the state of Georgia. This study advances previous regional BVAR approaches by (1) incorporating regional input-output coefficients, (2) using the coefficients both to specify the prior means in one model and to weight the variances of a Minnesota-type prior in a second model, and (3) including final-demand effects and links to national and world economies. Out-of-sample…

用于时间序列模型的扫描抽样器AI 解读

An algorithm, called the scan sampler, is developed and discussed. The scan sampler has a variety of uses for time series analysis based on the state space model with non-Gaussian observations. The algorithm is based on the Kalman filter/smoothing algorithm. It can be used for Bayesian inference using Markov chain Monte Carlo and to find posterior modes.

用于出版偏差建模的非参数权重函数类AI 解读

This paper addresses the use of weight functions to model publication bias in meta-analysis. Since publication bias is hard to gauge, a nonparametric ε-contamination class of weight functions is introduced. Sensitivity of conclusions to the specification of the weight function is explored by examining the range of results for the entire ε-contamination class. First, lower bounds are found on the coverage of confidence intervals. If little publication bias is suspected,…

互信息、度量熵与累积相对熵风险AI 解读

Assume ${P_{\theta}: \theta \epsilon \Theta}$ is a set of probability distributions with a common dominating measure on a complete separable metric space Y. A state $\theta^* \epsilon \Theta$ is chosen by Nature. A statistician obtains n independent observations $Y_1, \dots, Y_n$ from Y distributed according to $P_{\theta^*}$. For each time t between 1 and n, based on the observations $Y_1, \dots, Y_{t-1}$, the statistician produces an estimated distribution $\hat{P}_t$ for $P_{\theta^*}$…

粒度平滑AI 解读

A new method for smoothing a multivariate data set is introduced that is based on a simple geometric operation. This method is applied to the problem of estimating level sets of a density and minimum volume sets with given probability content. Building on existing techniques, the resulting estimator combines excellent theoretical and computational properties: It converges with the minimax rates (up to log factors) in most cases where these rates are known and, at the same…

非参数二元回归的贝叶斯方法AI 解读

This article outlines a general Bayesian approach to estimating a bivariate regression function in a nonparametric manner. It models the function using a bivariate regression spline basis with many terms. Binary indicator variables corresponding to these terms are introduced to explicitly model the uncertainty of whether or not the terms provide a significant contribution to the regression. The regression function is estimated using an estimate of its posterior mean,…

多元回归模型中经典与贝叶斯推断的稳健性AI 解读

We consider a one-to-one correspondence between points z ∈ Rn - {0} and pairs (y, r), where r > 0 and y lies in some space y, through z = r y. As an immediate consequence, we can represent random variables Z that take values in Rn - {0} as Z = R Y, where R is a positive random variable and Y takes values in y. By fixing the distribution of either R or Y while imposing independence between them, we generate classes of distributions on Rn . Many families of multivariate…

采用层次混合先验的贝叶斯总体模型及其血细胞计数应用AI 解读

Population pharmacokinetic and pharmacodynamic studies require analyzing nonlinear growth curves fit to multiple measurements from study subjects. We propose a class of nonlinear population models with nonparametric second-stage priors for analyzing such data. The proposed models apply a flexible class of mixtures to implement the nonparametric second stage. The discussion is based on a pharmacodynamic study involving longitudinal data consisting of hematologic profiles…

复杂调查中有限总体均值的经验贝叶斯估计AI 解读

Estimation of finite population means is considered when samples are collected using a stratified sampling design. Finite populations for different strata are assumed to be realizations from different superpopulations. The true means of the observations lie on a regression surface with random intercepts for different strata. The true sampling variances are also different and random for different strata. The strata are connected through two common prior distributions, one for…

变换高斯随机场的贝叶斯预测AI 解读

A model for prediction in some types of non-Gaussian random fields is presented. It extends the work of Handcock and Stein to prediction in transformed Gaussian random fields, where the transformation is known to belong to a parametric family of monotone transformations. The Bayesian transformed Gaussian model (BTG) provides an alternative to trans-Gaussian kriging taking into account the major sources of uncertainty, including uncertainty about the “normalizing…

动态条件独立模型与Markov链Monte Carlo方法AI 解读

In dynamic statistical modeling situations, observations arise sequentially, causing the model to expand by progressive incorporation of new data items and new unknown parameters. For example, in clinical monitoring, patients and data arrive sequentially, and new patient-specific parameters are introduced with each new patient. Markov chain Monte Carlo (MCMC) might be used for continuous updating of the evolving posterior distribution, but would need to be restarted from…

复杂调查中有限总体均值的经验贝叶斯估计AI 解读

Estimation of finite population means is considered when samples are collected using a stratified sampling design. Finite populations for different strata are assumed to be realizations from different superpopulations. The true means of the observations lie on a regression surface with random intercepts for different strata. The true sampling variances are also different and random for different strata. The strata are connected through two common prior distributions, one for…

非参数二维回归的贝叶斯方法AI 解读

This article outlines a general Bayesian approach to estimating a bivariate regression function in a nonparametric manner. It models the function using a bivariate regression spline basis with many terms. Binary indicator variables corresponding to these terms are introduced to explicitly model the uncertainty of whether or not the terms provide a significant contribution to the regression. The regression function is estimated using an estimate of its posterior mean,…

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采用贝叶斯非参数混合的层级广义线性模型与脆弱性模型AI 解读

Summary This paper proposes Bayesian nonparametric mixing for some well-known and popular models. The distribution of the observations is assumed to contain an unknown mixed effects term which includes a fixed effects term, a function of the observed covariates, and an additive or multiplicative random effects term. Typically these random effects are assumed to be independent of the observed covariates and independent and identically distributed from a distribution from some…

成分数量未知的混合模型贝叶斯分析（附讨论）AI 解读

Summary New methodology for fully Bayesian mixture analysis is developed, making use of reversible jump Markov chain Monte Carlo methods that are capable of jumping between the parameter subspaces corresponding to different numbers of components in the mixture. A sample from the full joint distribution of all unknown variables is thereby generated, and this can be used as a basis for a thorough presentation of many aspects of the posterior distribution. The methodology is…