Bayesian networks for discrete multivariate data: an algebraic approach to inference

In this paper we demonstrate how Gröbner bases and other algebraic techniques can be used to explore the geometry of the probability space of Bayesian networks with hidden variables. These techniques employ a parametrisation of Bayesian network by moments rather than conditional probabilities. We show that whilst Gröbner bases help to explain the local geometry of these spaces a complimentary analysis, modelling the positivity of probabilities, enhances and completes the geometrical picture. We report some recent geometrical results in this area and discuss a possible general methodology for the analyses of such problems.     

A Bayesian inference approach to identify a Robin coefficient in one-dimensional parabolic problems

This paper investigates a nonlinear inverse problem associated with the heat conduction problem of identifying a Robin coefficient from boundary temperature measurement. A Bayesian inference approach is presented for the solution of this problem. The prior modeling is achieved via the Markov random field (MRF). The use of a hierarchical Bayesian method for automatic selection of the regularization parameter in the function estimation inverse problem is discussed. The Markov chain Monte Carlo (MCMC) algorithm is used to explore the posterior state space. Numerical results indicate that MRF provides an effective prior regularization, and the Bayesian inference approach can provide accurate estimates as well as uncertainty quantification to the solution of the inverse problem.     

A semiparametric Bayesian approach to the analysis of financial time series with applications to value at risk estimation

GARCH models are commonly used for describing, estimating and predicting the dynamics of financial returns. Here, we relax the usual parametric distributional assumptions of GARCH models and develop a Bayesian semiparametric approach based on modeling the innovations using the class of scale mixtures of Gaussian distributions with a Dirichlet process prior on the mixing distribution. The proposed specification allows for greater flexibility in capturing the usual patterns observed in financial returns. It is also shown how to undertake Bayesian prediction of the Value at Risk (VaR). The performance of the proposed semiparametric method is illustrated using simulated and real data from the Hang Seng Index (HSI) and Bombay Stock Exchange index (BSE30).     

Statistical inference for the nonparametric and semiparametric hidden Markov model via the composite likelihood approach

In this paper, we propose a new estimation method for a nonparametric hidden Markov model(HMM), in which both the emission model and the transition matrix are nonparametric, and a semiparametric HMM, in which the transition matrix is parametric while emission models are nonparametric. The estimation is based on a novel composite likelihood method, where the pairs of consecutive observations are treated as independent bivariate random variables. Therefore, the model is transformed into a mixture ...     

A semiparametric panel approach to mortality modeling

During the past twenty years, there has been a rapid growth in life expectancy and an increased attention on funding for old age. Attempts to forecast improving life expectancy have been boosted by the development of stochastic mortality modeling, for example the Cairns–Blake–Dowd (CBD) 2006 model. The most common optimization method for these models is maximum likelihood estimation (MLE) which relies on the assumption that the number of deaths follows a Poisson distribution. However, several recent studies have found that the true underlying distribution of death data is overdispersed in nature (see Cairns et al. 2009 and Dowd et al. 2010). Semiparametric models have been applied to many areas in economics but there are very few applications of such models in mortality modeling. In this paper we propose a local linear panel fitting methodology to the CBD model which would free the Poisson assumption on number of deaths. The parameters in the CBD model will be considered as smooth functions of time instead of being treated as a bivariate random walk with drift process in the current literature. Using the mortality data of several developed countries, we find that the proposed estimation methods provide comparable fitting results with the MLE method but without the need of additional assumptions on number of deaths. Further, the 5-year-ahead forecasting results show that our method significantly improves the accuracy of the forecast.     

Two-step generalised empirical likelihood inference for semiparametric models

This paper shows how the generalised empirical likelihood method can be used to obtain valid asymptotic inference for the finite dimensional component of semiparametric models defined by a set of moment conditions. The results of the paper are illustrated using three well-known semiparametric regression models: partially linear single index, linear transformation with random censoring, and quantile regression with random censoring. Monte Carlo simulations suggest that some of the proposed test statistics have competitive finite sample properties. The results of the paper are applied to test for functional misspecification in a hedonic price model of a housing market.     

Bayesian semiparametric Markov switching stochastic volatility model

This paper proposes a novel Bayesian semiparametric stochastic volatility model with Markov switching regimes for modeling the dynamics of the financial returns. The distribution of the error term of the returns is modeled as an infinite mixture of Normals; meanwhile, the intercept of the volatility equation is allowed to switch between two regimes. The proposed model is estimated using a novel sequential Monte Carlo method called particle learning that is especially well suited for state‐space models. The model is tested on simulated data and, using real financial times series, compared to a model without the Markov switching regimes. The results show that including a Markov switching specification provides higher predictive power for the entire distribution, as well as in the tails of the distribution. Finally, the estimate of the persistence parameter decreases significantly, a finding consistent with previous empirical studies.     

Functional inference in semiparametric models using the piggyback bootstrap

This paper introduces the “piggyback bootstrap.” Like the weighted bootstrap, this bootstrap procedure can be used to generate random draws that approximate the joint sampling distribution of the parametric and nonparametric maximum likelihood estimators in various semiparametric models, but the dimension of the maximization problem for each bootstrapped likelihood is smaller. This reduction results in significant computational savings in comparison to the weighted bootstrap. The procedure can be stated quite simply. First obtain a valid random draw for the parametric component of the model. Then take the draw for the nonparametric component to be the maximizer of the weighted bootstrap likelihood with the parametric component fixed at the parametric draw. We prove the procedure is valid for a class of semiparametric models that includes frailty regression models airsing in survival analysis and biased sampling models that have application to vaccine efficacy trials. Bootstrap confidence sets from the piggyback, and weighted bootstraps are compared for biased sampling data from simulated vaccine efficacy trials.     

A Bayesian approach for analyzing case 2 interval-censored data under the semiparametric proportional odds model

Analyzing interval-censored data is difficult due to its complex data structure containing left-, interval-, and right-censored observations. An easy-to-implement Bayesian approach is proposed under the proportional odds (PO) model for analyzing such data. The nondecreasing baseline log odds function is modeled with a linear combination of monotone splines. Two efficient Gibbs samplers are developed based on two different data augmentations using the relationship between the PO model and the logistic distribution. In the first data augmentation, the logistic distribution is achieved by the scaled normal mixture with the scale parameter related to the Kolmogorov-Smirnove distribution. In the second data augmentation, the logistic distribution is approximated by a Student’s t distribution up to a scale constant. The proposed methods are evaluated by simulation studies and illustrated with an application of an HIV data set.     

Bayesian inference in Markovian queues

This paper is concerned with the Bayesian analysis of general queues with Poisson input and exponential service times. Joint posterior distribution of the arrival rate and the individual service rate is obtained from a sample consisting inn observations of the interarrival process andm complete service times. Posterior distribution of traffic intensity inM/M/c is also obtained and the statistical analysis of the ergodic condition from a decision point of view is discussed.     

工序能力Bayes推断

本文从Ｂａｙｅｓ观点研究工序能力，对无信息先验和共轭先验，给出了Ｃｐ的后验分布、条件期望估计和最大后验估计、Ｂａｙｅｓ置信下限和判断工序是否有能力的临界值，适于对相似工序作统计推断。     

Bayesian inference for clustered extremes

We consider Bayesian inference for the extremes of dependent stationary series. We discuss the virtues of the Bayesian approach to inference for the extremal index, and for related characteristics of clustering behaviour. We develop an inference procedure based on an automatic declustering scheme, and using simulated data we implement and assess this procedure, making inferences for the extremal index, and for two cluster functionals. We then apply our procedure to a set of real data, specifically a time series of wind-speed measurements, where the clusters correspond to storms. Here the two cluster functionals selected previously correspond to the mean storm length and the mean inter-storm interval. We also consider inference for long-period return levels, advocating the posterior predictive distribution as being most representative of the information required by engineers interested in design level specifications.      

A continuous approach to inductive inference

In this paper we describe an interior point mathematical programming approach to inductive inference. We list several versions of this problem and study in detail the formulation based on hidden Boolean logic. We consider the problem of identifying a hidden Boolean function:{0, 1} ⁿ {0, 1} using outputs obtained by applying a limited number of random inputs to the hidden function. Given this input—output sample, we give a method to synthesize a Boolean function that describes the sample. We pose the Boolean Function Synthesis Problem as a particular type of Satisfiability Problem. The Satisfiability Problem is translated into an integer programming feasibility problem, that is solved with an interior point algorithm for integer programming. A similar integer programming implementation has been used in a previous study to solve randomly generated instances of the Satisfiability Problem. In this paper we introduce a new variant of this algorithm, where the Riemannian metric used for defining the search region is dynamically modified. Computational results on 8-, 16- and 32-input, 1-output functions are presented. Our implementation successfully identified the majority of hidden functions in the experiment.     

Bayesian semiparametric analysis for a single item maintenance optimization

We address the problem of a finite horizon single item maintenance optimization structured as a combination of preventive and corrective maintenance in a nuclear power plant environment. We present Bayesian semiparametric models to estimate the failure time distribution and costs involved. The objective function for the optimization is the expected total cost of maintenance over the pre-defined finite time horizon. Typically, the mathematical modeling of failure times are based on parametric models. These models fail to capture the true underlying relationships in the data; indeed, under a parametric assumption, the hazard rates are treated as unimodal, which, as shown in this paper, is incorrect. Importantly, assuming an increasing failure rate, as is typically done, we show, is way off the mark in the present context. Since hazard and cost estimates feed into the optimization phase, from a risk management perspective, potentially gross errors, resulting from purely parametric models, can be obviated. We show the effectiveness of our approach using real data from the South Texas Project Nuclear Operating Company (STPNOC) located in Bay City, Texas.     

Bayesian network inference using marginal trees

Variable elimination (VE) and join tree propagation (JTP) are two alternatives to inference in Bayesian networks (BNs). VE, which can be viewed as one-way propagation in a join tree, answers each query against the BN meaning that computation can be repeated. On the other hand, answering a single query with JTP involves two-way propagation, of which some computation may remain unused. In this paper, we propose marginal tree inference (MTI) as a new approach to exact inference in discrete BNs. MTI seeks to avoid recomputation, while at the same time ensuring that no constructed probability information remains unused. Thereby, MTI stakes out middle ground between VE and JTP. The usefulness of MTI is demonstrated in multiple probabilistic reasoning sessions.     

Generalized empirical likelihood inference in semiparametric regression model for longitudinal data

In this paper, we consider the semiparametric regression model for longitudinal data. Due to the correlation within groups, a generalized empirical log-likelihood ratio statistic for the unknown parameters in the model is suggested by introducing the working covariance matrix. It is proved that the proposed statistic is asymptotically standard chi-squared under some suitable conditions, and hence it can be used to construct the confidence regions of the parameters. A simulation study is conducted to compare the proposed method with the generalized least squares method in terms of coverage accuracy and average lengths of the confidence intervals.     

A weighted strategy to handle likelihood uncertainty in Bayesian inference

The sensitivity of posterior inferences to model specification can be considered as an indicator of the presence of outliers, that are to be considered as highly unlikely values under the assumed model. The occurrence of anomalous values can seriously alter the shape of the likelihood function and lead to posterior distributions far from those one would obtain without these data inadequacies. In order to deal with these hindrances, a robust approach is discussed, which allows us to obtain outliers’ resistant posterior distributions with properties similar to those of a proper posterior distribution. The methodology is based on the replacement of the genuine likelihood by a weighted likelihood function in the Bayes’ formula.     

Robust semiparametric inference for polytomous logistic regression with complex survey design

Advances in Data Analysis and Classification - Analyzing polytomous response from a complex survey scheme, like stratified or cluster sampling is very crucial in several socio-economics...     

纵向数据下半参数联合均值协方差模型的贝叶斯分析

基于改进的Cholesky分解,研究分析了纵向数据下半参数联合均值协方差模型的贝叶斯估计和贝叶斯统计诊断,其中非参数部分采用B样条逼近.主要通过应用Gibbs抽样和Metropolis-Hastings算法相结合的混合算法获得模型中未知参数的贝叶斯估计和贝叶斯数据删除影响诊断统计量.并利用诊断统计量的大小来识别数据的异常点.模拟研究和实例分析都表明提出的贝叶斯估计和诊断方法是可行有效的.