A model of the ring-recovery reporting process for the Cape Griffon Gyps coprotheres

By their very nature, statistical models are constructed on the basis of a number of simplifying assumptions. It is usual to assume that all the individuals in a 'group' or 'cohort' have similar survival, recovery or reporting probabilities. From a number of earlier studies of the Cape Griffon Gyps coprotheres in southern Africa, it is clear that there have been many violations of these assumptions of homogeneity. To get a better understanding of the process whereby a dead ringed bird is found and reported, an analysis was undertaken of 575 recoveries from 7130 individuals ringed as nestlings. From a series of univariate generalized linear models, it was found that the proportion of ringed birds reported dead varied with the following factors: (1) ring prefix (representing different grades and thicknesses of aluminium): there was considerable variation in reporting rate between cohorts fitted with different ring prefix series used; (2) metal type: birds fitted with monel metal rings were reported at a rate twice that of those bearing aluminium rings; (3) colour rings: recoveries of birds with colour rings were much more likely to be reported than birds with only a metal ring; (4) epoch: the reporting rate has increased steadily from the 1950s through to the mid-1980s. All of these factors are confounded and so a number of multivariate generalized linear models were constructed. It was found that the variations in the cohort-specific reporting rate could be described well by a model including factors for metal-ring type and the presence or absence of colour rings. Using the tougher monel metal ring along with a set of colour rings more than doubles the reporting rate and their continued use is strongly recommended for future studies. The year-to-year variations could be accounted for by this model but the colony of ringing did not enter the model. The models used were based on two assumptions: (i) the reporting rate was constant for all individuals within a given cohort and (ii) the recoveries were complete. It is argued that the results are congruent with these assumptions. There is now a clearer model of the manner in which the ring-recovery reporting process proceeds and this has opened the way to building a more realistic statistical model to estimate survival in the Cape Griffon.     

A latent process model for dementia and psychometric tests

We jointly model longitudinal values of a psychometric test and diagnosis of dementia. The model is based on a continuous-time latent process representing cognitive ability. The link between the latent process and the observations is modeled in two phases. Intermediate variables are noisy observations of the latent process; scores of the psychometric test and diagnosis of dementia are obtained by categorizing these intermediate variables. We propose maximum likelihood inference for this model and we propose algorithms for performing this task. We estimated the parameters of such a model using the data of the 5 year follow-up of the PAQUID study. In particular this analysis yielded interesting results about the effect of educational level on both latent cognitive ability and specific performance in the mini mental test examination. The predictive ability of the model is illustrated by predicting diagnosis of dementia at the 8 year follow-up of the PAQUID study based on the information from the first 5 years.     

A functional marked point process model for lupus data

Modelling for marked point processes is an important problem, but has received remarkably little attention in the statistical literature. The authors developed a marked point process model that incorporates the use of functional data analysis in a joint estimation of the frequency function of the point process and the intensity of the mark, with application to data from 22 lupus patients consisting of times of flares in symptom severity combined with a quantitative assessment of the severity. The data indicate that a rapid decrease in drug dose is significantly associated with a decrease in flare frequency. Experiments with simulated data designed to model the actual data further support this conclusion. The Canadian Journal of Statistics 40: 517–529; 2012 © 2012 Statistical Society of Canada     

A semiparametric additive rate model for a modulated renewal process

Recurrent event data from a long single realization are widely encountered in point process applications. Modeling and analyzing such data are different from those for independent and identical short sequences, and the development of statistical methods requires careful consideration of the underlying dependence structure of the long single sequence. In this paper, we propose a semiparametric additive rate model for a modulated renewal process, and develop an estimating equation approach for the model parameters. The asymptotic properties of the resulting estimators are established by applying the limit theory for stationary mixing sequences. A block-based bootstrap procedure is presented for the variance estimation. Simulation studies are conducted to assess the finite-sample performance of the proposed estimators. An application to a data set from a cardiovascular mortality study is provided.     

A dependent Dirichlet process model for survival data with competing risks

In this paper, we first propose a dependent Dirichlet process (DDP) model using a mixture of Weibull models with each mixture component resembling a Cox model for survival data. We then build a Dirichlet process mixture model for competing risks data without regression covariates. Next we extend this model to a DDP model for competing risks regression data by using a multiplicative covariate effect on subdistribution hazards in the mixture components. Though built on proportional hazards (or subdistribution hazards) models, the proposed nonparametric Bayesian regression models do not require the assumption of constant hazard (or subdistribution hazard) ratio. An external time-dependent covariate is also considered in the survival model. After describing the model, we discuss how both cause-specific and subdistribution hazard ratios can be estimated from the same nonparametric Bayesian model for competing risks regression. For use with the regression models proposed, we introduce an omnibus prior that is suitable when little external information is available about covariate effects. Finally we compare the models’ performance with existing methods through simulations. We also illustrate the proposed competing risks regression model with data from a breast cancer study. An R package “DPWeibull” implementing all of the proposed methods is available at CRAN.

     

Nonparametric empirical Bayes for the Dirichlet process mixture model

The Dirichlet process prior allows flexible nonparametric mixture modeling. The number of mixture components is not specified in advance and can grow as new data arrive. However, analyses based on the Dirichlet process prior are sensitive to the choice of the parameters, including an infinite-dimensional distributional parameter G ₀. Most previous applications have either fixed G ₀ as a member of a parametric family or treated G ₀ in a Bayesian fashion, using parametric prior specifications. In contrast, we have developed an adaptive nonparametric method for constructing smooth estimates of G ₀. We combine this method with a technique for estimating α, the other Dirichlet process parameter, that is inspired by an existing characterization of its maximum-likelihood estimator. Together, these estimation procedures yield a flexible empirical Bayes treatment of Dirichlet process mixtures. Such a treatment is useful in situations where smooth point estimates of G ₀ are of intrinsic interest, or where the structure of G ₀ cannot be conveniently modeled with the usual parametric prior families. Analysis of simulated and real-world datasets illustrates the robustness of this approach.     

A tampered Brownian motion process model for partial step-stress accelerated life testing

In partial step-stress accelerated life testing, models extrapolating data obtained under more severe conditions to infer the lifetime distribution under normal use conditions are needed. Bhattacharyya (Invited paper for 46th session of the ISI, 1987) proposed a tampered Brownian motion process model and later derived the probability distribution from a decay process perspective without linear assumption. In this paper, the model is described and the features of the failure time distribution are discussed. The maximum likelihood estimates of the parameters in the model and their asymptotic properties are presented. An application of models for step-stress accelerated life test to fields other than engineering is described and illustrated by applying the tampered Brownian motion process model to data taken from a clinical trial.     

A new model and class of designs for mixture experiments with process variables

Experiments that involve the blending of several components are known as mixture experiments. In some mixture experiments, the response depends not only on the proportion of the mixture components, but also on the processing conditions, A new combined model is proposed which is based on Taylor series approximation and is intended to be a compromise between standard mixture models and standard response surface models. Cost and/or time constraints often limit the size of industrial experiments. With this in mind, we present a new class of designs that will accommodate the fitting of the new combined model.     

A geometric process warranty model using a combination policy

This paper proposes a geometric process warranty model. Assume that a combination policy (W, T) is applied after selling a product, so that a free warranty is offered in [0, W), followed by a pro-rata warranty in [W, T). Assume further the successive operating times (repair times) of the product form a decreasing (increasing) geometric process. The average cost rate of the product to the manufacturer and a consumer can be derived respectively. For exponential distribution case, the explicit formulas of the average cost rate are obtained, and an finite algorithm for determination of an optimal combination policy is suggested.     

A discrete-time risk model with Poisson ARCH claim-number process

Abstract

In this paper, we propose a discrete-time risk model with the claim number following an integer-valued autoregressive conditional heteroscedasticity (ARCH) process with Poisson deviates. In this model, the current claim number depends on the previous observations. Within this framework, the equation for finding the adjustment coefficient is derived. Numerical studies are also carried out to examine the impact of the Poisson ARCH dependence structure on the ruin probability.     

A semi-Markov decision model for the optimal control of a simple immigration-birth-death process through the introduction of a predator

ABSTRACT

This article is concerned with the problem of controlling a simple immigration-birth-death process, which represents a pest population, by the introduction of a predator in the habitat of the pests. The optimization criterion is the minimization of the expected long-run average cost per unit time. It is possible to construct an appropriate semi-Markov decision model with a finite set of states if and only if the difference between the per capita birth rate and the per capita death rate of the pests is smaller than half of the rate at which the predator is introduced in the habitat.     

Effect of reporting bias in the analysis of spontaneous reporting data

It is well‐known that a spontaneous reporting system suffers from significant under‐reporting of adverse drug reactions from the source population. The existing methods do not adjust for such under‐reporting for the calculation of measures of association between a drug and the adverse drug reaction under study. Often there is direct and/or indirect information on the reporting probabilities. This work incorporates the reporting probabilities into existing methodologies, specifically to Bayesian confidence propagation neural network and DuMouchel's empirical Bayesian methods, and shows how the two methods lead to biased results in the presence of under‐reporting. Considering all the cases to be reported, the association measure for the source population can be estimated by using only exposure information through a reference sample from the source population. Copyright © 2014 John Wiley & Sons, Ltd.     

An extended Gaussian max-stable process model for spatial extremes

The extremes of environmental processes are often of interest due to the damage that can be caused by extreme levels of the processes. These processes are often spatial in nature and modelling the extremes jointly at many locations can be important. In this paper, an extension of the Gaussian max-stable process is developed, enabling data from a number of locations to be modelled under a more flexible framework than in previous applications. The model is applied to annual maximum rainfall data from five sites in South-West England. For estimation we employ a pairwise likelihood within a Bayesian analysis, incorporating informative prior information.     

Study of a Markov model for a high-quality dependent process

For high-quality processes, non-conforming items are seldom observed and the traditional p (or np) charts are not suitable for monitoring the state of the process. A type of chart based on the count of cumulative conforming items has recently been introduced and it is especially useful for automatically collected one-at-a-time data. However, in such a case, it is common that the process characteristics become dependent as items produced one after another are inspected. In this paper, we study the problem of process monitoring when the process is of high quality and measurement values possess a certain serial dependence. The problem of assuming independence is examined and a Markov model for this type of process is studied, upon which suitable control procedures can be developed.     

Semiparametric inference for the recurrent events process by means of a single-index model

In this paper, we introduce new parametric and semiparametric regression techniques for a recurrent event process subject to random right censoring. We develop models for the cumulative mean function and provide asymptotically normal estimators. Our semiparametric model which relies on a single-index assumption can be seen as a dimension reduction technique that, contrary to a fully nonparametric approach, is not stroke by the curse of dimensionality when the number of covariates is high. We discuss data-driven techniques to choose the parameters involved in the estimation procedures and provide a simulation study to support our theoretical results.     

A grouped beta process model for multivariate resting‐state EEG microstate analysis on twins

EEG microstate analysis investigates the collection of distinct temporal blocks that characterize the electrical activity of the brain. Brain activity within each microstate is stable, but activity switches rapidly between different microstates in a nonrandom way. We propose a Bayesian nonparametric model that concurrently estimates the number of microstates and their underlying behaviour. We use a Markov switching vector autoregressive (VAR) framework, where a hidden Markov model (HMM) controls the nonrandom state switching dynamics of the EEG activity and a VAR model defines the behaviour of all time points within a given state. We analyze the resting‐state EEG data from twin pairs collected through the Minnesota Twin Family Study, consisting of 70 epochs per participant, where each epoch corresponds to 2 s of EEG data. We fit our model at the twin pair level, sharing information within epochs from the same participant and within epochs from the same twin pair. We capture within twin‐pair similarity, using an Indian buffet process, to consider an infinite library of microstates, allowing each participant to select a finite number of states from this library. The state spaces of highly similar twins may completely overlap while dissimilar twins could select distinct state spaces. In this way, our Bayesian nonparametric model defines a sparse set of states that describe the EEG data. All epochs from a single participant use the same set of states and are assumed to adhere to the same state switching dynamics in the HMM model, enforcing within‐participant similarity.     

Empirical likelihood inference for semiparametric model with linear process errors

The purpose of this article is to use the empirical likelihood method to study the confidence regions construction for the parameters of interest in semiparametric model with linear process errors under martingale difference. It is shown that the adjusted empirical log-likelihood ratio at the true parameters is asymptotically chi-squared. A simulation study indicates that the adjusted empirical likelihood works better than a normal approximation-based approach.     

Specification test for a linear regression model with ARCH process

ARCH models are used widely in analyzing economic and financial time series data. Many tests are available to detect the presence of ARCH; however, there is no acceptable procedure available for testing an estimated ARCH model.. In this paper we develop a test for a linear regression model with ARCH disturbances using the framework of the information matrix (IM) test. For the ARCH specification, the covariance matrix of the indicator vector is not block diagonal, and the IM test is turned out to be a test for variation in the fourth moment, i.e., a test for heterokurtosis. An illustrative example is provided to demonstrate the usefulness of the proposed test.     

Cascade model with Dirichlet process for analyzing multiple dyadic matrices

Dyadic matrices are natural data representations in a wide range of domains. A dyadic matrix often involves two types of abstract objects and is based on observations of pairs of elements with one element from each object. Owing to the increasing needs from practical applications, dyadic data analysis has recently attracted increasing attention and many techniques have been developed. However, most existing approaches, such as co-clustering and relational reasoning, only handle a single dyadic table and lack flexibility to perform prediction using multiple dyadic matrices. In this article, we propose a general nonparametric Bayesian framework with a cascaded structure to model multiple dyadic matrices and then describe an efficient hybrid Gibbs sampling algorithm for posterior inference and analysis. Empirical evaluations using both synthetic data and real data show that the proposed model captures the hidden structure of data and generalizes the predictive inference in a unique way.