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.

R5 clade C SHIV strains with tier 1 or 2 neutralization sensitivity: tools to dissect env evolution and to develop AIDS vaccines in primate models.

BACKGROUND: HIV-1 clade C (HIV-C) predominates worldwide, and anti-HIV-C vaccines are urgently needed. Neutralizing antibody (nAb) responses are considered important but have proved difficult to elicit. Although some current immunogens elicit antibodies that neutralize highly neutralization-sensitive (tier 1) HIV strains, most circulating HIVs exhibiting a less sensitive (tier 2) phenotype are not neutralized. Thus, both tier 1 and 2 viruses are needed for vaccine discovery in nonhuman primate models. METHODOLOGY/PRINCIPAL FINDINGS: We constructed a tier 1 simian-human immunodeficiency virus, SHIV-1157ipEL, by inserting an "early," recently transmitted HIV-C env into the SHIV-1157ipd3N4 backbone [1] encoding a "late" form of the same env, which had evolved in a SHIV-infected rhesus monkey (RM) with AIDS. SHIV-1157ipEL was rapidly passaged to yield SHIV-1157ipEL-p, which remained exclusively R5-tropic and had a tier 1 phenotype, in contrast to "late" SHIV-1157ipd3N4 (tier 2). After 5 weekly low-dose intrarectal exposures, SHIV-1157ipEL-p systemically infected 16 out of 17 RM with high peak viral RNA loads and depleted gut CD4+ T cells. SHIV-1157ipEL-p and SHIV-1157ipd3N4 env genes diverge mostly in V1/V2. Molecular modeling revealed a possible mechanism for the increased neutralization resistance of SHIV-1157ipd3N4 Env: V2 loops hindering access to the CD4 binding site, shown experimentally with nAb b12. Similar mutations have been linked to decreased neutralization sensitivity in HIV-C strains isolated from humans over time, indicating parallel HIV-C Env evolution in humans and RM. CONCLUSIONS/SIGNIFICANCE: SHIV-1157ipEL-p, the first tier 1 R5 clade C SHIV, and SHIV-1157ipd3N4, its tier 2 counterpart, represent biologically relevant tools for anti-HIV-C vaccine development in primates.

The role of GRK6 in animal models of Parkinson's disease and L-DOPA treatment.

G protein-coupled Receptor Kinase 6 (GRK6) belongs to a family of kinases that phosphorylate GPCRs. GRK6 levels were found to be altered in Parkinson's Disease (PD) and D(2) dopamine receptors are supersensitive in mice lacking GRK6 (GRK6-KO mice). To understand how GRK6 modulates the behavioral manifestations of dopamine deficiency and responses to L-DOPA, we used three approaches to model PD in GRK6-KO mice: 1) the cataleptic response to haloperidol; 2) introducing GRK6 mutation to an acute model of absolute dopamine deficiency, DDD mice; 3) hemiparkinsonian 6-OHDA model. Furthermore, dopamine-related striatal signaling was analyzed by assessing the phosphorylation of AKT/GSK3β and ERK1/2. GRK6 deficiency reduced cataleptic behavior, potentiated the acute effect of L-DOPA in DDD mice, reduced rotational behavior in hemi-parkinsonian mice, and reduced abnormal involuntary movements induced by chronic L-DOPA. These data indicate that approaches to regulate GRK6 activity could be useful in modulating both therapeutic and side-effects of L-DOPA.

Interpreting Human Genetic Variation through Genomics and In Vivo Models

Improvements in genomic technology, both in the increased speed and reduced cost of sequencing, have expanded the appreciation of the abundance of human genetic variation. However the sheer amount of variation, as well as the varying type and genomic content of variation, poses a challenge in understanding the clinical consequence of a single mutation. This work uses several methodologies to interpret the observed variation in the human genome, and presents novel strategies for the prediction of allele pathogenicity.

Using the zebrafish model system as an in vivo assay of allele function, we identified a novel driver of Bardet-Biedl Syndrome (BBS) in CEP76. A combination of targeted sequencing of 785 cilia-associated genes in a cohort of BBS patients and subsequent in vivo functional assays recapitulating the human phenotype gave strong evidence for the role of CEP76 mutations in the pathology of an affected family. This portion of the work demonstrated the necessity of functional testing in validating disease-associated mutations, and added to the catalogue of known BBS disease genes.

Further study into the role of copy-number variations (CNVs) in a cohort of BBS patients showed the significant contribution of CNVs to disease pathology. Using high-density array comparative genomic hybridization (aCGH) we were able to identify pathogenic CNVs as small as several hundred bp. Dissection of constituent gene and in vivo experiments investigating epistatic interactions between affected genes allowed for an appreciation of several paradigms by which CNVs can contribute to disease. This study revealed that the contribution of CNVs to disease in BBS patients is much higher than previously expected, and demonstrated the necessity of consideration of CNV contribution in future (and retrospective) investigations of human genetic disease.

Finally, we used a combination of comparative genomics and in vivo complementation assays to identify second-site compensatory modification of pathogenic alleles. These pathogenic alleles, which are found compensated in other species (termed compensated pathogenic deviations [CPDs]), represent a significant fraction (from 3 – 10%) of human disease-associated alleles. In silico pathogenicity prediction algorithms, a valuable method of allele prioritization, often misrepresent these alleles as benign, leading to omission of possibly informative variants in studies of human genetic disease. We created a mathematical model that was able to predict CPDs and putative compensatory sites, and functionally showed in vivo that second-site mutation can mitigate the pathogenicity of disease alleles. Additionally, we made publically available an in silico module for the prediction of CPDs and modifier sites.

These studies have advanced the ability to interpret the pathogenicity of multiple types of human variation, as well as made available tools for others to do so as well.

Bayesian Inference in Large-scale Problems

Many modern applications fall into the category of "large-scale" statistical problems, in which both the number of observations n and the number of features or parameters p may be large. Many existing methods focus on point estimation, despite the continued relevance of uncertainty quantification in the sciences, where the number of parameters to estimate often exceeds the sample size, despite huge increases in the value of n typically seen in many fields. Thus, the tendency in some areas of industry to dispense with traditional statistical analysis on the basis that "n=all" is of little relevance outside of certain narrow applications. The main result of the Big Data revolution in most fields has instead been to make computation much harder without reducing the importance of uncertainty quantification. Bayesian methods excel at uncertainty quantification, but often scale poorly relative to alternatives. This conflict between the statistical advantages of Bayesian procedures and their substantial computational disadvantages is perhaps the greatest challenge facing modern Bayesian statistics, and is the primary motivation for the work presented here.

Two general strategies for scaling Bayesian inference are considered. The first is the development of methods that lend themselves to faster computation, and the second is design and characterization of computational algorithms that scale better in n or p. In the first instance, the focus is on joint inference outside of the standard problem of multivariate continuous data that has been a major focus of previous theoretical work in this area. In the second area, we pursue strategies for improving the speed of Markov chain Monte Carlo algorithms, and characterizing their performance in large-scale settings. Throughout, the focus is on rigorous theoretical evaluation combined with empirical demonstrations of performance and concordance with the theory.

One topic we consider is modeling the joint distribution of multivariate categorical data, often summarized in a contingency table. Contingency table analysis routinely relies on log-linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a reduced rank tensor factorization of the probability mass function for multivariate categorical data, while log-linear models achieve dimensionality reduction through sparsity. Little is known about the relationship between these notions of dimensionality reduction in the two paradigms. In Chapter 2, we derive several results relating the support of a log-linear model to nonnegative ranks of the associated probability tensor. Motivated by these findings, we propose a new collapsed Tucker class of tensor decompositions, which bridge existing PARAFAC and Tucker decompositions, providing a more flexible framework for parsimoniously characterizing multivariate categorical data. Taking a Bayesian approach to inference, we illustrate empirical advantages of the new decompositions.

Latent class models for the joint distribution of multivariate categorical, such as the PARAFAC decomposition, data play an important role in the analysis of population structure. In this context, the number of latent classes is interpreted as the number of genetically distinct subpopulations of an organism, an important factor in the analysis of evolutionary processes and conservation status. Existing methods focus on point estimates of the number of subpopulations, and lack robust uncertainty quantification. Moreover, whether the number of latent classes in these models is even an identified parameter is an open question. In Chapter 3, we show that when the model is properly specified, the correct number of subpopulations can be recovered almost surely. We then propose an alternative method for estimating the number of latent subpopulations that provides good quantification of uncertainty, and provide a simple procedure for verifying that the proposed method is consistent for the number of subpopulations. The performance of the model in estimating the number of subpopulations and other common population structure inference problems is assessed in simulations and a real data application.

In contingency table analysis, sparse data is frequently encountered for even modest numbers of variables, resulting in non-existence of maximum likelihood estimates. A common solution is to obtain regularized estimates of the parameters of a log-linear model. Bayesian methods provide a coherent approach to regularization, but are often computationally intensive. Conjugate priors ease computational demands, but the conjugate Diaconis--Ylvisaker priors for the parameters of log-linear models do not give rise to closed form credible regions, complicating posterior inference. In Chapter 4 we derive the optimal Gaussian approximation to the posterior for log-linear models with Diaconis--Ylvisaker priors, and provide convergence rate and finite-sample bounds for the Kullback-Leibler divergence between the exact posterior and the optimal Gaussian approximation. We demonstrate empirically in simulations and a real data application that the approximation is highly accurate, even in relatively small samples. The proposed approximation provides a computationally scalable and principled approach to regularized estimation and approximate Bayesian inference for log-linear models.

Another challenging and somewhat non-standard joint modeling problem is inference on tail dependence in stochastic processes. In applications where extreme dependence is of interest, data are almost always time-indexed. Existing methods for inference and modeling in this setting often cluster extreme events or choose window sizes with the goal of preserving temporal information. In Chapter 5, we propose an alternative paradigm for inference on tail dependence in stochastic processes with arbitrary temporal dependence structure in the extremes, based on the idea that the information on strength of tail dependence and the temporal structure in this dependence are both encoded in waiting times between exceedances of high thresholds. We construct a class of time-indexed stochastic processes with tail dependence obtained by endowing the support points in de Haan's spectral representation of max-stable processes with velocities and lifetimes. We extend Smith's model to these max-stable velocity processes and obtain the distribution of waiting times between extreme events at multiple locations. Motivated by this result, a new definition of tail dependence is proposed that is a function of the distribution of waiting times between threshold exceedances, and an inferential framework is constructed for estimating the strength of extremal dependence and quantifying uncertainty in this paradigm. The method is applied to climatological, financial, and electrophysiology data.

The remainder of this thesis focuses on posterior computation by Markov chain Monte Carlo. The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis. It has long been common to control computation time by making approximations to the Markov transition kernel. Comparatively little attention has been paid to convergence and estimation error in these approximating Markov Chains. In Chapter 6, we propose a framework for assessing when to use approximations in MCMC algorithms, and how much error in the transition kernel should be tolerated to obtain optimal estimation performance with respect to a specified loss function and computational budget. The results require only ergodicity of the exact kernel and control of the kernel approximation accuracy. The theoretical framework is applied to approximations based on random subsets of data, low-rank approximations of Gaussian processes, and a novel approximating Markov chain for discrete mixture models.

Data augmentation Gibbs samplers are arguably the most popular class of algorithm for approximately sampling from the posterior distribution for the parameters of generalized linear models. The truncated Normal and Polya-Gamma data augmentation samplers are standard examples for probit and logit links, respectively. Motivated by an important problem in quantitative advertising, in Chapter 7 we consider the application of these algorithms to modeling rare events. We show that when the sample size is large but the observed number of successes is small, these data augmentation samplers mix very slowly, with a spectral gap that converges to zero at a rate at least proportional to the reciprocal of the square root of the sample size up to a log factor. In simulation studies, moderate sample sizes result in high autocorrelations and small effective sample sizes. Similar empirical results are observed for related data augmentation samplers for multinomial logit and probit models. When applied to a real quantitative advertising dataset, the data augmentation samplers mix very poorly. Conversely, Hamiltonian Monte Carlo and a type of independence chain Metropolis algorithm show good mixing on the same dataset.

Mixtures of g-priors in Generalized Linear Models

Mixtures of Zellner's g-priors have been studied extensively in linear models and have been shown to have numerous desirable properties for Bayesian variable selection and model averaging. Several extensions of g-priors to Generalized Linear Models (GLMs) have been proposed in the literature; however, the choice of prior distribution of g and resulting properties for inference have received considerably less attention. In this paper, we extend mixtures of g-priors to GLMs by assigning the truncated Compound Confluent Hypergeometric (tCCH) distribution to 1/(1+g) and illustrate how this prior distribution encompasses several special cases of mixtures of g-priors in the literature, such as the Hyper-g, truncated Gamma, Beta-prime, and the Robust prior. Under an integrated Laplace approximation to the likelihood, the posterior distribution of 1/(1+g) is in turn a tCCH distribution, and approximate marginal likelihoods are thus available analytically. We discuss the local geometric properties of the g-prior in GLMs and show that specific choices of the hyper-parameters satisfy the various desiderata for model selection proposed by Bayarri et al, such as asymptotic model selection consistency, information consistency, intrinsic consistency, and measurement invariance. We also illustrate inference using these priors and contrast them to others in the literature via simulation and real examples.

If smoking increases absences, does quitting reduce them?

OBJECTIVE: This study examined the impact of smoking, quitting, and time since quit on absences from work. METHODS: Data from the nationally representative Tobacco Use Supplements of the 1992/93, 1995/96, and 1998/99 Current Population Surveys were used. The study included full time workers aged between 18-64 years, yielding a sample size of 383 778 workers. A binary indicator of absence due to sickness in the last week was analysed as a function of smoking status including time since quit for former smokers. Extensive demographic variables were included as controls in all models. RESULTS: In initial comparisons between current and former smokers, smoking increased absences, but quitting did not reduce them. However, when length of time since quit was examined, it was discovered that those who quit within the last year, and especially the last three months, had a much greater probability of absences than did current smokers. As the time since quitting increased, absences returned to a rate somewhere between that of never and current smokers. Interactions between health and smoking status significantly improved the fit of the model. CONCLUSIONS: Smokers who quit reduced their absences over time but increase their absences immediately after quitting. Quitting ill may account for some but not all of this short run impact.

B-lymphocyte effector functions in health and disease.

B-lymphocytes have traditionally been thought to contribute to immunity and autoimmune disease through terminal differentiation into plasma cells that secrete antibody. However, studies in mice and recent clinical studies have demonstrated that genetically altered B-cell function and B-cell-targeted therapies can significantly affect autoimmune diseases that were predominantly thought to be T-cell-mediated. B-cell depletion in mouse models of disease has also led to the identification of alternative B-cell effector functions that regulate normal immune responses and autoimmune disease. This review highlights multiple B-cell effector mechanisms, including the promotion of cellular immunity, the negative regulation of immune responses, and the production of pathogenic antibodies.

The impact of shame on health-related quality of life among HIV-positive adults with a history of childhood sexual abuse.

Childhood sexual abuse is prevalent among people living with HIV, and the experience of shame is a common consequence of childhood sexual abuse and HIV infection. This study examined the role of shame in health-related quality of life among HIV-positive adults who have experienced childhood sexual abuse. Data from 247 HIV-infected adults with a history of childhood sexual abuse were analyzed. Hierarchical linear regression was conducted to assess the impact of shame regarding both sexual abuse and HIV infection, while controlling for demographic, clinical, and psychosocial factors. In bivariate analyses, shame regarding sexual abuse and HIV infection were each negatively associated with health-related quality of life and its components (physical well-being, function and global well-being, emotional and social well-being, and cognitive functioning). After controlling for demographic, clinical, and psychosocial factors, HIV-related, but not sexual abuse-related, shame remained a significant predictor of reduced health-related quality of life, explaining up to 10% of the variance in multivariable models for overall health-related quality of life, emotional, function and global, and social well-being and cognitive functioning over and above that of other variables entered into the model. Additionally, HIV symptoms, perceived stress, and perceived availability of social support were associated with health-related quality of life in multivariable models. Shame is an important and modifiable predictor of health-related quality of life in HIV-positive populations, and medical and mental health providers serving HIV-infected populations should be aware of the importance of shame and its impact on the well-being of their patients.

Polymorphisms in the ACE and ADRB2 genes and risks of aging-associated phenotypes: the case of myocardial infarction.

Multiple functions of the beta2-adrenergic receptor (ADRB2) and angiotensin-converting enzyme (ACE) genes warrant studies of their associations with aging-related phenotypes. We focus on multimarker analyses and analyses of the effects of compound genotypes of two polymorphisms in the ADRB2 gene, rs1042713 and rs1042714, and 11 polymorphisms of the ACE gene, on the risk of such an aging-associated phenotype as myocardial infarction (MI). We used the data from a genotyped sample of the Framingham Heart Study Offspring (FHSO) cohort (n = 1500) followed for about 36 years with six examinations. The ADRB2 rs1042714 (C-->G) polymorphism and two moderately correlated (r(2) = 0.77) ACE polymorphisms, rs4363 (A-->G) and rs12449782 (A-->G), were significantly associated with risks of MI in this aging cohort in multimarker models. Predominantly linked ACE genotypes exhibited opposite effects on MI risks, e.g., the AA (rs12449782) genotype had a detrimental effect, whereas the predominantly linked AA (rs4363) genotype exhibited a protective effect. This trade-off occurs as a result of the opposite effects of rare compound genotypes of the ACE polymorphisms with a single dose of the AG heterozygote. This genetic trade-off is further augmented by the selective modulating effect of the rs1042714 ADRB2 polymorphism. The associations were not altered by adjustment for common MI risk factors. The results suggest that effects of single specific genetic variants of the ADRB2 and ACE genes on MI can be readily altered by gene-gene or/and gene-environmental interactions, especially in large heterogeneous samples. Multimarker genetic analyses should benefit studies of complex aging-associated phenotypes.

Evaluating intra-articular drug delivery for the treatment of osteoarthritis in a rat model.

Osteoarthritis (OA) is a degenerative joint disease that can result in joint pain, loss of joint function, and deleterious effects on activity levels and lifestyle habits. Current therapies for OA are largely aimed at symptomatic relief and may have limited effects on the underlying cascade of joint degradation. Local drug delivery strategies may provide for the development of more successful OA treatment outcomes that have potential to reduce local joint inflammation, reduce joint destruction, offer pain relief, and restore patient activity levels and joint function. As increasing interest turns toward intra-articular drug delivery routes, parallel interest has emerged in evaluating drug biodistribution, safety, and efficacy in preclinical models. Rodent models provide major advantages for the development of drug delivery strategies, chiefly because of lower cost, successful replication of human OA-like characteristics, rapid disease development, and small joint volumes that enable use of lower total drug amounts during protocol development. These models, however, also offer the potential to investigate the therapeutic effects of local drug therapy on animal behavior, including pain sensitivity thresholds and locomotion characteristics. Herein, we describe a translational paradigm for the evaluation of an intra-articular drug delivery strategy in a rat OA model. This model, a rat interleukin-1beta overexpression model, offers the ability to evaluate anti-interleukin-1 therapeutics for drug biodistribution, activity, and safety as well as the therapeutic relief of disease symptoms. Once the action against interleukin-1 is confirmed in vivo, the newly developed anti-inflammatory drug can be evaluated for evidence of disease-modifying effects in more complex preclinical models.

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.

Understanding GPU programming for statistical computation: Studies in massively parallel massive mixtures

This article describes advances in statistical computation for large-scale data analysis in structured Bayesian mixture models via graphics processing unit (GPU) programming. The developments are partly motivated by computational challenges arising in fitting models of increasing heterogeneity to increasingly large datasets. An example context concerns common biological studies using high-throughput technologies generating many, very large datasets and requiring increasingly high-dimensional mixture models with large numbers of mixture components.We outline important strategies and processes for GPU computation in Bayesian simulation and optimization approaches, give examples of the benefits of GPU implementations in terms of processing speed and scale-up in ability to analyze large datasets, and provide a detailed, tutorial-style exposition that will benefit readers interested in developing GPU-based approaches in other statistical models. Novel, GPU-oriented approaches to modifying existing algorithms software design can lead to vast speed-up and, critically, enable statistical analyses that presently will not be performed due to compute time limitations in traditional computational environments. Supplementalmaterials are provided with all source code, example data, and details that will enable readers to implement and explore the GPU approach in this mixture modeling context. © 2010 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.