Adaptive approximate Bayesian computation for complex models

We propose a new approximate Bayesian computation (ABC) algorithm that aims at minimizing the number of model runs for reaching a given quality of the posterior approximation. This algorithm automatically determines its sequence of tolerance levels and makes use of an easily interpretable stopping criterion. Moreover, it avoids the problem of particle duplication found when using a MCMC kernel. When applied to a toy example and to a complex social model, our algorithm is 2–8 times faster than the three main sequential ABC algorithms currently available.     

Kalman filtering on approximate state-space models

Several state-space models for estimating a second-order stochastic process are proposed in this paper on the basis of the approximate Karhunen-Loève expansion. Properties of these models are studied and then the Kalman filtering method is applied. The accuracy of the models on the basis of two different situations, deterministic or random inputs, is studied by means of a simulation of a Brownian motion.This work was supported in part by DGICYT, Project No. PS93-0201.     

Bayesian estimation and inference for log-ACD models

This paper adapts Bayesian Markov chain Monte Carlo methods for application to some auto-regressive conditional duration models. Subsequently, the properties of these estimators are examined and assessed across a range of possible conditional error distributions and dynamic specifications, including under error mis-specification. A novel model error distribution, employing a truncated skewed Student-t distribution is proposed and the Bayesian estimator assessed for it. The results of an extensive simulation study reveal that favourable estimation properties are achieved under a range of possible error distributions, but that the generalised gamma distribution assumption is most robust and best preserves these properties, including when it is incorrectly specified. The results indicate that the powerful numerical methods underlying the Bayesian estimator allow more efficiency than the (quasi-) maximum likelihood estimator for the cases considered.     

动态异方差随机前沿模型的Bayesian推断

随机前沿模型中如果忽略单边干扰项的异质性(heterogeneity)往往导致错误的效率估计.从个体特征的影响和方差的时变性两方面对单边干扰项进行考虑,提出异方差动态随机前沿模型.利用Gibbs抽样方法对动态异方差随机前沿模型进行Bayesian分析.导出了模型参数的后验条件分布,对中小样本的模拟实验显示在最小后验均方误差准则下得到的参数估计值非常接近真值.对电力公司的实际数据进行分析显示对数无效率项的方差有一定的时变性.     

An efficient approximate solution for stochastic Lanchester models

Combat modeling is one of the essential topics for military decision making. The Lanchester equation is a classic method for modeling warfare, and many variations have extended its limitations and relaxed its assumptions. As a model becomes more complex, solving it analytically becomes intractable or computationally expensive. Hence, we propose two approximation methods: moment-matching scheme and a supporting method called battle-end approximation. These methods give an approximate solution in a short amount of time, while maintaining a high level of accuracy in simulation results in terms of hypothesis testing and numerical verification. They can be applied to computationally intensive problems, such as optimal resource allocation and analysis with asymmetric power like snipers or stealth aircrafts.     

Bayesian inference for dependent elliptical measurement error models

In this article we provide a Bayesian analysis for dependent elliptical measurement error models considering nondifferential and differential errors. In both cases we compute posterior distributions for structural parameters by using squared radial prior distributions for the precision parameters. The main result is that the posterior distribution of location parameters, for specific priors, is invariant with respect to changes in the generator function, in agreement with previous results obtained in the literature under different assumptions. Finally, although the results obtained are valid for any elliptical distribution for the error term, we illustrate those results by using the student-t distribution and a real data set.     

Statistical inference for the index parameter in single-index models

In this paper, we are concerned with statistical inference for the index parameter in the single-index model . Based on the estimates obtained by the local linear method, we extend the generalized likelihood ratio test to the single-index model. We investigate the asymptotic behaviour of the proposed test and demonstrate that its limiting null distribution follows a χ²-distribution, with the scale constant and the number of degrees of freedom being independent of nuisance parameters or functions, which is called the Wilks phenomenon. A simulated example is used to illustrate the performance of the testing approach.     

潜伏期变化的随机流行病模型及其贝叶斯推断

本文讨论了潜伏期和传染期均服从威布尔分布、易感性随机变化的一类随机流行病模型,并利用M CM C算法对潜伏期、传染期的参数和易感性的超参数作了贝叶期推断.这种分析方法比以往各种方法更适用于各类疾病.     

Some remarks on Bayesian inference for one-way ANOVA models

We consider the standard one-way ANOVA model; it is well-known that classical statistical procedures are based on a scalar non-centrality parameter. In this paper we explore both marginal likelihood and integrated likelihood functions for this parameter and we show that they exactly lead to the same answer. On the other hand, we prove that a fully Bayesian testing procedure may provide different conclusions, depending on what is considered to be the real quantity of interest in the model or, said differently, which are the competing hypotheses. We illustrate these issues via a real data example.     

Spatially varying SAR models and Bayesian inference for high-resolution lattice data

We discuss a new class of spatially varying, simultaneous autoregressive (SVSAR) models motivated by interests in flexible, non-stationary spatial modelling scalable to higher dimensions. SVSAR models are hierarchical Markov random fields extending traditional SAR models. We develop Bayesian analysis using Markov chain Monte Carlo methods of SVSAR models, with extensions to spatio-temporal contexts to address problems of data assimilation in computer models. A motivating application in atmospheric science concerns global CO emissions where prediction from computer models is assessed and refined based on high-resolution global satellite imagery data. Application to synthetic and real CO data sets demonstrates the potential of SVSAR models in flexibly representing inhomogeneous spatial processes on lattices, and their ability to improve estimation and prediction of spatial fields. The SVSAR approach is computationally attractive in even very large problems; computational efficiencies are enabled by exploiting sparsity of high-dimensional precision matrices.     

Bayesian networks for mathematical models: Techniques for automatic construction and efficient inference

Expert knowledge in the form of mathematical models can be considered sufficient statistics of all prior experimentation in the domain, embodying generic or abstract knowledge of it. When used in a probabilistic framework, such models provide a sound foundation for data mining, inference, and decision making under uncertainty.We describe a methodology for encapsulating knowledge in the form of ordinary differential equations (ODEs) in dynamic Bayesian networks (DBNs). The resulting DBN framework can handle both data and model uncertainty in a principled manner, can be used for temporal data mining with noisy and missing data, and can be used to re-estimate model parameters automatically using data streams. A standard assumption when performing inference in DBNs is that time steps are fixed. Generally, the time step chosen is small enough to capture the dynamics of the most rapidly changing variable. This can result in DBNs having a natural time step that is very short, leading to inefficient inference; this is particularly an issue for DBNs derived from ODEs and for systems where the dynamics are not uniform over time.We propose an alternative to the fixed time step inference used in standard DBNs. In our algorithm, the DBN automatically adapts the time step lengths to suit the dynamics in each step. The resulting system allows us to efficiently infer probable values of hidden variables using multiple time series of evidence, some of which may be sparse, noisy or incomplete.We evaluate our approach with a DBN based on a variant of the van der Pol oscillator, and demonstrate an example where it gives more accurate results than the standard approach, but using only one tenth the number of time steps.We also apply our approach to a real-world example in critical care medicine. By incorporating knowledge in the form of an existing ODE model, we have built a DBN framework for efficiently predicting individualised patient responses using the available bedside and lab data.     

Bayesian inference in spherical linear models: robustness and conjugate analysis

The early work of Zellner on the multivariate Student-t linear model has been extended to Bayesian inference for linear models with dependent non-normal error terms, particularly through various papers by Osiewalski, Steel and coworkers. This article provides a full Bayesian analysis for a spherical linear model. The density generator of the spherical distribution is here allowed to depend both on the precision parameter φ and on the regression coefficients β. Another distinctive aspect of this paper is that proper priors for the precision parameter are discussed.The normal-chi-squared family of prior distributions is extended to a new class, which allows the posterior analysis to be carried out analytically. On the other hand, a direct joint modelling of the data vector and of the parameters leads to conjugate distributions for the regression and the precision parameters, both individually and jointly. It is shown that some model specifications lead to Bayes estimators that do not depend on the choice of the density generator, in agreement with previous results obtained in the literature under different assumptions. Finally, the distribution theory developed to tackle the main problem is useful on its own right.     

Simulated likelihood inference for stochastic volatility models using continuous particle filtering

Discrete-time stochastic volatility (SV) models have generated a considerable literature in financial econometrics. However, carrying out inference for these models is a difficult task and often relies on carefully customized Markov chain Monte Carlo techniques. Our contribution here is twofold. First, we propose a new SV model, namely SV–GARCH, which bridges the gap between SV and GARCH models: it has the attractive feature of inheriting unconditional properties similar to the standard GARCH model but being conditionally heavier tailed. Second, we propose a likelihood-based inference technique for a large class of SV models relying on the recently introduced continuous particle filter. The approach is robust and simple to implement. The technique is applied to daily returns data for S&P 500 and Dow Jones stock price indices for various spans.     

Classical and Bayesian inference in two parameter exponential distribution with randomly censored data

This paper deal with the classical and Bayesian estimation for two parameter exponential distribution having scale and location parameters with randomly censored data. The censoring time is also assumed to follow a two parameter exponential distribution with different scale but same location parameter. The main stress is on the location parameter in this paper. This parameter has not yet been studied with random censoring in literature. Fitting and using exponential distribution on the range \((0, \infty )\), specially when the minimum observation in the data set is significantly large, will give estimates far from accurate. First we obtain the maximum likelihood estimates of the unknown parameters with their variances and asymptotic confidence intervals. Some other classical methods of estimation such as method of moment, L-moments and least squares are also employed. Next, we discuss the Bayesian estimation of the unknown parameters using Gibbs sampling procedures under generalized entropy loss function with inverted gamma priors and Highest Posterior Density credible intervals. We also consider some reliability and experimental characteristics and their estimates. A Monte Carlo simulation study is performed to compare the proposed estimates. Two real data examples are given to illustrate the importance of the location parameter.     

An alternative to EM for Gaussian mixture models: batch and stochastic Riemannian optimization

Mathematical Programming - We consider maximum likelihood estimation for Gaussian Mixture Models (Gmm s). This task is almost invariably solved (in theory and practice) via the Expectation...     

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.      

Asymptotic inference for stochastic processes

This is a survey of some aspects of large-sample inference for stochastic processes. A unified framework is used to study the asymptotic properties of tests and estimators parameters in discrete-time, continuous-time jump-type, and diffusion processes. Two broad families of processes, viz, ergodic and non-ergodic type are introduced and the qualitative differences in the asymptotic results for the two families are discussed and illustrated with several examples. Some results on estimation and testing via Bayesian, nonparametric, and sequential methods are also surveyed briefly.     

EM algorithm for stochastic hybrid systems

Statistical Inference for Stochastic Processes - A stochastic hybrid system, also known as a switching diffusion, is a continuous-time Markov process with state space consisting of discrete and...