A Bayesian analysis of spherical pattern based on finite Langevin mixture

Parameter estimation is a cornerstone of most fundamental problems of statistical research and practice. In particular, finite mixture models have long been heavily relied on deterministic approaches such as expectation maximization (EM). Despite their successful utilization in wide spectrum of areas, they have inclined to converge to local solutions. An alternative approach is the adoption of Bayesian inference that naturally addresses data uncertainty while ensuring good generalization. To this end, in this paper we propose a fully Bayesian approach for Langevin mixture model estimation and selection via MCMC algorithm based on Gibbs sampler, Metropolis–Hastings and Bayes factors. We demonstrate the effectiveness and the merits of the proposed learning framework through synthetic data and challenging applications involving topic detection and tracking and image categorization.     

GPU accelerated MCMC for modeling terrorist activity

The use of graphical processing unit (GPU) parallel processing is becoming a part of mainstream statistical practice. The reliance of Bayesian statistics on Markov Chain Monte Carlo (MCMC) methods makes the applicability of parallel processing not immediately obvious. It is illustrated that there are substantial gains in improved computational time for MCMC and other methods of evaluation by computing the likelihood using GPU parallel processing. Examples use data from the Global Terrorism Database to model terrorist activity in Colombia from 2000 through 2010 and a likelihood based on the explicit convolution of two negative-binomial processes. Results show decreases in computational time by a factor of over 200. Factors influencing these improvements and guidelines for programming parallel implementations of the likelihood are discussed.     

MCMC algorithms for Subset Simulation

Subset Simulation is an adaptive simulation method that efficiently solves structural reliability problems with many random variables. The method requires sampling from conditional distributions, which is achieved through Markov Chain Monte Carlo (MCMC) algorithms. This paper discusses different MCMC algorithms proposed for Subset Simulation and introduces a novel approach for MCMC sampling in the standard normal space. Two variants of the algorithm are proposed: a basic variant, which is simpler than existing algorithms with equal accuracy and efficiency, and a more efficient variant with adaptive scaling. It is demonstrated that the proposed algorithm improves the accuracy of Subset Simulation, without the need for additional model evaluations.     

A Bayesian approach to model dispersal for decision support

In agricultural and environmental sciences dispersal models are often used for risk assessment to predict the risk associated with a given configuration and also to test scenarios that are likely to minimise those risks. Like any biological process, dispersal is subject to biological, climatic and environmental variability and its prediction relies on models and parameter values which can only approximate the real processes. In this paper, we present a Bayesian method to model dispersal using spatial configuration and climatic data (distances between emitters and receptors; main wind direction) while accounting for uncertainty, with an application to the prediction of adventitious presence rate of genetically modified maize (GM) in a non-GM field. This method includes the design of candidate models, their calibration, selection and evaluation on an independent dataset. A group of models was identified that is sufficiently robust to be used for prediction purpose. The group of models allows to include local information and it reflects reliably enough the observed variability in the data so that probabilistic model predictions can be performed and used to quantify risk under different scenarios or derive optimal sampling schemes.     

A Bayesian MCMC approach to survival analysis with doubly-censored data

Doubly-censored data refers to time to event data for which both the originating and failure times are censored. In studies involving AIDS incubation time or survival after dementia onset, for example, data are frequently doubly-censored because the date of the originating event is interval-censored and the date of the failure event usually is right-censored. The primary interest is in the distribution of elapsed times between the originating and failure events and its relationship to exposures and risk factors. The estimating equation approach [Sun et al. (1999). Regression analysis of doubly censored failure time data with applications to AIDS studies. Biometrics 55, 909-914] and its extensions assume the same distribution of originating event times for all subjects. This paper demonstrates the importance of utilizing additional covariates to impute originating event times, i.e., more accurate estimation of originating event times may lead to less biased parameter estimates for elapsed time. The Bayesian MCMC method is shown to be a suitable approach for analyzing doubly-censored data and allows a rich class of survival models. The performance of the proposed estimation method is compared to that of other conventional methods through simulations. Two examples, an AIDS cohort study and a population-based dementia study, are used for illustration. Sample code is shown in Appendix A and Appendix B.     

Characterization of seasonal variation of forest canopy in a temperate deciduous broadleaf forest, using daily MODIS data

In this paper, we present an improved procedure for collecting no or little atmosphere- and snow-contaminated observations from the Moderate Resolution Imaging Spectroradiometer (MODIS) sensor. The resultant time series of daily MODIS data of a temperate deciduous broadleaf forest (the Bartlett Experimental Forest) in 2004 show strong seasonal dynamics of surface reflectance of green, near infrared and shortwave infrared bands, and clearly delineate leaf phenology and length of plant growing season. We also estimate the fractions of photosynthetically active radiation (PAR) absorbed by vegetation canopy (FAPAR_canopy), leaf (FAPAR_leaf), and chlorophyll (FAPAR_chl), respectively, using a coupled leaf-canopy radiative transfer model (PROSAIL-2) and daily MODIS data. The Markov Chain Monte Carlo (MCMC) method (the Metropolis algorithm) is used for model inversion, which provides probability distributions of the retrieved variables. A two-step procedure is used to estimate the fractions of absorbed PAR: (1) to retrieve biophysical and biochemical variables from MODIS images using the PROSAIL-2 model; and (2) to calculate the fractions with the estimated model variables from the first step. Inversion and forward simulations of the PROSAIL-2 model are carried out for the temperate deciduous broadleaf forest during day of year (DOY) 184 to 201 in 2005. The reproduced reflectance values from the PROSAIL-2 model agree well with the observed MODIS reflectance for the five spectral bands (green, red, NIR₁, NIR₂, and SWIR₁). The estimated leaf area index, leaf dry matter, leaf chlorophyll content and FAPAR_canopy values are close to field measurements at the site. The results also showed significant differences between FAPAR_canopy and FAPAR_chl at the site. Our results show that MODIS imagery provides important information on biophysical and biochemical variables at both leaf and canopy levels.     

Bayesian testing for non-linearity in volatility modeling

Neural networks provide a tool for describing non-linearity in volatility processes of financial data and help to answer the question “how much” non-linearity is present in the data. Non-linearity is studied under three different specifications of the conditional distribution: Gaussian, Student-t and mixture of Gaussians. To rank the volatility models, a Bayesian framework is adopted to perform a Bayesian model selection within the different classes of models. In the empirical analysis, the return series of the Dow Jones Industrial Average index, FTSE 100 and NIKKEI 225 indices over a period of 16 years are studied. The results show different behavior across the three markets. In general, if a statistical model accounts for non-normality and explains most of the fat tails in the conditional distribution, then there is less need for complex non-linear specifications.     

Using duration models to reduce fragmentation in audio segmentation

We investigate explicit segment duration models in addressing the problem of fragmentation in musical audio segmentation. The resulting probabilistic models are optimised using Markov Chain Monte Carlo methods; in particular, we introduce a modification to Wolff’s algorithm to make it applicable to a segment classification model with an arbitrary duration prior. We apply this to a collection of pop songs, and show experimentally that the generated segmentations suffer much less from fragmentation than those produced by segmentation algorithms based on clustering, and are closer to an expert listener’s annotations, as evaluated by two different performance measures. Editor: Gerhard Widmer     

Bayesian estimation of unrestricted and order-restricted association models for a two-way contingency table

In two-way contingency tables analysis, a popular class of models for describing the structure of the association between the two categorical variables are the so-called “association” models. Such models assign scores to the classification variables which can be either fixed and prespecified or unknown parameters to be estimated. Under the row-column (RC) association model, both row and column scores are unknown parameters without any restriction concerning their ordinality. It is natural to impose order restrictions on the scores when the classification variables are ordinal. The Bayesian approach for the RC (unrestricted and restricted) model is adopted. MCMC methods are facilitated in order the parameters to be estimated. Furthermore, an alternative parametrization of the association models is proposed. This new parametrization simplifies computation in the MCMC procedure and leads to a natural parameter space for the order constrained model. The proposed methodology is illustrated via a popular dataset.     

Study on Storage Reliability Evaluation for Ammunition Using Gibbs Sampler

For the gradual maturity of Bayesian survival analysis theory, as well as the defects of the traditional methods for storage reliability evaluation, the Bayesian survival analysis method is proposed to build regression models for reliability in the random truncated test. These models can reflect the influences of different environments on the ammunition storage lifetime. As an example, the common exponential distribution is used here, and Markov chain Monte Carlo（MCMC） method based on Gibbs sampling dynamically simulates the Markov chain of the parameters＇ posterior distribution. Also, the parameters＇ Bayesian estimations are calculated in the random truncated condition. The simulation results show that the proposed method is effective and directly perceived.