We propose a Bayesian nonparametric approach to the problem of jointly modeling multiple related time series. Our model discovers a latent set of dynamical behaviors shared among the sequences, and segments each time series into regions defined by a subset of these behaviors. Using a beta process prior, the size of the behavior set and the sharing pattern are both inferred from data. We develop Markov chain Monte Carlo (MCMC) methods based on the Indian buffet process representation of the predictive distribution of the beta process. Our MCMC inference algorithm efficiently adds and removes behaviors via novel split-merge moves as well as data-driven birth and death proposals, avoiding the need to consider a truncated model. We demonstrate promising results on unsupervised segmentation of human motion capture data.

Fingerprint individuality refers to the extent of uniqueness of fingerprints and is the main criteria for deciding between a match versus nonmatch in forensic testimony. Often, prints are subject to varying levels of noise, for example, the image quality may be low when a print is lifted from a crime scene. A poor image quality causes human experts as well as automatic systems to make more errors in feature detection by either missing true features or detecting spurious ones. This error lowers the extent to which one can claim individualization of fingerprints that are being matched. The aim of this paper is to quantify the decrease in individualization as image quality degrades based on fingerprint images in real databases. This, in turn, can be used by forensic experts along with their testimony in a court of law. An important practical concern is that the databases used typically consist of a large number of fingerprint images so computational algorithms such as the Gibbs sampler can be extremely slow. We develop algorithms based on the Laplace approximation of the likelihood and infer the unknown parameters based on this approximate likelihood. Two publicly available databases, namely, FVC2002 and FVC2006, are analyzed from which estimates of individuality are obtained. From a statistical perspective, the contribution can be treated as an innovative application of Generalized Linear Mixed Models (GLMMs) to the field of fingerprint-based authentication.

Lung tumor tracking for radiotherapy requires real-time, multiple-step ahead forecasting of a quasi-periodic time series recording instantaneous tumor locations. We introduce a location-mixture autoregressive (LMAR) process that admits multimodal conditional distributions, fast approximate inference using the EM algorithm and accurate multiple-step ahead predictive distributions. LMAR outperforms several commonly used methods in terms of out-of-sample prediction accuracy using clinical data from lung tumor patients. With its superior predictive performance and real-time computation, the LMAR model could be effectively implemented for use in current tumor tracking systems.

We analyze the timing and extent of Northern European temperature falls during the Little Ice Age, using standard temperature reconstructions. However, we can find little evidence of temporal dependence or structural breaks in European weather before the twentieth century. Instead, European weather between the fifteenth and nineteenth centuries resembles uncorrelated draws from a distribution with a constant mean (although there are occasional decades of markedly lower summer temperature) and variance, with the same behavior holding more tentatively back to the twelfth century. Our results suggest that observed conditions during the Little Ice Age in Northern Europe are consistent with random climate variability. The existing consensus about apparent cold conditions may stem in part from a Slutsky effect, where smoothing data gives the spurious appearance of irregular oscillations when the underlying time series is white noise.

Additive manufacturing, or 3D printing, is a promising manufacturing technique marred by product deformation due to material solidification in the printing process. Control of printed product deformation can be achieved by a compensation plan. However, little attention has been paid to interference in compensation, which is thought to result from the inevitable discretization of a compensation plan. We investigate interference with an experiment involving the application of discretized compensation plans to cylinders. Our treatment illustrates a principled framework for detecting and modeling interference, and ultimately provides a new step toward better understanding quality control for 3D printing.

We discuss functional clustering procedures for nested designs, where multiple curves are collected for each subject in the study. We start by considering the application of standard functional clustering tools to this problem, which leads to groupings based on the average profile for each subject. After discussing some of the shortcomings of this approach, we present a mixture model based on a generalization of the nested Dirichlet process that clusters subjects based on the distribution of their curves. By using mixtures of generalized Dirichlet processes, the model induces a much more flexible prior on the partition structure than other popular model-based clustering methods, allowing for different rates of introduction of new clusters as the number of observations increases. The methods are illustrated using hormone profiles from multiple menstrual cycles collected for women in the Early Pregnancy Study.

Reverse-phase protein array (RPPA) analysis is a powerful, relatively new platform that allows for high-throughput, quantitative analysis of protein networks. One of the challenges that currently limit the potential of this technology is the lack of methods that allow for accurate data modeling and identification of related networks and samples. Such models may improve the accuracy of biological sample classification based on patterns of protein network activation and provide insight into the distinct biological relationships underlying different types of cancer. Motivated by RPPA data, we propose a Bayesian sparse graphical modeling approach that uses selection priors on the conditional relationships in the presence of class information. The novelty of our Bayesian model lies in the ability to draw information from the network data as well as from the associated categorical outcome in a unified hierarchical model for classification. In addition, our method allows for intuitive integration of a priori network information directly in the model and allows for posterior inference on the network topologies both within and between classes. Applying our methodology to an RPPA data set generated from panels of human breast cancer and ovarian cancer cell lines, we demonstrate that the model is able to distinguish the different cancer cell types more accurately than several existing models and to identify differential regulation of components of a critical signaling network (the PI3K-AKT pathway) between these two types of cancer. This approach represents a powerful new tool that can be used to improve our understanding of protein networks in cancer.

Statistical methods for analyzing large-scale biomolecular data are commonplace in computational biology. A notable example is phenotype prediction from gene expression data, for instance, detecting human cancers, differentiating subtypes and predicting clinical outcomes. Still, clinical applications remain scarce. One reason is that the complexity of the decision rules that emerge from standard statistical learning impedes biological understanding, in particular, any mechanistic interpretation. Here we explore decision rules for binary classification utilizing only the ordering of expression among several genes; the basic building blocks are then two-gene expression comparisons. The simplest example, just one comparison, is the TSP classifier, which has appeared in a variety of cancer-related discovery studies. Decision rules based on multiple comparisons can better accommodate class heterogeneity, and thereby increase accuracy, and might provide a link with biological mechanism. We consider a general framework (“rank-in-context”) for designing discriminant functions, including a data-driven selection of the number and identity of the genes in the support (“context”). We then specialize to two examples: voting among several pairs and comparing the median expression in two groups of genes. Comprehensive experiments assess accuracy relative to other, more complex, methods, and reinforce earlier observations that simple classifiers are competitive.

Self-selected samples are frequently obtained due to different levels of survey participation propensity of the survey individuals. When the survey participation is related to the survey topic of interest, propensity score weighting adjustment using auxiliary information may lead to biased estimation. In this paper, we consider a parametric model for the response probability that includes the study variable itself in the covariates of the model and proposes a novel application of two-phase sampling to estimate the parameters of the propensity model. The proposed method includes an experiment in which data are collected again from a subset of the original self-selected sample. With this two-phase sampling experiment, we can estimate the parameters in a propensity score model consistently. Then the propensity score adjustment can be applied to the self-selected sample to estimate the population parameters. Sensitivity of the selection model assumption is investigated from two limited simulation studies. The proposed method is applied to the 2012 Iowa Caucus Survey.

Bacterial growth models are commonly used for the prediction of microbial safety and the shelf life of perishable foods. Growth is affected by several environmental factors such as temperature, acidity level and salt concentration. In this study, we develop two models to describe bacterial growth for multiple populations under both equal and different environmental conditions. First, a semi-parametric model based on the Gompertz equation is proposed. Assuming that the parameters of the Gompertz equation may vary in relation to the running conditions under which the experiment is performed, we use feedforward neural networks to model the influence of these environmental factors on the growth parameters. Second, we propose a more general model which does not assume any underlying parametric form for the growth function. Thus, we consider a neural network as a primary growth model which includes the influencing environmental factors as inputs to the network. One of the main disadvantages of neural networks models is that they are often very difficult to tune, which complicates fitting procedures. Here, we show that a simple Bayesian approach to fitting these models can be implemented via the software package WinBugs. Our approach is illustrated using real experimental Listeria monocytogenes growth data.

Spatio-temporal prediction of levels of an environmental exposure is an important problem in environmental epidemiology. Our work is motivated by multiple studies on the spatio-temporal distribution of mobile source, or traffic related, particles in the greater Boston area. When multiple sources of exposure information are available, a joint model that pools information across sources maximizes data coverage over both space and time, thereby reducing the prediction error.

We consider a Bayesian hierarchical framework in which a joint model consists of a set of submodels, one for each data source, and a model for the latent process that serves to relate the submodels to one another. If a submodel depends on the latent process nonlinearly, inference using standard MCMC techniques can be computationally prohibitive. The implications are particularly severe when the data for each submodel are aggregated at different temporal scales.

To make such problems tractable, we linearize the nonlinear components with respect to the latent process and induce sparsity in the covariance matrix of the latent process using compactly supported covariance functions. We propose an efficient MCMC scheme that takes advantage of these approximations. We use our model to address a temporal change of support problem whereby interest focuses on pooling daily and multiday black carbon readings in order to maximize the spatial coverage of the study region.

House price increases have been steady over much of the last 40 years, but there have been occasional declines, most notably in the recent housing bust that started around 2007, on the heels of the preceding housing bubble. We introduce a novel growth model that is motivated by time-warping models in functional data analysis and includes a nonmonotone time-warping component that allows the inclusion and description of boom–bust cycles and facilitates insights into the dynamics of asset bubbles. The underlying idea is to model longitudinal growth trajectories for house prices and other phenomena, where temporal setbacks and deflation may be encountered, by decomposing such trajectories into two components. A first component corresponds to underlying steady growth driven by inflation that anchors the observed trajectories on a simple first order linear differential equation, while a second boom–bust component is implemented as time warping. Time warping is a commonly encountered phenomenon and reflects random variation along the time axis. Our approach to time warping is more general than previous approaches by admitting the inclusion of nonmonotone warping functions. The anchoring of the trajectories on an underlying linear dynamic system also makes the time-warping component identifiable and enables straightforward estimation procedures for all model components. The application to the dynamics of housing prices as observed for 19 metropolitan areas in the U.S. from December 1998 to July 2013 reveals that the time setbacks corresponding to nonmonotone time warping vary substantially across markets and we find indications that they are related to market-specific growth rates.

We predict the popularity of short messages called tweets created in the micro-blogging site known as Twitter. We measure the popularity of a tweet by the time-series path of its retweets, which is when people forward the tweet to others. We develop a probabilistic model for the evolution of the retweets using a Bayesian approach, and form predictions using only observations on the retweet times and the local network or “graph” structure of the retweeters. We obtain good step ahead forecasts and predictions of the final total number of retweets even when only a small fraction (i.e., less than one tenth) of the retweet path is observed. This translates to good predictions within a few minutes of a tweet being posted, and has potential implications for understanding the spread of broader ideas, memes or trends in social networks.

Short-time human travel behaviour can be described by a power law with respect to distance. We incorporate this information in space–time models for infectious disease surveillance data to better capture the dynamics of disease spread. Two previously established model classes are extended, which both decompose disease risk additively into endemic and epidemic components: a spatio-temporal point process model for individual-level data and a multivariate time-series model for aggregated count data. In both frameworks, a power-law decay of spatial interaction is embedded into the epidemic component and estimated jointly with all other unknown parameters using (penalised) likelihood inference. Whereas the power law can be based on Euclidean distance in the point process model, a novel formulation is proposed for count data where the power law depends on the order of the neighbourhood of discrete spatial units. The performance of the new approach is investigated by a reanalysis of individual cases of invasive meningococcal disease in Germany (2002–2008) and count data on influenza in 140 administrative districts of Southern Germany (2001–2008). In both applications, the power law substantially improves model fit and predictions, and is reasonably close to alternative qualitative formulations, where distance and order of neighbourhood, respectively, are treated as a factor. Implementation in the R package surveillance allows the approach to be applied in other settings.

This paper explores the topic of preferential sampling, specifically situations where monitoring sites in environmental networks are preferentially located by the designers. This means the data arising from such networks may not accurately characterize the spatio-temporal field they intend to monitor. Approaches that have been developed to mitigate the effects of preferential sampling in various contexts are reviewed and, building on these approaches, a general framework for dealing with the effects of preferential sampling in environmental monitoring is proposed. Strategies for implementation are proposed, leading to a method for improving the accuracy of official statistics used to report trends and inform regulatory policy. An essential feature of the method is its capacity to learn the preferential selection process over time and hence to reduce bias in these statistics. Simulation studies suggest dramatic reductions in bias are possible. A case study demonstrates use of the method in assessing the levels of air pollution due to black smoke in the UK over an extended period (1970–1996). In particular, dramatic reductions in the estimates of the number of sites out of compliance are observed.

Degradation modeling has traditionally relied on historical signals to estimate the behavior of the underlying degradation process. Many models assume that these historical signals are acquired under the same environmental conditions and can be observed along the entire lifespan of a component. In this paper, we relax these assumptions and present a more general statistical framework for modeling degradation signals that may have been collected under different types of environmental conditions. In addition, we consider applications where the historical signals are not necessarily observed continuously, that is, historical signals are sparse or fragmented. We consider the case where historical degradation signals are collected under known environmental states and another case where the environmental conditions are unknown during the acquisition of these historical data. For the first case, we use a classification algorithm to identify the environmental state of the units operating in the field. In the second case, a clustering step is required for clustering the historical degradation signals. The proposed model can provide accurate predictions of the lifetime or residual life distributions of engineering components that are still operated in the field. This is demonstrated by using simulated degradation signals as well as vibration-based degradation signals acquired from a rotating machinery setup.

In astrophysics a common goal is to infer the flux distribution of populations of scientifically interesting objects such as pulsars or supernovae. In practice, inference for the flux distribution is often conducted using the cumulative distribution of the number of sources detected at a given sensitivity. The resulting “$\log(N>S)$–$\log(S)$” relationship can be used to compare and evaluate theoretical models for source populations and their evolution. Under restrictive assumptions the relationship should be linear. In practice, however, when simple theoretical models fail, it is common for astrophysicists to use prespecified piecewise linear models. This paper proposes a methodology for estimating both the number and locations of “breakpoints” in astrophysical source populations that extends beyond existing work in this field.

An important component of the proposed methodology is a new interwoven EM algorithm that computes parameter estimates. It is shown that in simple settings such estimates are asymptotically consistent despite the complex nature of the parameter space. Through simulation studies it is demonstrated that the proposed methodology is capable of accurately detecting structural breaks in a variety of parameter configurations. This paper concludes with an application of our methodology to the Chandra Deep Field North (CDFN) data set.

Many commercial products are sold with warranties and indirectly through dealers. The manufacturer-retailer distribution mechanism results in serious missing data problems in field return data, as the sales date for an unreturned unit is generally unknown to the manufacturer. This study considers a general setting for field failure data with unknown sales dates and a warranty limit. A stochastic expectation–maximization (SEM) algorithm is developed to estimate the distributions of the sales lag (time between shipment to a retailer and sale to a customer) and the lifetime of the product under study. Extensive simulations are used to evaluate the performance of the SEM algorithm and to compare with the imputation method proposed by Ghosh [Ann. Appl. Stat. 4 (2010) 1976–1999]. Three real examples illustrate the methodology proposed in this paper.

Climate change is expected to alter the distribution of ambient ozone levels and temperatures which, in turn, may impact public health. Much research has focused on the effect of short-term ozone exposures on mortality and morbidity while controlling for temperature as a confounder, but less is known about the joint effects of ozone and temperature. The extent of the health effects of changing ozone levels and temperatures will depend on whether these effects are additive or synergistic. In this paper we propose a spatial, semi-parametric model to estimate the joint ozone-temperature risk surfaces in 95 US urban areas. Our methodology restricts the ozone-temperature risk surfaces to be monotone in ozone and allows for both nonadditive and nonlinear effects of ozone and temperature. We use data from the National Mortality and Morbidity Air Pollution Study (NMMAPS) and show that the proposed model fits the data better than additive linear and nonlinear models. We then examine the synergistic effect of ozone and temperature both nationally and locally and find evidence of a nonlinear ozone effect and an ozone-temperature interaction at higher temperatures and ozone concentrations.

We consider the task of discovering gene regulatory networks, which are defined as sets of genes and the corresponding transcription factors which regulate their expression levels. This can be viewed as a variable selection problem, potentially with high dimensionality. Variable selection is especially challenging in high-dimensional settings, where it is difficult to detect subtle individual effects and interactions between predictors. Bayesian Additive Regression Trees [BART, Ann. Appl. Stat. 4 (2010) 266–298] provides a novel nonparametric alternative to parametric regression approaches, such as the lasso or stepwise regression, especially when the number of relevant predictors is sparse relative to the total number of available predictors and the fundamental relationships are nonlinear. We develop a principled permutation-based inferential approach for determining when the effect of a selected predictor is likely to be real. Going further, we adapt the BART procedure to incorporate informed prior information about variable importance. We present simulations demonstrating that our method compares favorably to existing parametric and nonparametric procedures in a variety of data settings. To demonstrate the potential of our approach in a biological context, we apply it to the task of inferring the gene regulatory network in yeast (Saccharomyces cerevisiae). We find that our BART-based procedure is best able to recover the subset of covariates with the largest signal compared to other variable selection methods. The methods developed in this work are readily available in the R package bartMachine.

Accurate short-term wind speed forecasting is needed for the rapid development and efficient operation of wind energy resources. This is, however, a very challenging problem. Although on the large scale, the wind speed is related to atmospheric pressure, temperature, and other meteorological variables, no improvement in forecasting accuracy was found by incorporating air pressure and temperature directly into an advanced space–time statistical forecasting model, the trigonometric direction diurnal (TDD) model. This paper proposes to incorporate the geostrophic wind as a new predictor in the TDD model. The geostrophic wind captures the physical relationship between wind and pressure through the observed approximate balance between the pressure gradient force and the Coriolis acceleration due to the Earth’s rotation. Based on our numerical experiments with data from West Texas, our new method produces more accurate forecasts than does the TDD model using air pressure and temperature for 1- to 6-hour-ahead forecasts based on three different evaluation criteria. Furthermore, forecasting errors can be further reduced by using moving average hourly wind speeds to fit the diurnal pattern. For example, our new method obtains between 13.9% and 22.4% overall mean absolute error reduction relative to persistence in 2-hour-ahead forecasts, and between 5.3% and 8.2% reduction relative to the best previous space–time methods in this setting.

Neuroimaging meta-analysis is an important tool for finding consistent effects over studies that each usually have 20 or fewer subjects. Interest in meta-analysis in brain mapping is also driven by a recent focus on so-called “reverse inference”: where as traditional “forward inference” identifies the regions of the brain involved in a task, a reverse inference identifies the cognitive processes that a task engages. Such reverse inferences, however, require a set of meta-analysis, one for each possible cognitive domain. However, existing methods for neuroimaging meta-analysis have significant limitations. Commonly used methods for neuroimaging meta-analysis are not model based, do not provide interpretable parameter estimates, and only produce null hypothesis inferences; further, they are generally designed for a single group of studies and cannot produce reverse inferences. In this work we address these limitations by adopting a nonparametric Bayesian approach for meta-analysis data from multiple classes or types of studies. In particular, foci from each type of study are modeled as a cluster process driven by a random intensity function that is modeled as a kernel convolution of a gamma random field. The type-specific gamma random fields are linked and modeled as a realization of a common gamma random field, shared by all types, that induces correlation between study types and mimics the behavior of a univariate mixed effects model. We illustrate our model on simulation studies and a meta-analysis of five emotions from 219 studies and check model fit by a posterior predictive assessment. In addition, we implement reverse inference by using the model to predict study type from a newly presented study. We evaluate this predictive performance via leave-one-out cross-validation that is efficiently implemented using importance sampling techniques.

The conditional intensity function of a point process is a useful tool for generating probability forecasts of earthquakes. The epidemic-type aftershock sequence (ETAS) model is defined by a conditional intensity function, and the corresponding point process is equivalent to a branching process, assuming that an earthquake generates a cluster of offspring earthquakes (triggered earthquakes or so-called aftershocks). Further, the size of the first-generation cluster depends on the magnitude of the triggering (parent) earthquake. The ETAS model provides a good fit to standard earthquake occurrences. However, there are nonstandard earthquake series that appear under transient stress changes caused by aseismic forces such as volcanic magma or fluid intrusions. These events trigger transient nonstandard earthquake swarms, and they are poorly fitted by the stationary ETAS model. In this study, we examine nonstationary extensions of the ETAS model that cover nonstandard cases. These models allow the parameters to be time-dependent and can be estimated by the empirical Bayes method. The best model is selected among the competing models to provide the inversion solutions of nonstationary changes. To address issues of the uniqueness and robustness of the inversion procedure, this method is demonstrated on an inland swarm activity induced by the 2011 Tohoku-Oki, Japan earthquake of magnitude 9.0.

A common and important problem arising in the study of networks is how to divide the vertices of a given network into one or more groups, called communities, in such a way that vertices of the same community are more interconnected than vertices belonging to different ones. We propose and investigate a testing based community detection procedure called Extraction of Statistically Significant Communities (ESSC). The ESSC procedure is based on $p$-values for the strength of connection between a single vertex and a set of vertices under a reference distribution derived from a conditional configuration network model. The procedure automatically selects both the number of communities in the network and their size. Moreover, ESSC can handle overlapping communities and, unlike the majority of existing methods, identifies “background” vertices that do not belong to a well-defined community. The method has only one parameter, which controls the stringency of the hypothesis tests. We investigate the performance and potential use of ESSC and compare it with a number of existing methods, through a validation study using four real network data sets. In addition, we carry out a simulation study to assess the effectiveness of ESSC in networks with various types of community structure, including networks with overlapping communities and those with background vertices. These results suggest that ESSC is an effective exploratory tool for the discovery of relevant community structure in complex network systems. Data and software are available at http://www.unc.edu/~jameswd/research.html.

Graphical models are widely used to make inferences concerning interplay in multivariate systems. In many applications, data are collected from multiple related but nonidentical units whose underlying networks may differ but are likely to share features. Here we present a hierarchical Bayesian formulation for joint estimation of multiple networks in this nonidentically distributed setting. The approach is general: given a suitable class of graphical models, it uses an exchangeability assumption on networks to provide a corresponding joint formulation. Motivated by emerging experimental designs in molecular biology, we focus on time-course data with interventions, using dynamic Bayesian networks as the graphical models. We introduce a computationally efficient, deterministic algorithm for exact joint inference in this setting. We provide an upper bound on the gains that joint estimation offers relative to separate estimation for each network and empirical results that support and extend the theory, including an extensive simulation study and an application to proteomic data from human cancer cell lines. Finally, we describe approximations that are still more computationally efficient than the exact algorithm and that also demonstrate good empirical performance.