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This paper is concerned with explicitly modeling the effect of terrain on wind power curves. Terrain characteristics are spatially-varying but temporally constant, whereas other power curve-affiliating variables such wind speed, temperature, and wind power vary both spatially and temporally. In order to effectively model such two modes of variation in the data, we employ a Bayesian hierarchical model (BHM) that connects the terrain characteristics with the parameters in a power curve. BHM jointly models the data from all turbines on a wind farm for attaining the turbine-specific, terrain-incorporating power curves. Our analysis shows that, out of the three terrain variables available in our data, ruggedness has the strongest effect on the power curve. We also evaluate the applicability of using the resulting power curve model for turbines on a different terrain and find that incorporating terrain information explicitly is beneficial. The specific BHM mechanism of using terrain information leads to 7–10% improvement over the group averaging approach.

With the increasing amount of distributed energy resources (DERs) integration, there is a significant need to model and analyze hosting capacity (HC) for future electric distribution grids. Hosting capacity analysis (HCA) examines the amount of DERs that can be safely integrated into the grid and is a challenging task in full generality because there are many possible integration of DERs in foresight. That is, there are numerous extreme points between feasible and infeasible sets. Moreover, HC depends on multiple factors such as (a) adoption patterns of DERs that depend on socioeconomic behaviors and (b) how DERs are controlled and managed. These two factors are intrinsic to the problem space because not all integration of DERs may be centrally planned, and could largely change our understanding about HC. This paper addresses the research gap by capturing the two factors (a) and (b) in HCA and by identifying a few most insightful HC scenarios at the cost of domain knowledge. We propose a data-driven HCA framework and introduce active learning in HCA to effectively explore scenarios. Active learning in HCA and characteristics of HC with respect to the two factors (a) and (b) are illustrated in a 3-bus example. Next, detailed large-scale studies are proposed to understand the significance of (a) and (b). Our findings suggest that HC and its interpretations significantly change subject to the two factors (a) and (b).

In this paper, we examine the performance of satellite state estimation algorithms in the modified equinoctial coordinate system, defined on the cylindrical manifold of ℝ5×S, where ℝis the space of reals and Sdenotes circular space. A comparison is made between an optimal transport based filter and ensemble Kalman filter algorithm in the context of satellite state estimation. The initial state joint probability density function is modeled in ℝ5×Susing the Gauss von Mises distribution. The sensor noise for optimal transport filtering is modeled in the same manifold. The ensemble Kalman filter, by definition, requires the sensor noise to be Gaussian and is modeled in ℝ6for this problem. We observe that there is a clear advantage in using an optimal transport based filtering algorithm where we represent the initial condition uncertainty and sensor noise, in the cylindrical manifold. These two filtering algorithms are implemented on a simulated International Space Station orbit, with measurement at equal intervals. We compare two distinct scenarios in this simulation based study. In the first one, sensor noise characteristics are assumed to be known. For the second one, we present a new algorithm within the optimal transport framework with unknown sensor noise characteristics, a practical and relevant issue in the space-tracking problems. The optimal transport based algorithm provides more consistent and robust estimates compared to that of ensemble Kalman filter, in each of these scenarios.

This article introduces a flexible Bayesian semiparametric approach to analyzing crash data that are of hierarchical or multilevel nature. We extend the traditional varying intercept (random effects) multilevel model by relaxing its standard parametric distributional assumption. While accounting for unobserved cross-group heterogeneity in the data through intercept, the proposed method allows identifying latent subpopulations (and consequently outliers) in data based on a Dirichlet process mixture. It also allows estimating the number of latent subpopulations using an elegant mathematical structure instead of prespecifying this number arbitrarily as in conventional latent class or finite mixture models. In this paper, we evaluate our method on two recent railway grade crossing crash datasets, at province and municipality levels, from Canada for the years 2008–2013. We use cross-validation predictive densities and pseudo-Bayes factor for Bayesian model selection. While confirming the need for a multilevel modeling approach for both datasets, the results reveal the inadequacy of the standard parametric assumption in the varying intercept model for the municipality-level dataset. In fact, our proposed method is shown to improve model fitting significantly for the latter data. In a fully probabilistic framework, we also identify the expected number of latent clusters that share similar unidentified features among Canadian provinces and municipalities. It is possible thus to further investigate the reasons for such similarities and dissimilarities. This can have important policy implications for various safety management programs.

Abstract A Bayesian blind source separation (BSS) algorithm is proposed in this paper to recover independent sources from observed multivariate spatial patterns. As a widely used mechanism, Gaussian mixture model is adopted to represent the sources for statistical description and machine learning. In the context of linear latent variable BSS model, some conjugate priors are incorporated into the hyperparameters estimation of mixing matrix. The proposed algorithm then approximates the full posteriors over model structure and source parameters in an analytical manner based on variational Bayesian treatment. Experimental studies demonstrate that this Bayesian source separation algorithm is appropriate for systematic spatial pattern analysis by modeling arbitrary sources and identify their effects on high dimensional measurement data. The identified patterns will serve as diagnosis aids for gaining insight into the nature of physical process for the potential use of statistical quality control.

Bayesian spatial prediction using the elliptical distribution is proposed. Sometimes the family of distributions has a dimensional coherency (consistency) property which is important for spatial prediction. We examine Bayesian posterior and predictive distributions for a spatial prediction which turns out to have the same results as in a Gaussian process. [Copyright &y& Elsevier]

Moments of skew t random vectors and their quadratic forms are derived. It is shown that the moments of the sample autocovariance function and of the sample variogram estimator depend on a measure of multivariate kurtosis, but not on a skewness parameter. [Copyright &y& Elsevier]

Selection of significant genes via expression patterns is an important problem in microarray experiments. Owing to small sample size and the large number of variables (genes), the selection process can be unstable. This paper proposes a hierarchical Bayesian model for gene (variable) selection. We employ latent variables to specialize the model to a regression setting and uses a Bayesian mixture prior to perform the variable selection. We control the size of the model by assigning a prior distribution over the dimension (number of significant genes) of the model. The posterior distributions of the parameters are not in explicit form and we need to use a combination of truncated sampling and Markov Chain Monte Carlo (MCMC) based computation techniques to simulate the parameters from the posteriors. The Bayesian model is flexible enough to identify significant genes as well as to perform future predictions. The method is applied to cancer classification via cDNA microarrays where the genes BRCA1 and BRCA2 are associated with a hereditary disposition to breast cancer, and the method is used to identify a set of significant genes. The method is also applied successfully to the leukemia data.

Summary. We construct Bayesian methods for semiparametric modeling of a monotonic regression function when the predictors are measured with classical error, Berkson error, or a mixture of the two. Such methods require a distribution for the unobserved (latent) predictor, a distribution we also model semi‐parametrically. Such combinations of semiparametric methods for the dose‐response as well as the latent variable distribution have not been considered in the measurement error literature for any form of measurement error. In addition, our methods represent a new approach to those problems where the measurement error combines Berkson and classical components. While the methods are general, we develop them around a specific application, namely, the study of thyroid disease in relation to radiation fallout from the Nevada test site. We use this data to illustrate our methods, which suggest a point estimate (posterior mean) of relative risk at high doses nearly double that of previous analyses but that also suggest much greater uncertainty in the relative risk.

Summary. A Bayesian semiparametric approach is described for an accelerated failure time model. The error distribution is assigned a Polya tree prior and the regression parameters a noninformative hierarchical prior. Two cases are considered: the first assumes error terms are exchangeable; the second assumes that error terms are partially exchangeable. A Markov chain Monte Carlo algorithm is described to obtain a predictive distribution for a future observation given both uncensored and censored data.

Summary. A Bayesian multivariate adaptive regression spline fitting approach is used to model univariate and multivariate survival data with censoring. The possible models contain the proportional hazards model as a subclass and automatically detect departures from this. A reversible jump Markov chain Monte Carlo algorithm is described to obtain the estimate of the hazard function as well as the survival curve.

This paper proposes Bayesian nonparametric mixing for some well-known and popular models. The distribution of the observations is assumed to contain an unknown mixed effects term which includes a fixed effects term, a function of the observed covariates, and an additive or multiplicative random effects term. Typically these random effects are assumed to be independent of the observed covariates and independent and identically distributed from a distribution from some known parametric family. This assumption may be suspect if either there is interaction between observed covariates and unobserved covariates or the fixed effects predictor of observed covariates is misspecified. Another cause for concern might be simply that the covariates affect more than just the location of the mixed effects distribution. As a consequence the distribution of the random effects could be highly irregular in modality and skewness leaving parametric families unable to model the distribution adequately. This paper therefore proposes a Bayesian nonparametric prior for the random effects to capture possible deviances in modality and skewness and to explore the observed covariates’ effect on the distribution of the mixed effects.

Generalized linear models are widely used by data analysis. However, the choice of the link function is often made arbitrarily. Here we permit the data to estimate the link function by incorporating it as an unknown in the model. Since the link function is usually taken to be strictly increasing, by a strictly increasing transformation of its range to the unit interval we can model it as a strictly increasing cumulative distribution function. The transformation results in a domain which is [0, 1]. We model the cumulative distribution function as a mixture of Beta cumulative distribution functions, noting that the latter family is dense within the collection of all continuous densities on [0, 1]. For the fitting of the model we take a Bayesian approach, encouraging vague priors, to focus upon the likehood. We discuss choices of such priors as well as the integrability of the resultant posteriors.Implementation of the Bayesian approach is carried out using sampling based methods, in particular, a tailored Metropolis-within-Gibbs algorithm. An illustrative example utilising data involving wave damage to cargo ships is provided.

Abstract: The multivariate kurtosis of skew distribution is corrected. [Copyright &y& Elsevier]

We propose statistical methods for comparing phenomics data generated by the Biolog Phenotype Microarray (PM) platform for high-throughput phenotyping. Instead of the routinely used visual inspection of data with no sound inferential basis, we develop two approaches. The first approach is based on quantifying the distance between mean or median curves from two treatments and then applying a permutation test; we also consider a permutation test applied to areas under mean curves. The second approach employs functional principal component analysis. Properties of the proposed methods are investigated on both simulated data and data sets from the PM platform.

Motivation: Our aim was to predict protein interdomain linker regions using sequence alone, without requiring known homology. Identifying linker regions will delineate domain boundaries, and can be used to computationally dissect proteins into domains prior to clustering them into families. We developed a hidden Markov model of linker/non-linker sequence regions using a linker index derived from amino acid propensity. We employed an efficient Bayesian estimation of the model using Markov Chain Monte Carlo, Gibbs sampling in particular, to simulate parameters from the posteriors. Our model recognizes sequence data to be continuous rather than categorical, and generates a probabilistic output. Results: We applied our method to a dataset of protein sequences in which domains and interdomain linkers had been delineated using the Pfam-A database. The prediction results are superior to a simpler method that also uses linker index. Contact: c-elsik@tamu.edu Supplementary information: http://racerx00.tamu.edu/kbae

Motivation: The standard paradigm for a classifier design is to obtain a sample of feature-label pairs and then to apply a classification rule to derive a classifier from the sample data. Typically in laboratory situations the sample size is limited by cost, time or availability of sample material. Thus, an investigator may wish to consider a sequential approach in which there is a sufficient number of patients to train a classifier in order to make a sound decision for diagnosis while at the same time keeping the number of patients as small as possible to make the studies affordable. Results: A sequential classification procedure is studied via the martingale central limit theorem. It updates the classification rule at each step and provides stopping criteria to ensure with a certain confidence that at stopping a future subject will have misclassification probability smaller than a predetermined threshold. Simulation studies and applications to microarray data analysis are provided. The procedure possesses several attractive properties: (1) it updates the classification rule sequentially and thus does not rely on distributions of primary measurements from other studies; (2) it assesses the stopping criteria at each sequential step and thus can substantially reduce cost via early stopping; and (3) it is not restricted to any particular classification rule and therefore applies to any parametric or non-parametric method, including feature selection or extraction. Availability: R-code for the sequential stopping rule is available at http://stat.tamu.edu/~wfu/microarray/sequential/R-code.html Contact: wfu@stat.tamu.edu

Summary: The fundamental problem of gene selection via cDNA data is to identify which genes are differentially expressed across different kinds of tissue samples (e.g. normal and cancer). cDNA data contain large number of variables (genes) and usually the sample size is relatively small so the selection process can be unstable. Therefore, models which incorporate sparsity in terms of variables (genes) are desirable for this kind of problem. This paper proposes a two-level hierarchical Bayesian model for variable selection which assumes a prior that favors sparseness. We adopt a Markov chain Monte Carlo (MCMC) based computation technique to simulate the parameters from the posteriors. The method is applied to leukemia data from a previous study and a published dataset on breast cancer. Supplementary information: http://stat.tamu.edu/people/faculty/bmallick.html