Bayesian Gaussian Copula Factor Models for Mixed Data.

Gaussian factor models have proven widely useful for parsimoniously characterizing dependence in multivariate data. There is a rich literature on their extension to mixed categorical and continuous variables, using latent Gaussian variables or through generalized latent trait models acommodating measurements in the exponential family. However, when generalizing to non-Gaussian measured variables the latent variables typically influence both the dependence structure and the form of the marginal distributions, complicating interpretation and introducing artifacts. To address this problem we propose a novel class of Bayesian Gaussian copula factor models which decouple the latent factors from the marginal distributions. A semiparametric specification for the marginals based on the extended rank likelihood yields straightforward implementation and substantial computational gains. We provide new theoretical and empirical justifications for using this likelihood in Bayesian inference. We propose new default priors for the factor loadings and develop efficient parameter-expanded Gibbs sampling for posterior computation. The methods are evaluated through simulations and applied to a dataset in political science. The models in this paper are implemented in the R package bfa.

Bayesian Analysis of Latent Threshold Dynamic Models

We discuss a general approach to dynamic sparsity modeling in multivariate time series analysis. Time-varying parameters are linked to latent processes that are thresholded to induce zero values adaptively, providing natural mechanisms for dynamic variable inclusion/selection. We discuss Bayesian model specification, analysis and prediction in dynamic regressions, time-varying vector autoregressions, and multivariate volatility models using latent thresholding. Application to a topical macroeconomic time series problem illustrates some of the benefits of the approach in terms of statistical and economic interpretations as well as improved predictions. Supplementary materials for this article are available online. © 2013 Copyright Taylor and Francis Group, LLC.

Latent factor analysis to discover pathway-associated putative segmental aneuploidies in human cancers.

Tumor microenvironmental stresses, such as hypoxia and lactic acidosis, play important roles in tumor progression. Although gene signatures reflecting the influence of these stresses are powerful approaches to link expression with phenotypes, they do not fully reflect the complexity of human cancers. Here, we describe the use of latent factor models to further dissect the stress gene signatures in a breast cancer expression dataset. The genes in these latent factors are coordinately expressed in tumors and depict distinct, interacting components of the biological processes. The genes in several latent factors are highly enriched in chromosomal locations. When these factors are analyzed in independent datasets with gene expression and array CGH data, the expression values of these factors are highly correlated with copy number alterations (CNAs) of the corresponding BAC clones in both the cell lines and tumors. Therefore, variation in the expression of these pathway-associated factors is at least partially caused by variation in gene dosage and CNAs among breast cancers. We have also found the expression of two latent factors without any chromosomal enrichment is highly associated with 12q CNA, likely an instance of "trans"-variations in which CNA leads to the variations in gene expression outside of the CNA region. In addition, we have found that factor 26 (1q CNA) is negatively correlated with HIF-1alpha protein and hypoxia pathways in breast tumors and cell lines. This agrees with, and for the first time links, known good prognosis associated with both a low hypoxia signature and the presence of CNA in this region. Taken together, these results suggest the possibility that tumor segmental aneuploidy makes significant contributions to variation in the lactic acidosis/hypoxia gene signatures in human cancers and demonstrate that latent factor analysis is a powerful means to uncover such a linkage.

Bayesian inference of the number of factors in gene-expression analysis: application to human virus challenge studies.

BACKGROUND: Nonparametric Bayesian techniques have been developed recently to extend the sophistication of factor models, allowing one to infer the number of appropriate factors from the observed data. We consider such techniques for sparse factor analysis, with application to gene-expression data from three virus challenge studies. Particular attention is placed on employing the Beta Process (BP), the Indian Buffet Process (IBP), and related sparseness-promoting techniques to infer a proper number of factors. The posterior density function on the model parameters is computed using Gibbs sampling and variational Bayesian (VB) analysis. RESULTS: Time-evolving gene-expression data are considered for respiratory syncytial virus (RSV), Rhino virus, and influenza, using blood samples from healthy human subjects. These data were acquired in three challenge studies, each executed after receiving institutional review board (IRB) approval from Duke University. Comparisons are made between several alternative means of per-forming nonparametric factor analysis on these data, with comparisons as well to sparse-PCA and Penalized Matrix Decomposition (PMD), closely related non-Bayesian approaches. CONCLUSIONS: Applying the Beta Process to the factor scores, or to the singular values of a pseudo-SVD construction, the proposed algorithms infer the number of factors in gene-expression data. For real data the "true" number of factors is unknown; in our simulations we consider a range of noise variances, and the proposed Bayesian models inferred the number of factors accurately relative to other methods in the literature, such as sparse-PCA and PMD. We have also identified a "pan-viral" factor of importance for each of the three viruses considered in this study. We have identified a set of genes associated with this pan-viral factor, of interest for early detection of such viruses based upon the host response, as quantified via gene-expression data.

Bayesian Emulation for Sequential Modeling, Inference and Decision Analysis

The advances in three related areas of state-space modeling, sequential Bayesian learning, and decision analysis are addressed, with the statistical challenges of scalability and associated dynamic sparsity. The key theme that ties the three areas is Bayesian model emulation: solving challenging analysis/computational problems using creative model emulators. This idea defines theoretical and applied advances in non-linear, non-Gaussian state-space modeling, dynamic sparsity, decision analysis and statistical computation, across linked contexts of multivariate time series and dynamic networks studies. Examples and applications in financial time series and portfolio analysis, macroeconomics and internet studies from computational advertising demonstrate the utility of the core methodological innovations.

Chapter 1 summarizes the three areas/problems and the key idea of emulating in those areas. Chapter 2 discusses the sequential analysis of latent threshold models with use of emulating models that allows for analytical filtering to enhance the efficiency of posterior sampling. Chapter 3 examines the emulator model in decision analysis, or the synthetic model, that is equivalent to the loss function in the original minimization problem, and shows its performance in the context of sequential portfolio optimization. Chapter 4 describes the method for modeling the steaming data of counts observed on a large network that relies on emulating the whole, dependent network model by independent, conjugate sub-models customized to each set of flow. Chapter 5 reviews those advances and makes the concluding remarks.

Prediction in dynamic models with time-dependent conditional variances

This paper considers forecasting the conditional mean and variance from a single-equation dynamic model with autocorrelated disturbances following an ARMA process, and innovations with time-dependent conditional heteroskedasticity as represented by a linear GARCH process. Expressions for the minimum MSE predictor and the conditional MSE are presented. We also derive the formula for all the theoretical moments of the prediction error distribution from a general dynamic model with GARCH(1, 1) innovations. These results are then used in the construction of ex ante prediction confidence intervals by means of the Cornish-Fisher asymptotic expansion. An empirical example relating to the uncertainty of the expected depreciation of foreign exchange rates illustrates the usefulness of the results. © 1992.

Data to Decision in a Dynamic Ocean: Robust Species Distribution Models and Spatial Decision Frameworks

Human use of the oceans is increasingly in conflict with conservation of endangered species. Methods for managing the spatial and temporal placement of industries such as military, fishing, transportation and offshore energy, have historically been post hoc; i.e. the time and place of human activity is often already determined before assessment of environmental impacts. In this dissertation, I build robust species distribution models in two case study areas, US Atlantic (Best et al. 2012) and British Columbia (Best et al. 2015), predicting presence and abundance respectively, from scientific surveys. These models are then applied to novel decision frameworks for preemptively suggesting optimal placement of human activities in space and time to minimize ecological impacts: siting for offshore wind energy development, and routing ships to minimize risk of striking whales. Both decision frameworks relate the tradeoff between conservation risk and industry profit with synchronized variable and map views as online spatial decision support systems.

For siting offshore wind energy development (OWED) in the U.S. Atlantic (chapter 4), bird density maps are combined across species with weights of OWED sensitivity to collision and displacement and 10 km2 sites are compared against OWED profitability based on average annual wind speed at 90m hub heights and distance to transmission grid. A spatial decision support system enables toggling between the map and tradeoff plot views by site. A selected site can be inspected for sensitivity to a cetaceans throughout the year, so as to capture months of the year which minimize episodic impacts of pre-operational activities such as seismic airgun surveying and pile driving.

Routing ships to avoid whale strikes (chapter 5) can be similarly viewed as a tradeoff, but is a different problem spatially. A cumulative cost surface is generated from density surface maps and conservation status of cetaceans, before applying as a resistance surface to calculate least-cost routes between start and end locations, i.e. ports and entrance locations to study areas. Varying a multiplier to the cost surface enables calculation of multiple routes with different costs to conservation of cetaceans versus cost to transportation industry, measured as distance. Similar to the siting chapter, a spatial decisions support system enables toggling between the map and tradeoff plot view of proposed routes. The user can also input arbitrary start and end locations to calculate the tradeoff on the fly.

Essential to the input of these decision frameworks are distributions of the species. The two preceding chapters comprise species distribution models from two case study areas, U.S. Atlantic (chapter 2) and British Columbia (chapter 3), predicting presence and density, respectively. Although density is preferred to estimate potential biological removal, per Marine Mammal Protection Act requirements in the U.S., all the necessary parameters, especially distance and angle of observation, are less readily available across publicly mined datasets.

In the case of predicting cetacean presence in the U.S. Atlantic (chapter 2), I extracted datasets from the online OBIS-SEAMAP geo-database, and integrated scientific surveys conducted by ship (n=36) and aircraft (n=16), weighting a Generalized Additive Model by minutes surveyed within space-time grid cells to harmonize effort between the two survey platforms. For each of 16 cetacean species guilds, I predicted the probability of occurrence from static environmental variables (water depth, distance to shore, distance to continental shelf break) and time-varying conditions (monthly sea-surface temperature). To generate maps of presence vs. absence, Receiver Operator Characteristic (ROC) curves were used to define the optimal threshold that minimizes false positive and false negative error rates. I integrated model outputs, including tables (species in guilds, input surveys) and plots (fit of environmental variables, ROC curve), into an online spatial decision support system, allowing for easy navigation of models by taxon, region, season, and data provider.

For predicting cetacean density within the inner waters of British Columbia (chapter 3), I calculated density from systematic, line-transect marine mammal surveys over multiple years and seasons (summer 2004, 2005, 2008, and spring/autumn 2007) conducted by Raincoast Conservation Foundation. Abundance estimates were calculated using two different methods: Conventional Distance Sampling (CDS) and Density Surface Modelling (DSM). CDS generates a single density estimate for each stratum, whereas DSM explicitly models spatial variation and offers potential for greater precision by incorporating environmental predictors. Although DSM yields a more relevant product for the purposes of marine spatial planning, CDS has proven to be useful in cases where there are fewer observations available for seasonal and inter-annual comparison, particularly for the scarcely observed elephant seal. Abundance estimates are provided on a stratum-specific basis. Steller sea lions and harbour seals are further differentiated by ‘hauled out’ and ‘in water’. This analysis updates previous estimates (Williams & Thomas 2007) by including additional years of effort, providing greater spatial precision with the DSM method over CDS, novel reporting for spring and autumn seasons (rather than summer alone), and providing new abundance estimates for Steller sea lion and northern elephant seal. In addition to providing a baseline of marine mammal abundance and distribution, against which future changes can be compared, this information offers the opportunity to assess the risks posed to marine mammals by existing and emerging threats, such as fisheries bycatch, ship strikes, and increased oil spill and ocean noise issues associated with increases of container ship and oil tanker traffic in British Columbia’s continental shelf waters.

Starting with marine animal observations at specific coordinates and times, I combine these data with environmental data, often satellite derived, to produce seascape predictions generalizable in space and time. These habitat-based models enable prediction of encounter rates and, in the case of density surface models, abundance that can then be applied to management scenarios. Specific human activities, OWED and shipping, are then compared within a tradeoff decision support framework, enabling interchangeable map and tradeoff plot views. These products make complex processes transparent for gaming conservation, industry and stakeholders towards optimal marine spatial management, fundamental to the tenets of marine spatial planning, ecosystem-based management and dynamic ocean management.

Volume, volatility, and leverage: A dynamic analysis

This paper uses dynamic impulse response analysis to investigate the interrelationships among stock price volatility, trading volume, and the leverage effect. Dynamic impulse response analysis is a technique for analyzing the multi-step-ahead characteristics of a nonparametric estimate of the one-step conditional density of a strictly stationary process. The technique is the generalization to a nonlinear process of Sims-style impulse response analysis for linear models. In this paper, we refine the technique and apply it to a long panel of daily observations on the price and trading volume of four stocks actively traded on the NYSE: Boeing, Coca-Cola, IBM, and MMM.

Growth factor erv1-like modulates Drp1 to preserve mitochondrial dynamics and function in mouse embryonic stem cells.

The relationship of mitochondrial dynamics and function to pluripotency are rather poorly understood aspects of stem cell biology. Here we show that growth factor erv1-like (Gfer) is involved in preserving mouse embryonic stem cell (ESC) mitochondrial morphology and function. Knockdown (KD) of Gfer in ESCs leads to decreased pluripotency marker expression, embryoid body (EB) formation, cell survival, and loss of mitochondrial function. Mitochondria in Gfer-KD ESCs undergo excessive fragmentation and mitophagy, whereas those in ESCs overexpressing Gfer appear elongated. Levels of the mitochondrial fission GTPase dynamin-related protein 1 (Drp1) are highly elevated in Gfer-KD ESCs and decreased in Gfer-overexpressing cells. Treatment with a specific inhibitor of Drp1 rescues mitochondrial function and apoptosis, whereas expression of Drp1-dominant negative resulted in the restoration of pluripotency marker expression in Gfer-KD ESCs. Altogether, our data reveal a novel prosurvival role for Gfer in maintaining mitochondrial fission-fusion dynamics in pluripotent ESCs.

Multiple Dynamic Processes Contribute to the Complex Steady Shear Behavior of Cross-Linked Supramolecular Networks of Semidilute Entangled Polymer Solutions.

Molecular theories of shear thickening and shear thinning in associative polymer networks are typically united in that they involve a single kinetic parameter that describes the network -- a relaxation time that is related to the lifetime of the associative bonds. Here we report the steady-shear behavior of two structurally identical metallo-supramolecular polymer networks, for which single-relaxation parameter models break down in dramatic fashion. The networks are formed by the addition of reversible cross-linkers to semidilute entangled solutions of PVP in DMSO, and they differ only in the lifetime of the reversible cross-links. Shear thickening is observed for cross-linkers that have a slower dissociation rate (17 s(-1)), while shear thinning is observed for samples that have a faster dissociation rate (ca. 1400 s(-1)). The difference in the steady shear behavior of the unentangled vs. entangled regime reveals an unexpected, additional competing relaxation, ascribed to topological disentanglement in the semidilute entangled regime that contributes to the rheological properties.

MYC activity mitigates response to rapamycin in prostate cancer through eukaryotic initiation factor 4E-binding protein 1-mediated inhibition of autophagy.

Loss of PTEN and activation of phosphoinositide 3-kinase are commonly observed in advanced prostate cancer. Inhibition of mammalian target of rapamycin (mTOR), a downstream target of phosphoinositide 3-kinase signaling, results in cell cycle arrest and apoptosis in multiple in vitro and in vivo models of prostate cancer. However, single-agent use of mTOR inhibition has limited clinical success, and the identification of molecular events mitigating tumor response to mTOR inhibition remains a critical question. Here, using genetically engineered human prostate epithelial cells (PrEC), we show that MYC, a frequent target of genetic gain in prostate cancers, abrogates sensitivity to rapamycin by decreasing rapamycin-induced cytostasis and autophagy. Analysis of MYC and the mTOR pathway in human prostate tumors and PrEC showed selective increased expression of eukaryotic initiation factor 4E-binding protein 1 (4EBP1) with gain in MYC copy number or forced MYC expression, respectively. We have also found that MYC binds to regulatory regions of the 4EBP1 gene. Suppression of 4EBP1 expression resulted in resensitization of MYC-expressing PrEC to rapamycin and increased autophagy. Taken together, our findings suggest that MYC expression abrogates sensitivity to rapamycin through increased expression of 4EBP1 and reduced autophagy.

Adaptive Mixture Modelling Metropolis Methods for Bayesian Analysis of Non-linear State-Space Models.

We describe a strategy for Markov chain Monte Carlo analysis of non-linear, non-Gaussian state-space models involving batch analysis for inference on dynamic, latent state variables and fixed model parameters. The key innovation is a Metropolis-Hastings method for the time series of state variables based on sequential approximation of filtering and smoothing densities using normal mixtures. These mixtures are propagated through the non-linearities using an accurate, local mixture approximation method, and we use a regenerating procedure to deal with potential degeneracy of mixture components. This provides accurate, direct approximations to sequential filtering and retrospective smoothing distributions, and hence a useful construction of global Metropolis proposal distributions for simulation of posteriors for the set of states. This analysis is embedded within a Gibbs sampler to include uncertain fixed parameters. We give an example motivated by an application in systems biology. Supplemental materials provide an example based on a stochastic volatility model as well as MATLAB code.

Comparison of dynamic balance in adolescent male soccer players from rwanda and the United States.

PURPOSE/BACKGROUND: Dynamic balance is an important component of motor skill development. Poor dynamic balance has previously been associated with sport related injury. However, the vast majority of dynamic balance studies as they relate to sport injury have occurred in developed North American or European countries. Thus, the purpose of this study was to compare dynamic balance in adolescent male soccer players from Rwanda to a matched group from the United States. METHODS: Twenty-six adolescent male soccer players from Rwanda and 26 age- and gender-matched control subjects from the United States were screened using the Lower Quarter Y Balance Test during their pre-participation physical. Reach asymmetry (cm) between limbs was examined for all reach directions. In addition, reach distance in each direction (normalized to limb length, %LL) and the composite reach score (also normalized to %LL) were examined. Dependent samples t-tests were performed with significant differences identified at p<0.05. RESULTS: Twenty-six male soccer players from Rwanda (R) were matched to twenty-six male soccer players from the United States (US). The Rwandan soccer players performed better in the anterior (R: 83.9 ± 3.2 %LL; US: 76.5 ± 6.6 %LL, p<0.01), posterolateral (R: 114.4 ± 8.3 %LL ; US: 106.5 ± 8.2 %LL, p<0.01) and composite (R: 105.6 ± 1.3 %LL; US: 97.8 ± 6.2 %LL, p<0.01) reach scores. No significant differences between groups were observed for reach asymmetry. CONCLUSIONS: Adolescent soccer players from Rwanda exhibit superior performance on a standardized dynamic balance test as comparison to similar athletes from the United States. The examination of movement abilities of athletes from countries of various origins may allow for a greater understanding of the range of true normative values for dynamic balance. LEVELS OF EVIDENCE: 3b.

Implant healing in experimental animal models of diabetes.

Diabetes mellitus is becoming increasingly prevalent worldwide. Additionally, there is an increasing number of patients receiving implantable devices such as glucose sensors and orthopedic implants. Thus, it is likely that the number of diabetic patients receiving these devices will also increase. Even though implantable medical devices are considered biocompatible by the Food and Drug Administration, the adverse tissue healing that occurs adjacent to these foreign objects is a leading cause of their failure. This foreign body response leads to fibrosis, encapsulation of the device, and a reduction or cessation of device performance. A second adverse event is microbial infection of implanted devices, which can lead to persistent local and systemic infections and also exacerbates the fibrotic response. Nearly half of all nosocomial infections are associated with the presence of an indwelling medical device. Events associated with both the foreign body response and implant infection can necessitate device removal and may lead to amputation, which is associated with significant morbidity and cost. Diabetes mellitus is generally indicated as a risk factor for the infection of a variety of implants such as prosthetic joints, pacemakers, implantable cardioverter defibrillators, penile implants, and urinary catheters. Implant infection rates in diabetic patients vary depending upon the implant and the microorganism, however, for example, diabetes was found to be a significant variable associated with a nearly 7.2% infection rate for implantable cardioverter defibrillators by the microorganism Candida albicans. While research has elucidated many of the altered mechanisms of diabetic cutaneous wound healing, the internal healing adjacent to indwelling medical devices in a diabetic model has rarely been studied. Understanding this healing process is crucial to facilitating improved device design. The purpose of this article is to summarize the physiologic factors that influence wound healing and infection in diabetic patients, to review research concerning diabetes and biomedical implants and device infection, and to critically analyze which diabetic animal model might be advantageous for assessing internal healing adjacent to implanted devices.