Random effects regression models for count data with excess zeros in caries research

We extend the family of Poisson and negative binomial models to derive the joint distribution of clustered count outcomes with extra zeros. Two random effects models are formulated. The first model assumes a shared random effects term between the conditional probability of perfect zeros and the conditional mean of the imperfect state. The second formulation relaxes the shared random effects assumption by relating the conditional probability of perfect zeros and the conditional mean of the imperfect state to two different but correlated random effects variables. Under the conditional independence and the missing data at random assumption, a direct optimization of the marginal likelihood and an EM algorithm are proposed to fit the proposed models. Our proposed models are fitted to dental caries counts of children under the age of six in the city of Detroit.     

Extensions of Fill's algorithm for perfect simulation

Fill's algorithm for perfect simulation for attractive finite state space models, unbiased for user impatience, is presented in terms of stochastic recursive sequences and extended in two ways. Repulsive discrete Markov random fields with two coding sets like the auto-Poisson distribution on a lattice with 4-neighbourhood can be treated as monotone systems if a particular partial ordering and quasi-maximal and quasi-minimal states are used. Fill's algorithm then applies directly. Combining Fill's rejection sampling with sandwiching leads to a version of the algorithm which works for general discrete conditionally specified repulsive models. Extensions to other types of models are briefly discussed.     

Perfect linear models and perfect parametric functions

General linear models with a common design matrix and with various structures of the variance–covariance matrix are considered. We say that a model is perfect for a linearly estimable parametric function, or the function is perfect in the model, if there exists the best linear unbiased estimator. All perfect models for a given function and all perfect functions in a given model are characterized.     

Perfect value and outlier detection in logistic binary choice models

Tins paper discussed some diagnostic tools for logistics binary choice models using techniques based on perfect values. The concept of perfect value fit is defined for logistic models in an analogous approach used when dealing with non ignorable non-iespouse in contingency tables. Performance ol outlier diagnostics based on perfect values is illustrated on a set of data on incidents in pre-Challenger launches.     

Direct simulation for discrete mixture distributions

We demonstrate how to perform direct simulation for discrete mixture models. The approach is based on directly calculating the posterior distribution using a set of recursions which are similar to those of the Forward-Backward algorithm. Our approach is more practicable than existing perfect simulation methods for mixtures. For example, we analyse 1096 observations from a 2 component Poisson mixture, and 240 observations under a 3 component Poisson mixture (with unknown mixture proportions and Poisson means in each case). Simulating samples of 10,000 perfect realisations took about 17 minutes and an hour respectively on a 900 MHz ultraSPARC computer. Our method can also be used to perform perfect simulation from Markov-dependent mixture models. A byproduct of our approach is that the evidence of our assumed models can be calculated, which enables different models to be compared.     

Convergence in the Wasserstein Metric for Markov Chain Monte Carlo Algorithms with Applications to Image Restoration

Abstract

In this paper, we show how the time for convergence to stationarity of a Markov chain can be assessed using the Wasserstein metric, rather than the usual choice of total variation distance. The Wasserstein metric may be more easily applied in some applications, particularly those on continuous state spaces. Bounds on convergence time are established by considering the number of iterations required to approximately couple two realizations of the Markov chain to within ε tolerance. The particular application considered is the use of the Gibbs sampler in the Bayesian restoration of a degraded image, with pixels that are a continuous grey-scale and with pixels that can only take two colours. On finite state spaces, a bound in the Wasserstein metric can be used to find a bound in total variation distance. We use this relationship to get a precise O(N log N) bound on the convergence time of the stochastic Ising model that holds for appropriate values of its parameter as well as other binary image models. Our method employing convergence in the Wasserstein metric can also be applied to perfect sampling algorithms involving coupling from the past to obtain estimates of their running times.     

Ranked set sampling,coherent rankings and size-biased permutations

The paper examines the effect of the set size upon the performance (reciprocal variance) of balanced ranked set sampling for estimation of a population mean. Performance is shown to be monotone increasing with the set size for the wide class of ranking models that satisfy a property called coherence. This class includes perfect ranking as well as ranking by concomitant variable. Stochastic ranking models based upon size-biased permutations are also shown to satisfy coherence and, consequently, monotonicity.     

高速公路路段畅通状态综合评价

为合理分析高速公路畅通状态,为公路建设项目优化提供依据,在分析畅通内涵的基础上,补充运输需求满足度、公路供给有效性两指标,完善了高速公路路段畅通状态评价指标体系。针对传统畅通状态评价等级只有“畅通”、“拥堵”两级,无法体现公路运营状态渐变性的缺陷,将畅通状态评语集划分为“过度拥堵”、“拥堵”、“畅通”、“过度畅通”四个级别。拥堵和过度畅通都是公路的不合理运营状态。     

Power-linear models for incomplete contingency tables with nonignorable non-responses

For categorical data exhibiting nonignorable non-responses, it is well known that maximum likelihood (ML) estimates with a boundary solution are implausible and do not provide a perfect fit to the observed data even for saturated models. We provide the conditions under which ML estimates for the generalized linear model (GLM) with the usual log/logit link function have a boundary solution. These conditions introduce a new GLM with appropriately defined power link functions where its ML estimates resolve the problems arising from a boundary solution and offer useful statistics for identifying the non-response mechanism. This model is applied to a real dataset and compared with Bayesian models.     

The Consumer’s Risk and Costs in Zero-Acceptance Number Sampling

The primary purpose of sampling inspection is the protection of consumer’s interests. Although under simple cost models, sampling inspection never serves the producer’s interest, some form of sampling inspection can be beneficial to the consumer under the same assumptions. We consider the case of isolated lot inspection and examine the consumer risk, economic sample design, and errors in the inspection process. Acceptance sampling is shown to be cost-effective to the consumer whenever the lot quality is less than perfect, and even for perfect lot quality in the presence of inspection errors.     

Panel—Data下Granger因果检验的理论和应用发展综述

Panel-Data下Granger因果检验的相关理论是最近几年才发展起来的,现有的研究提出了关于Panel-Data下Granger因果检验的四个基本假设:同质无因果关系假设(HNCH)、同质因果关系假设(HCH)、异质因果关系假设(HECH)以及异质无因果关系假设(HENCH),根据检验参数的特点给出三种类型的检验模型:固定系数模型、随机系数模型和混合固定随机系数模型。目前,还只有固定系数模型的相关理论较为完善,另外两种模型的检验还都存在一定的难度。因此,只有从理论研究和实际应用两个方面对该理论进行阐述,并对现有的理论进行简要的评述,才可指出其存在的不足及可能的改进方向。     

State space mixed models for longitudinal observations with binary and binomial responses

We propose a new class of state space models for longitudinal discrete response data where the observation equation is specified in an additive form involving both deterministic and random linear predictors. These models allow us to explicitly address the effects of trend, seasonal or other time-varying covariates while preserving the power of state space models in modeling serial dependence in the data. We develop a Markov chain Monte Carlo algorithm to carry out statistical inference for models with binary and binomial responses, in which we invoke de Jong and Shephard’s (Biometrika 82(2):339–350, 1995) simulation smoother to establish an efficient sampling procedure for the state variables. To quantify and control the sensitivity of posteriors on the priors of variance parameters, we add a signal-to-noise ratio type parameter in the specification of these priors. Finally, we illustrate the applicability of the proposed state space mixed models for longitudinal binomial response data in both simulation studies and data examples.     

Monte Carlo Kalman filter and smoothing for multivariate discrete state space models

The author studies state space models for multivariate binomial time series, focussing on the development of the Kalman filter and smoothing for state variables. He proposes a Monte Carlo approach employing the latent variable representation which transplants the classical Kalman filter and smoothing developed for Gaussian state space models to discrete models and leads to a conceptually simple and computationally convenient approach. The method is illustrated through simulations and concrete examples.     

Assessing Type I error and power of multistate Markov models for panel data—A simulation study

Ordinal outcomes collected at multiple follow-up visits are common in clinical trials. Sometimes, one visit is chosen for the primary analysis and the scale is dichotomized amounting to loss of information. Multistate Markov models describe how a process moves between states over time. Here, simulation studies are performed to investigate the Type I error and power characteristics of multistate Markov models for panel data with limited non-adjacent state transitions. The results suggest that the multistate Markov models preserve the Type I error and adequate power is achieved with modest sample sizes for panel data with limited non-adjacent state transitions.     

A bayesian analysis of imperfect inspection models

An examination of sampling inspection models is provided for the case where inspection is not perfect and classification errors can be made. The conjugate family of distributions is obtained under t h e assumption that defective items are generated according to a Bernoulli process. To simplify analysis, the use of a single beta prior distribution is considered. Relevant predictive distributions are obtained.     

Perfect simulation of an inventory model for perishable products

We study an inventory model for perishable products with a critical-number ordering policy under the assumption that demand for the product forms an i.i.d. sequence, so that the state of the system forms a Markov chain. Explicit calculation of the stationary distribution has proved impractical in cases where items have reasonably long lifetimes and for systems with large under-up-to levels. Using the recently developed coupling-from-the-past method, we introduce a technique to estimate the stationary distribution of the Markov chain via perfect simulation. The Markov chain that results from the use of a critical-number policy is particularly amenable to these simulation techniques, despite not being ordered in its initial state, since the recursive equations satisfied by the Markov chain enable us to identify specific demand patterns where the backward coupling occurs.     

BAYESIAN HIDDEN MARKOV MODELS FOR LONGITUDINAL COUNTS

This paper describes a Bayesian approach to modelling carcinogenity in animal studies where the data consist of counts of the number of tumours present over time. It compares two autoregressive hidden Markov models. One of them models the transitions between three latent states: an inactive transient state, a multiplying state for increasing counts and a reducing state for decreasing counts. The second model introduces a fourth tied state to describe non‐zero observations that are neither increasing nor decreasing. Both these models can model the length of stay upon entry of a state. A discrete constant hazards waiting time distribution is used to model the time to onset of tumour growth. Our models describe between‐animal‐variability by a single hierarchy of random effects and the within‐animal variation by first‐order serial dependence. They can be extended to higher‐order serial dependence and multi‐level hierarchies. Analysis of data from animal experiments comparing the influence of two genes leads to conclusions that differ from those of Dunson (2000). The observed data likelihood defines an information criterion to assess the predictive properties of the three‐ and four‐state models. The deviance information criterion is appropriately defined for discrete parameters.     

Learning discrete decomposable graphical models via constraint optimization

Statistical model learning problems are traditionally solved using either heuristic greedy optimization or stochastic simulation, such as Markov chain Monte Carlo or simulated annealing. Recently, there has been an increasing interest in the use of combinatorial search methods, including those based on computational logic. Some of these methods are particularly attractive since they can also be successful in proving the global optimality of solutions, in contrast to stochastic algorithms that only guarantee optimality at the limit. Here we improve and generalize a recently introduced constraint-based method for learning undirected graphical models. The new method combines perfect elimination orderings with various strategies for solution pruning and offers a dramatic improvement both in terms of time and memory complexity. We also show that the method is capable of efficiently handling a more general class of models, called stratified/labeled graphical models, which have an astronomically larger model space.     

Age–period–cohort decompositions using principal components and partial least squares

Age–period–cohort decomposition requires an identification assumption because there is a linear relationship between age, survey period, and birth cohort (age+cohort=period). This paper proposes new decomposition methods based on factor models such as principal components model and partial least squares model. Although factor models have been applied to overcome the problem of many observed variables with possible co-linearity, they are applied to overcome the perfect co-linearity among age, period, and cohort dummy variables. Since any unobserved factor in the factor model is represented as a linear combination of the observed variables, the parameter estimates for age, period, and cohort effects are automatically obtained after the application of these factor models. Simulation results suggest that in almost all cases, the performance of the proposed method is better than that of a conventional econometric method. Empirical examples are also provided.     

基于状态空间图模型方法的投资组合优化决策

将lasso图理论合并到状态空间模型中,利用条件独立性且通过范数惩罚法对协方差阵进行估计。新方法兼具图模型和动态状态空间模型的优点。最后将该方法应用于欧洲股票市场进行投资组合优化决策,结果表明基于lasso图方法的状态空间模型的投资组合业绩要优于自回归和一般的状态空间模型。