Transdimensional approximate Bayesian computation for inference on invasive species models with latent variables of unknown dimension

Accurate information on patterns of introduction and spread of non-native species is essential for making predictions and management decisions. In many cases, estimating unknown rates of introduction and spread from observed data requires evaluating intractable variable-dimensional integrals. In general, inference on the large class of models containing latent variables of large or variable dimension precludes the use of exact sampling techniques. Approximate Bayesian computation (ABC) methods provide an alternative to exact sampling but rely on inefficient conditional simulation of the latent variables. To accomplish this task efficiently, a new transdimensional Monte Carlo sampler is developed for approximate Bayesian model inference and used to estimate rates of introduction and spread for the non-native earthworm species Dendrobaena octaedra (Savigny) along roads in the boreal forest of northern Alberta. Using low and high estimates of introduction and spread rates, the extent of earthworm invasions in northeastern Alberta is simulated to project the proportion of suitable habitat invaded in the year following data collection.     

Bayesian analysis of the patterns of biological susceptibility via reversible jump MCMC sampling

In some biological experiments, it is quite common that laboratory subjects differ in their patterns of susceptibility to a treatment. Finite mixture models are useful in those situations. In this paper we model the number of components and the component parameters jointly, and base inference about these quantities on their posterior probabilities, making use of the reversible jump Markov chain Monte Carlo methods. In particular, we apply the methodology to the analysis of univariate normal mixtures with multidimensional parameters, using a hierarchical prior model that allows weak priors while avoiding improper priors in the mixture context. The practical significance of the proposed method is illustrated with a dose-response data set.     

Choice of B-splines with free parameters in the flexible discriminant analysis context

Flexible discriminant analysis (FDA) is a general methodology which aims at providing tools for multigroup non linear classification. It consists in a nonparametric version of discriminant analysis by replacing linear regression by any nonparametric regression method. A new option for FDA, consisting in a nonparametric regression method based on B-spline functions, will be introduced. The relevance of the transformation (hence the discrimination) depends on the parameters defining the spline functions: degree, number and location of the knots for each continuous variable. This method called FDA-FKBS (Free Knot B-Splines) allows to determine all these parameters without the necessity of many prior parameters. It is inspired by Reversible Jumps Monte Carlo Markov Chains but the objective function is different and the Bayesian aspect is put aside.     

基于标值点过程的遥感影像道路网络提取

针对高分辨率遥感影像道路网络的特点,采用基于贝叶斯理论的全自动方法从遥感影像中提取道路.根据道路的局部和全局特征,使用标值点过程对道路建模,采用结合可逆跳跃马尔可夫链蒙特卡罗算法的模拟退火算法优化求得全局最优解.提出新的预处理方法得到道路的位置和方向信息,提出基于预处理的生灭转移核以降低算法的搜索空间,提出基于连接的移动转移核以加快算法的收敛速度.实验结果表明.该方法可以快速、有效地从不同的遥感影像(光学、SAR)提取道路网络.     

Generalized spatial dynamic factor models

This paper introduces a new class of spatio-temporal models for measurements belonging to the exponential family of distributions. In this new class, the spatial and temporal components are conditionally independently modeled via a latent factor analysis structure for the (canonical) transformation of the measurements mean function. The factor loadings matrix is responsible for modeling spatial variation, while the common factors are responsible for modeling the temporal variation. One of the main advantages of our model with spatially structured loadings is the possibility of detecting similar regions associated to distinct dynamic factors. We also show that the new class outperforms a large class of spatial-temporal models that are commonly used in the literature. Posterior inference for fixed parameters and dynamic latent factors is performed via a custom tailored Markov chain Monte Carlo scheme for multivariate dynamic systems that combines extended Kalman filter-based Metropolis-Hastings proposal densities with block-sampling schemes. Factor model uncertainty is also fully addressed by a reversible jump Markov chain Monte Carlo algorithm designed to learn about the number of common factors. Three applications, two based on synthetic Gamma and Bernoulli data and one based on real Bernoulli data, are presented in order to illustrate the flexibility and generality of the new class of models, as well as to discuss features of the proposed MCMC algorithm.     

基于RJMCMC的视觉多目标跟踪算法

研究了基于MCMC的多目标跟踪算法。针对MCMC迭代过程中抽样置信度低以及不能进行有效迭代的问题,提出一种新的基于RJMCMC的视觉多目标跟踪算法。给定观测量,将跟踪问题建模为状态量的最大后验估计(MAP)、关于MAP的先验与似然的估计。借助匹配阵给出了目标先验建议分布,设计了4种马氏链可逆运动方式;似然度量采用随空间加权的颜色直方图匹配衡量。MCMC抽样过程中的状态由MS迭代产生,而不是随机走生成。基于似然度量导出了MS迭代式。实验结果及定量分析评估结果说明了本算法的有效性。     

Comparison of nonnested asymmetric heteroskedastic models

The GJR-GARCH model is a popular choice among nonlinear models of the well-known asymmetric volatility phenomenon in financial market data. However, recent work employs double threshold nonlinear models to capture both mean and volatility asymmetry. A Bayesian model comparison procedure is proposed to compare the GJR-GARCH with various double threshold GARCH specifications, by designing a reversible jump Markov chain Monte Carlo algorithm. A simulation experiment illustrates good performance in estimation and model selection over reasonable sample sizes. In a study of seven markets strong evidence is found that the DTGARCH, with US market news as threshold variable, outperforms the GJR-GARCH and traditional self-exciting DTGARCH models. This result was consistent across six markets, excluding Canada.     

Some exact tests for manifest properties of latent trait models

Item response theory is one of the modern test theories with applications in educational and psychological testing. Recent developments made it possible to characterize some desired properties in terms of a collection of manifest ones, so that hypothesis tests on these traits can, in principle, be performed. But the existing test methodology is based on asymptotic approximation, which is impractical in most applications since the required sample sizes are often unrealistically huge. To overcome this problem, a class of tests is proposed for making exact statistical inference about four manifest properties: covariances given the sum are non-positive (CSN), manifest monotonicity (MM), conditional association (CA), and vanishing conditional dependence (VCD). One major advantage is that these exact tests do not require large sample sizes. As a result, tests for CSN and MM can be routinely performed in empirical studies. For testing CA and VCD, the exact methods are still impractical in most applications, due to the unusually large number of parameters to be tested. However, exact methods are still derived for them as an exploration toward practicality. Some numerical examples with applications of the exact tests for CSN and MM are provided.     

Parallel Bayesian inference of range and reflectance from LaDAR profiles

Bayesian analysis using reversible jump Markov chain Monte Carlo (RJMCMC) algorithms improves the measurement accuracy, resolution and sensitivity of full waveform laser detection and ranging (LaDAR), but at a significant computational cost. Parallel processing has the potential to significantly reduce the processing time, but although there have been several strategies for Markov chain Monte Carlo (MCMC) parallelization, adaptation of these strategies to RJMCMC may degrade parallel performance.     

Automatic glottal inverse filtering with the Markov chain Monte Carlo method

This paper presents a new glottal inverse filtering (GIF) method that utilizes a Markov chain Monte Carlo (MCMC) algorithm. First, initial estimates of the vocal tract and glottal flow are evaluated by an existing GIF method, iterative adaptive inverse filtering (IAIF). Simultaneously, the initially estimated glottal flow is synthesized using the Rosenberg–Klatt (RK) model and filtered with the estimated vocal tract filter to create a synthetic speech frame. In the MCMC estimation process, the first few poles of the initial vocal tract model and the RK excitation parameter are refined in order to minimize the error between the synthetic and original speech signals in the time and frequency domain. MCMC approximates the posterior distribution of the parameters, and the final estimate of the vocal tract is found by averaging the parameter values of the Markov chain. Experiments with synthetic vowels produced by a physical modeling approach show that the MCMC-based GIF method gives more accurate results compared to two known reference methods.     

Improved MCMC sampling methods for estimating weighted sums in Winnow with application to DNF learning

A Markov chain Monte Carlo method has previously been introduced to estimate weighted sums in multiplicative weight update algorithms when the number of inputs is exponential. However, the original algorithm still required extensive simulation of the Markov chain in order to get accurate estimates of the weighted sums. We propose an optimized version of the original algorithm that produces exactly the same classifications while often using fewer Markov chain simulations. We also apply three other sampling techniques and empirically compare them with the original Metropolis sampler to determine how effective each is in drawing good samples in the least amount of time, in terms of accuracy of weighted sum estimates and in terms of Winnow’s prediction accuracy. We found that two other samplers (Gibbs and Metropolized Gibbs) were slightly better than Metropolis in their estimates of the weighted sums. For prediction errors, there is little difference between any pair of MCMC techniques we tested. Also, on the data sets we tested, we discovered that all approximations of Winnow have no disadvantage when compared to brute force Winnow (where weighted sums are exactly computed), so generalization accuracy is not compromised by our approximation. This is true even when very small sample sizes and mixing times are used. An early version of this paper appeared as Tao and Scott (2003).     

A unified Bayesian inference on treatment means with order constraints

In some applications involving comparison of treatment means, it is known a priori that population means are ordered in a certain way. In such situations, imposing constraints on the treatment means can greatly increase the effectiveness of statistical procedures.This paper proposes a unified Bayesian method which performs a simultaneous comparison of treatment means and parameter estimation in ANOVA models with order constraints on the means. A continuous prior restricted to order constraints is employed, and posterior samples of parameters are generated using a Markov chain Monte Carlo method. Posterior probabilities of all possible hypotheses on the equality/inequality of treatment means are obtained using Savage-Dickey density ratios, for which we propose a simple and computationally efficient estimation method. Posterior densities and HPD intervals of parameters of interest are estimated with almost no extra cost, given some by-products from the test procedure.Simulation study results show that the proposed method outperforms the test without constraints and that the method is powerful in detecting the true hypothesis. The method is applied to the ramus bone sizes of 20 boys, which were measured at four time points. The proposed Bayesian test reveals that there are two growth spurts in the ramus bone size during the observed period, which could not be detected by pairwise comparisons of the means.     

基于标值点过程改进的遥感道路提取新算法

研究了标值点过程的道路提取算法,针对传统数据模型提取道路不够准确的缺点,改进了数据模型。提出了基于边缘检测的生灭转移核,避免了传统的生灭过程搜索的盲目性,大大加快了算法的收敛速度。针对传统转移核容易破坏线段的连接性的缺点,定义了多种新型的RJMCMC转移核,重新设计了基于邻域的生灭转移核及线段参数转移核。仿真结果表明,改进算法大大提高了收敛速度,并且提取的道路网络更准确,更连续。     

Parallel and interacting Markov chain Monte Carlo algorithm

In many situations it is important to be able to propose N independent realizations of a given distribution law. We propose a strategy for making N parallel Monte Carlo Markov chains (MCMC) interact in order to get an approximation of an independent N-sample of a given target law. In this method each individual chain proposes candidates for all other chains. We prove that the set of interacting chains is itself a MCMC method for the product of N target measures. Compared to independent parallel chains this method is more time consuming, but we show through examples that it possesses many advantages. This approach is applied to a biomass evolution model.     

Estimation of sample selection models with two selection mechanisms

This paper focuses on estimating sample selection models with two incidentally truncated outcomes and two corresponding selection mechanisms. The method of estimation is an extension of the Markov chain Monte Carlo (MCMC) sampling algorithm from Chib (2007) and Chib et al. (2009). Contrary to conventional data augmentation strategies when dealing with missing data, the proposed algorithm augments the posterior with only a small subset of the total missing data caused by sample selection. This results in improved convergence of the MCMC chain and decreased storage costs, while maintaining tractability in the sampling densities. The methods are applied to estimate the effects of residential density on vehicle miles traveled and vehicle holdings in California.     

A Noninformative Prior for Neural Networks

While many implementations of Bayesian neural networks use large, complex hierarchical priors, in much of modern Bayesian statistics, noninformative (flat) priors are very common. This paper introduces a noninformative prior for feed-forward neural networks, describing several theoretical and practical advantages of this approach. In particular, a simpler prior allows for a simpler Markov chain Monte Carlo algorithm. Details of MCMC implementation are included.     

Application of Biased Metropolis Algorithms: From protons to proteins

We show that sampling with a biased Metropolis scheme is essentially equivalent to using the heatbath algorithm. However, the biased Metropolis method can also be applied when an efficient heatbath algorithm does not exist. This is first illustrated with an example from high energy physics (lattice gauge theory simulations). We then illustrate the Rugged Metropolis method, which is based on a similar biased updating scheme, but aims at very different applications. The goal of such applications is to locate the most likely configurations in a rugged free energy landscape, which is most relevant for simulations of biomolecules.     

On almost sure stability of continuous-time Markov jump linear systems

In this paper, we study the almost sure stability of continuous-time jump linear systems with a finite-state Markov form process. A sufficient condition for almost sure stability is derived that refers to the statistics of the transition matrix over m switches. It is shown that, if the system is exponentially almost sure stable, there exists a finite m such that the criterion is satisfied. In order to evaluate the expected value appearing in the condition, an efficient Monte Carlo algorithm is worked out.