Belief and recollection of autobiographical memories.

In three experiments, undergraduates rated autobiographical memories on scales derived from existing theories of memory. In multiple regression analyses, ratings of the degree to which subjects recollected (i.e., relived) their memories were predicted by visual imagery, auditory imagery, and emotions, whereas ratings of belief in the accuracy of their memories were predicted by knowledge of the setting. Recollection was predicted equally well in between- and within-subjects analyses, but belief consistently had smaller correlations and multiple regression predictions between subjects; individual differences in the cognitive scales that we measured could not account well for individual differences in belief. In contrast, measures of mood (Beck Depression Index) and dissociation (Dissociative Experience Scale) added predictive value for belief, but not for recollection. We also found that highly relived memories almost always had strong visual images and that remember/know judgments made on autobiographical memories were more closely related to belief than to recollection.

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.

Three-dimensional broadband omnidirectional acoustic ground cloak.

The control of sound propagation and reflection has always been the goal of engineers involved in the design of acoustic systems. A recent design approach based on coordinate transformations, which is applicable to many physical systems, together with the development of a new class of engineered materials called metamaterials, has opened the road to the unconstrained control of sound. However, the ideal material parameters prescribed by this methodology are complex and challenging to obtain experimentally, even using metamaterial design approaches. Not surprisingly, experimental demonstration of devices obtained using transformation acoustics is difficult, and has been implemented only in two-dimensional configurations. Here, we demonstrate the design and experimental characterization of an almost perfect three-dimensional, broadband, and, most importantly, omnidirectional acoustic device that renders a region of space three wavelengths in diameter invisible to sound.

Adaptive intervention design in mobile health: Intervention design and development in the Cell Phone Intervention for You trial.

BACKGROUND/AIMS: The obesity epidemic has spread to young adults, and obesity is a significant risk factor for cardiovascular disease. The prominence and increasing functionality of mobile phones may provide an opportunity to deliver longitudinal and scalable weight management interventions in young adults. The aim of this article is to describe the design and development of the intervention tested in the Cell Phone Intervention for You study and to highlight the importance of adaptive intervention design that made it possible. The Cell Phone Intervention for You study was a National Heart, Lung, and Blood Institute-sponsored, controlled, 24-month randomized clinical trial comparing two active interventions to a usual-care control group. Participants were 365 overweight or obese (body mass index≥25 kg/m2) young adults. METHODS: Both active interventions were designed based on social cognitive theory and incorporated techniques for behavioral self-management and motivational enhancement. Initial intervention development occurred during a 1-year formative phase utilizing focus groups and iterative, participatory design. During the intervention testing, adaptive intervention design, where an intervention is updated or extended throughout a trial while assuring the delivery of exactly the same intervention to each cohort, was employed. The adaptive intervention design strategy distributed technical work and allowed introduction of novel components in phases intended to help promote and sustain participant engagement. Adaptive intervention design was made possible by exploiting the mobile phone's remote data capabilities so that adoption of particular application components could be continuously monitored and components subsequently added or updated remotely. RESULTS: The cell phone intervention was delivered almost entirely via cell phone and was always-present, proactive, and interactive-providing passive and active reminders, frequent opportunities for knowledge dissemination, and multiple tools for self-tracking and receiving tailored feedback. The intervention changed over 2 years to promote and sustain engagement. The personal coaching intervention, alternatively, was primarily personal coaching with trained coaches based on a proven intervention, enhanced with a mobile application, but where all interactions with the technology were participant-initiated. CONCLUSION: The complexity and length of the technology-based randomized clinical trial created challenges in engagement and technology adaptation, which were generally discovered using novel remote monitoring technology and addressed using the adaptive intervention design. Investigators should plan to develop tools and procedures that explicitly support continuous remote monitoring of interventions to support adaptive intervention design in long-term, technology-based studies, as well as developing the interventions themselves.

Muscle Logic: New Knowledge Resource for Anatomy Enables Comprehensive Searches of the Literature on the Feeding Muscles of Mammals.

BACKGROUND: In recent years large bibliographic databases have made much of the published literature of biology available for searches. However, the capabilities of the search engines integrated into these databases for text-based bibliographic searches are limited. To enable searches that deliver the results expected by comparative anatomists, an underlying logical structure known as an ontology is required. DEVELOPMENT AND TESTING OF THE ONTOLOGY: Here we present the Mammalian Feeding Muscle Ontology (MFMO), a multi-species ontology focused on anatomical structures that participate in feeding and other oral/pharyngeal behaviors. A unique feature of the MFMO is that a simple, computable, definition of each muscle, which includes its attachments and innervation, is true across mammals. This construction mirrors the logical foundation of comparative anatomy and permits searches using language familiar to biologists. Further, it provides a template for muscles that will be useful in extending any anatomy ontology. The MFMO is developed to support the Feeding Experiments End-User Database Project (FEED, https://feedexp.org/), a publicly-available, online repository for physiological data collected from in vivo studies of feeding (e.g., mastication, biting, swallowing) in mammals. Currently the MFMO is integrated into FEED and also into two literature-specific implementations of Textpresso, a text-mining system that facilitates powerful searches of a corpus of scientific publications. We evaluate the MFMO by asking questions that test the ability of the ontology to return appropriate answers (competency questions). We compare the results of queries of the MFMO to results from similar searches in PubMed and Google Scholar. RESULTS AND SIGNIFICANCE: Our tests demonstrate that the MFMO is competent to answer queries formed in the common language of comparative anatomy, but PubMed and Google Scholar are not. Overall, our results show that by incorporating anatomical ontologies into searches, an expanded and anatomically comprehensive set of results can be obtained. The broader scientific and publishing communities should consider taking up the challenge of semantically enabled search capabilities.