Likelihood Inference for Unions of Interacting Discs

Abstract. This is probably the first paper which discusses likelihood inference for a random set using a germ‐grain model, where the individual grains are unobservable, edge effects occur and other complications appear. We consider the case where the grains form a disc process modelled by a marked point process, where the germs are the centres and the marks are the associated radii of the discs. We propose to use a recent parametric class of interacting disc process models, where the minimal sufficient statistic depends on various geometric properties of the random set, and the density is specified with respect to a given marked Poisson model (i.e. a Boolean model). We show how edge effects and other complications can be handled by considering a certain conditional likelihood. Our methodology is illustrated by analysing Peter Diggle's heather data set, where we discuss the results of simulation‐based maximum likelihood inference and the effect of specifying different reference Poisson models.     

Inference for Observations of Integrated Diffusion Processes

Abstract.  Estimation of parameters in diffusion models is investigated when the observations are integrals over intervals of the process with respect to some weight function. This type of observations can, for example, be obtained when the process is observed after passage through an electronic filter. Another example is provided by the ice-core data on oxygen isotopes used to investigate paleo-temperatures. Finally, such data play a role in connection with the stochastic volatility models of finance. The integrated process is not a Markov process. Therefore, prediction-based estimating functions are applied to estimate parameters in the underlying diffusion model. The estimators are shown to be consistent and asymptotically normal. The theory developed in the paper also applies to integrals of processes other than diffusions. The method is applied to inference based on integrated data from Ornstein–Uhlenbeck processes and from the Cox–Ingersoll–Ross model, for both of which an explicit optimal estimating function is found.     

Accelerated Degradation Models for Failure Based on Geometric Brownian Motion and Gamma Processes

Based on a generalized cumulative damage approach with a stochastic process describing degradation, new accelerated life test models are presented in which both observed failures and degradation measures can be considered for parametric inference of system lifetime. Incorporating an accelerated test variable, we provide several new accelerated degradation models for failure based on the geometric Brownian motion or gamma process. It is shown that in most cases, our models for failure can be approximated closely by accelerated test versions of Birnbaum–Saunders and inverse Gaussian distributions. Estimation of model parameters and a model selection procedure are discussed, and two illustrative examples using real data for carbon-film resistors and fatigue crack size are presented.     

Predicting future discoveries of European marine species by using a non-homogeneous renewal process

Summary.  Predicting future rates of species discovery and the number of species remaining are important in efforts to preserve biodiversity, discussions on the rate of species extinction and comparisons on the state of knowledge of animals and plants of different taxa. Data on discovery dates of species in 32 European marine taxa are analysed by using a class of thinned temporal renewal process models. These models allow for both underdispersion and overdispersion with respect to the non-homogeneous Poisson process. An approach for implementing Bayesian inference for these models is described that uses Markov chain Monte Carlo simulation and that is applicable to other types of thinned process. Predictions are made on the number of species remaining to be discovered in each taxon.     

Modelling Aggregation on the Large Scale and Regularity on the Small Scale in Spatial Point Pattern Datasets

We consider a dependent thinning of a regular point process with the aim of obtaining aggregation on the large scale and regularity on the small scale in the resulting target point process of retained points. Various parametric models for the underlying processes are suggested and the properties of the target point process are studied. Simulation and inference procedures are discussed when a realization of the target point process is observed, depending on whether the thinned points are observed or not. The paper extends previous work by Dietrich Stoyan on interrupted point processes.     

Simulating Correlated Marked-point Processes

The area of marked-point processes is well developed but simulation is still a challenging problem when mark correlations are to be included. In this paper we propose the use of simulated annealing to incorporate the spatial mark correlation into the simulations of correlated marked-point processes. Such a simulation has wide applications in areas such as inference and goodness-of-fit investigations of proposed models. The technique is applied to a forest dataset for which the results are extremely encouraging.     

Bayesian Semiparametric Modelling in Quantile Regression

Abstract. We propose a Bayesian semiparametric methodology for quantile regression modelling. In particular, working with parametric quantile regression functions, we develop Dirichlet process mixture models for the error distribution in an additive quantile regression formulation. The proposed non‐parametric prior probability models allow the shape of the error density to adapt to the data and thus provide more reliable predictive inference than models based on parametric error distributions. We consider extensions to quantile regression for data sets that include censored observations. Moreover, we employ dependent Dirichlet processes to develop quantile regression models that allow the error distribution to change non‐parametrically with the covariates. Posterior inference is implemented using Markov chain Monte Carlo methods. We assess and compare the performance of our models using both simulated and real data sets.     

A hierarchical point process with application to storm cell modelling

In environmetrics, interest often centres around the development of models and methods for making inference on observed point patterns assumed to be generated by latent spatial or spatio‐temporal processes, which may have a hierarchical structure. In this research, motivated by the analysis of spatio‐temporal storm cell data, we generalize the Neyman–Scott parent–child process to account for hierarchical clustering. This is accomplished by allowing the parents to follow a log‐Gaussian Cox process thereby incorporating correlation and facilitating inference at all levels of the hierarchy. This approach is applied to monthly storm cell data from the Bismarck, North Dakota radar station from April through August 2003 and we compare these results to simpler cluster processes to demonstrate the advantages of accounting for both levels of correlation present in these hierarchically clustered point patterns. The Canadian Journal of Statistics 47: 46–64; 2019 © 2019 Statistical Society of Canada     

Functional Autoregression for Sparsely Sampled Data

We develop a hierarchical Gaussian process model for forecasting and inference of functional time series data. Unlike existing methods, our approach is especially suited for sparsely or irregularly sampled curves and for curves sampled with nonnegligible measurement error. The latent process is dynamically modeled as a functional autoregression (FAR) with Gaussian process innovations. We propose a fully nonparametric dynamic functional factor model for the dynamic innovation process, with broader applicability and improved computational efficiency over standard Gaussian process models. We prove finite-sample forecasting and interpolation optimality properties of the proposed model, which remain valid with the Gaussian assumption relaxed. An efficient Gibbs sampling algorithm is developed for estimation, inference, and forecasting, with extensions for FAR(p) models with model averaging over the lag p. Extensive simulations demonstrate substantial improvements in forecasting performance and recovery of the autoregressive surface over competing methods, especially under sparse designs. We apply the proposed methods to forecast nominal and real yield curves using daily U.S. data. Real yields are observed more sparsely than nominal yields, yet the proposed methods are highly competitive in both settings. Supplementary materials, including R code and the yield curve data, are available online.     

A method for combining inference across related nonparametric Bayesian models

Summary.  We consider the problem of combining inference in related nonparametric Bayes models. Analogous to parametric hierarchical models, the hierarchical extension formalizes borrowing strength across the related submodels. In the nonparametric context, modelling is complicated by the fact that the random quantities over which we define the hierarchy are infinite dimensional. We discuss a formal definition of such a hierarchical model. The approach includes a regression at the level of the nonparametric model. For the special case of Dirichlet process mixtures, we develop a Markov chain Monte Carlo scheme to allow efficient implementation of full posterior inference in the given model.     

Bayesian Semiparametric Regression for Median Residual Life

Abstract.  With survival data there is often interest not only in the survival time distribution but also in the residual survival time distribution. In fact, regression models to explain residual survival time might be desired. Building upon recent work of Kottas & Gelfand [ J. Amer. Statist. Assoc. 96 (2001) 1458], we formulate a semiparametric median residual life regression model induced by a semiparametric accelerated failure time regression model. We utilize a Bayesian approach which allows full and exact inference. Classical work essentially ignores covariates and is either based upon parametric assumptions or is limited to asymptotic inference in non-parametric settings. No regression modelling of median residual life appears to exist. The Bayesian modelling is developed through Dirichlet process mixing. The models are fitted using Gibbs sampling. Residual life inference is implemented extending the approach of Gelfand & Kottas [ J. Comput. Graph. Statist. 11 (2002) 289]. Finally, we present a fairly detailed analysis of a set of survival times with moderate censoring for patients with small cell lung cancer.     

Bayesian inference for a partially observed birth–death process using data on proportions

Stochastic kinetic models are often used to describe complex biological processes. Typically these models are analytically intractable and have unknown parameters which need to be estimated from observed data. Ideally we would have measurements on all interacting chemical species in the process, observed continuously in time. However, in practice, measurements are taken only at a relatively few time‐points. In some situations, only very limited observation of the process is available, for example settings in which experimenters can only observe noisy observations on the proportion of cells that are alive. This makes the inference task even more problematic. We consider a range of data‐poor scenarios and investigate the performance of various computationally intensive Bayesian algorithms in determining the posterior distribution using data on proportions from a simple birth‐death process.     

大数据背景下网络调查样本的建模推断问题研究——以广义Boosted模型的倾向得分推断为例

随着大数据和网络的不断发展,网络调查越来越广泛,大部分网络调查样本属于非概率样本,难以采用传统的抽样推断理论进行推断,如何解决网络调查样本的推断问题是大数据背景下网络调查发展的迫切需求。本文首次从建模的角度提出了解决该问题的基本思路：一是入样概率的建模推断,可以考虑构建基于机器学习与变量选择的倾向得分模型来估计入样概率推断总体;二是目标变量的建模推断,可以考虑直接对目标变量建立参数、非参数或半参数超总体模型进行估计;三是入样概率与目标变量的双重建模推断,可以考虑进行倾向得分模型与超总体模型的加权估计与混合推断。最后,以基于广义Boosted模型的入样概率建模推断为例演示了具体解决方法。     

On the foundations: Statistical models and inference

This paper presents an overview of some recent results concerning statistical models and inference. specifically: grounds for statistical models. types of models that simplify by standard probability analysis, the use of categorical information in the reduction of the model with data, and the role of additives in the inference process. The relevant technical material has been developed elsewhere.     

基于MCMC稳态模拟的异质性经济增长模型研究

 针对同质性增长模型无法描述各个经济体经济增长存在的异质性现象,提出了一类基于MCMC稳态模拟的异质性经济增长模型,它可以用来描述经济增长的异质性以及政策变量的差异影响。由于模型参数的后验条件分布没有确定的分布形式,通过数据扩充得到参数的完全条件分布从而实现模型参数的贝叶斯估计。对改革开放以来我国各省市区经济增长收敛性进行分析发现大规模股份制改革前经济增长具有同质性而大规模股份制改革后经济增长具有异质性,且可以用新古典经济增长理论来解释各地区经济的发展状况。     

Inference from Accelerated Degradation and Failure Data Based on Gaussian Process Models

An important problem in reliability and survival analysis is that of modeling degradation together with any observed failures in a life test. Here, based on a continuous cumulative damage approach with a Gaussian process describing degradation, a general accelerated test model is presented in which failure times and degradation measures can be combined for inference about system lifetime. Some specific models when the drift of the Gaussian process depends on the acceleration variable are discussed in detail. Illustrative examples using simulated data as well as degradation data observed in carbon-film resistors are presented.     

Hybrid Bayesian inference on HIV viral dynamic models

Modelling of HIV dynamics in AIDS research has greatly improved our understanding of the pathogenesis of HIV-1 infection and guided for the treatment of AIDS patients and evaluation of antiretroviral therapies. Some of the model parameters may have practical meanings with prior knowledge available, but others might not have prior knowledge. Incorporating priors can improve the statistical inference. Although there have been extensive Bayesian and frequentist estimation methods for the viral dynamic models, little work has been done on making simultaneous inference about the Bayesian and frequentist parameters. In this article, we propose a hybrid Bayesian inference approach for viral dynamic nonlinear mixed-effects models using the Bayesian frequentist hybrid theory developed in Yuan [Bayesian frequentist hybrid inference, Ann. Statist. 37 (2009), pp. 2458–2501]. Compared with frequentist inference in a real example and two simulation examples, the hybrid Bayesian approach is able to improve the inference accuracy without compromising the computational load.     

Gaussian models for degradation processes-part I: Methods for the analysis of biomarker data

We present two stochastic models that describe the relationship between biomarker process values at random time points, event times, and a vector of covariates. In both models the biomarker processes are degradation processes that represent the decay of systems over time. In the first model the biomarker process is a Wiener process whose drift is a function of the covariate vector. In the second model the biomarker process is taken to be the difference between a stationary Gaussian process and a time drift whose drift parameter is a function of the covariates. For both models we present statistical methods for estimation of the regression coefficients. The first model is useful for predicting the residual time from study entry to the time a critical boundary is reached while the second model is useful for predicting the latency time from the infection until the time the presence of the infection is detected. We present our methods principally in the context of conducting inference in a population of HIV infected individuals.     

On the Performance of Popular Unit-Root Tests Against Various Nonlinear Dynamic Models: A Simulation Study

ABSTRACT

There is a widespread perception that standard unit-root tests have poor discriminatory power when they are applied to time series with nonlinear dynamics. Via Monte Carlo simulations this study re-examines the finite sample properties of selected univariate tests for unit-root and stationarity under a broad class of nonlinear dynamic models. Our simulation experiments produce a couple of interesting findings. First, performance of tests is driven by the degree of underlying persistence rather than the nonlinear dynamics per se. Tests under study exhibit reasonable performance for nonlinear models with mild persistence, while the accuracy of inference deteriorates substantially when the models are highly persistent regardless of the linearity. Second, when it comes to deciding which one to identify first between linearity and stationarity, our results suggest to conduct linearity test first to enhance the reliability of test inference.     

Brownian motion simulation: a quantization approach

In this article we suggest a new simulation method for the Wiener process. The main idea is to use functional quantization theory and the decomposition of the Wiener process by Brownian bridges to construct a suitable approximation of the Brownian motion.