On an adaptive version of the Metropolis–Hastings algorithm with independent proposal distribution

In this paper, we present a general formulation of an algorithm, the adaptive independent chain (AIC), that was introduced in a special context in Gåsemyr et al . [ Methodol. Comput. Appl. Probab. 3 (2001)]. The algorithm aims at producing samples from a specific target distribution Π, and is an adaptive, non-Markovian version of the Metropolis–Hastings independent chain. A certain parametric class of possible proposal distributions is fixed, and the parameters of the proposal distribution are updated periodically on the basis of the recent history of the chain, thereby obtaining proposals that get ever closer to Π. We show that under certain conditions, the algorithm produces an exact sample from Π in a finite number of iterations, and hence that it converges to Π. We also present another adaptive algorithm, the componentwise adaptive independent chain (CAIC), which may be an alternative in particular in high dimensions. The CAIC may be regarded as an adaptive approximation to the Gibbs sampler updating parametric approximations to the conditionals of Π.     

A bayesian estimator for the dependence function of a bivariate extreme‐value distribution

Any continuous bivariate distribution can be expressed in terms of its margins and a unique copula. In the case of extreme‐value distributions, the copula is characterized by a dependence function while each margin depends on three parameters. The authors propose a Bayesian approach for the simultaneous estimation of the dependence function and the parameters defining the margins. They describe a nonparametric model for the dependence function and a reversible jump Markov chain Monte Carlo algorithm for the computation of the Bayesian estimator. They show through simulations that their estimator has a smaller mean integrated squared error than classical nonparametric estimators, especially in small samples. They illustrate their approach on a hydrological data set.     

A Non-parametric Frailty Model for Temporally Clustered Multivariate Failure Times

Abstract A model is introduced here for multivariate failure time data arising from heterogenous populations. In particular, we consider a situation in which the failure times of individual subjects are often temporally clustered, so that many failures occur during a relatively short age interval. The clustering is modelled by assuming that the subjects can be divided into ‘internally homogenous’ latent classes, each such class being then described by a time‐dependent frailty profile function. As an example, we reanalysed the dental caries data presented earlier in Härkänen et al. [Scand. J. Statist. 27 (2000) 577], as it turned out that our earlier model could not adequately describe the observed clustering.     

A Unified Approach to the Characterization of Equivalence Classes of DAGs, Chain Graphs with no Flags and Chain Graphs

Abstract.  A Markov property associates a set of conditional independencies to a graph. Two alternative Markov properties are available for chain graphs (CGs), the Lauritzen–Wermuth–Frydenberg (LWF) and the Andersson–Madigan– Perlman (AMP) Markov properties, which are different in general but coincide for the subclass of CGs with no flags . Markov equivalence induces a partition of the class of CGs into equivalence classes and every equivalence class contains a, possibly empty, subclass of CGs with no flags itself containing a, possibly empty, subclass of directed acyclic graphs (DAGs). LWF-Markov equivalence classes of CGs can be naturally characterized by means of the so-called largest CGs , whereas a graphical characterization of equivalence classes of DAGs is provided by the essential graphs . In this paper, we show the existence of largest CGs with no flags that provide a natural characterization of equivalence classes of CGs of this kind, with respect to both the LWF- and the AMP-Markov properties. We propose a procedure for the construction of the largest CGs, the largest CGs with no flags and the essential graphs, thereby providing a unified approach to the problem. As by-products we obtain a characterization of graphs that are largest CGs with no flags and an alternative characterization of graphs which are largest CGs. Furthermore, a known characterization of the essential graphs is shown to be a special case of our more general framework. The three graphical characterizations have a common structure: they use two versions of a locally verifiable graphical rule. Moreover, in case of DAGs, an immediate comparison of three characterizing graphs is possible.     

Dynamic reliability models with conditional proportional hazards

A dynamic approach to the stochastic modelling of reliability systems is further explored. This modelling approach is particularly appropriate for load-sharing, software reliability, and multivariate failure-time models, where component failure characteristics are affected by their degree of use, amount of load, or extent of stresses experienced. This approach incorporates the intuitive notion that when a set of components in a coherent system fail at a certain time, there is a jump from one structure function to another which governs the residual lifetimes of the remaining functioning components, and since the component lifetimes are intrinsically affected by the structure function which they constitute, then at such a failure time there should also be a jump in the stochastic structure of the lifetimes of the remaining components. For such dynamically-modelled systems, the stochastic characteristics of their jump times are studied. These properties of the jump times allow us to obtain the properties of the lifetime of the system. In particular, for a Markov dynamic model, specific expressions for the exact distribution functions of the jump times are obtained for a general coherent system, a parallel system, and a series-parallel system. We derive a new family of distribution functions which describes the distributions of the jump times for a dynamically-modelled system.     

Sample selection in radiocarbon dating

Archaeologists working on the island of O'ahu, Hawai'i, use radiocarbon dating of samples of organic matter found trapped in fish-pond sediments to help them to learn about the chronology of the construction and use of the aquicultural systems created by the Polynesians. At one particular site, Loko Kuwili, 25 organic samples were obtained and funds were available to date an initial nine. However, on calibration to the calendar scale, the radiocarbon determinations provided date estimates that had very large variances. As a result, major issues of chronology remained unresolved and the archaeologists were faced with the prospect of another expensive programme of radiocarbon dating. This paper presents results of research that tackles the problems associated with selecting samples from those which are still available. Building on considerable recent research that utilizes Markov chain Monte Carlo methods to aid archaeologists in their radiocarbon calibration and interpretation, we adopt the standard Bayesian framework of risk functions, which allows us to assess the optimal samples to be sent for dating. Although rather computer intensive, our algorithms are simple to implement within the Bayesian radiocarbon framework that is already in place and produce results that are capable of direct interpretation by the archaeologists. By dating just three more samples from Loko Kuwili the expected variance on the date of greatest interest could be substantially reduced.     

Application of Markov chain Monte Carlo methods to modelling birth prevalence of Down syndrome

Data collected before the routine application of prenatal screening are of unique value in estimating the natural live-birth prevalence of Down syndrome. However, much of these data are from births from over 20 years ago and they are of uncertain quality. In particular, they are subject to varying degrees of underascertainment. Published approaches have used ad hoc corrections to deal with this problem or have been restricted to data sets in which ascertainment is assumed to be complete. In this paper we adopt a Bayesian approach to modelling ascertainment and live-birth prevalence. We consider three prior specifications concerning ascertainment and compare predicted maternal-age-specific prevalence under these three different prior specifications. The computations are carried out by using Markov chain Monte Carlo methods in which model parameters and missing data are sampled.     

基于MCMC稳态模拟的贝叶斯经验费率厘定信用模型

B黨lmann-Straub model is one of the most famous applications of the Bayesian method for the experience rate making.However,by the traditional B黨lmann-Straub model one cannot get the unbiased posterior estimation of the parameters when there is not sufficient prior information for the structural parameters;What's more,the difficult of computing high dimension numeration limits the application of Bayesian method.This paper introduces the Markov chain Monte Carlo simulaton method based on the Gibbs sampling after analyzing the structure of the B黨lmann-Straub model and sets up the Bayesian credibility model for estimating the predictive risk premium.Also by using the results of the numeration analysis,this paper proves that from this model one can get the posterior distributions of the parameters dynamically and the posterior estimation of the censoring parameters in the situation that exists unknown parameters,as well as improve the precision of the numeration,which can be helpful to find the heterogeneity of the premium.     

货币政策对M2的动态效应时滞分析及危机效应测算

科学测算金融危机期间已出台货币政策对货币供应量M2的效应时滞和贡献程度具有一定的现实价值。文章利用Markov状态转换及HP滤波模型识别不同货币政策状态的时间区间;利用多项式滞后分布模型分析政策工具变量对货币供应量影响的滞后效应,并以此为先验信息,建立了货币政策的Bayesian-PDLS动态效应分布模型,对金融危机期间已出台的货币政策效果进行了实际测算。主要结果表明:(1)外汇储备为M2的决定性因素,存款准备金率为M2主要的限制性因素;(2)货币政策变量M2总体对利率的弹性变化呈"U"型分布;在紧缩型情况下M2对利率的弹性变化呈"W"型分布;在扩张情形下M2对利率的弹性变化呈"v"型分布。     

带有能力约束的多元马氏需求报童模型

在随机需求环境下考虑带有能力约束的多产品报童问题.为了对多产品的需求进行预测,并度量其需求间的关系,本文首先建立了多元马氏需求模型.其次,在该模型的理论基础上,提出了带有能力约束的多元马氏需求报童模型,进而给出多产品的最优订购策略解.最后,利用期望需求状态的概率值及其截尾概率分析了模型最优解的性质.模型的结论表明,在能力约束的条件下,最优订购量关于左截尾概率单调递减,关于右截尾概率单调递增,而期望需求状态的概率值对最优订购量具有双重的特殊影响.