Migration and fishing in Indonesian coastal villages.

The coastal ecosystems in Southeast Asia are under increased pressure from local and global change. This paper examines human migration and the use of marine resources in coastal villages in the Minahasa district of North Sulawesi, Indonesia. Primary data were collected through interviews with village leaders, focus groups, and a sample survey of 600 fishing households. Migration is responsible for at least one quarter of the total growth during the past decade. All groups of fishermen report falling productivity of the nearshore fisheries. Econometric analysis is used to examine the weekly fish catch of the artisanal fishing sector. Migration status and socioeconomic variables seem to have no systematic effect, while fishing effort (labor, boat, and gear), the degree of specialization, and the remoteness of villages are found to be positively related to weekly fish catches.

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.

Prayer and Depression: Women in Rural Pakistan

Background: Mental health, specifically depression, is a burden of disease in Pakistan. Religion and depression have not been studied in Pakistan currently, specially within a subset of a rural population. Methods: A secondary-data analysis was conducted using logistic regression for a non-parametrically distributed data set. The setting was in rural Pakistan, near Rawalpindi, and the sample size data was collected from the SHARE (South Asian Hub for Advocacy, Research, and Education). The measures used were the phq9 scaled for depression, prayer number, mother’s education, mother’s age, and if the mothers work. Results: This study demonstrated that there was no association between prayer and depression in this cohort. The mean prayer number between depressed and non-depressed women was 1.22 and 1.42, respectively, and a Wilcoxan rank sum test indicated that this was not significant. Conclusions: The primary finding indicates that increased frequency of prayer is not associated with a decreased rate of depression. This may be due to prayer number not being a significant enough measure. The implications of these findings stress the need for more depression intervention in rural Pakistan.

Control of cyclin B1 localization through regulated binding of the nuclear export factor CRM1.

Activation of the Cyclin B/Cdc2 kinase complex triggers entry into mitosis in all eukaryotic cells. Cyclin B1 localization changes dramatically during the cell cycle, precipitously transiting from the cytoplasm to the nucleus at the beginning of mitosis. Presumably, this relocalization promotes the phosphorylation of nuclear targets critical for chromatin condensation and nuclear envelope breakdown. We show here that the previously characterized cytoplasmic retention sequence of Cyclin B1, responsible for its interphase cytoplasmic localization, is actually an autonomous nuclear export sequence, capable of directing nuclear export of a heterologous protein, and able to bind specifically to the recently identified export mediator, CRM1. We propose that the observed cytoplasmic localization of Cyclin B1 during interphase reflects the equilibrium between ongoing nuclear import and rapid CRM1-mediated export. In support of this hypothesis, we found that treatment of cells with leptomycin B, which disrupted Cyclin B1-CRM1 interactions, led to a marked nuclear accumulation of Cyclin B1. In mitosis, Cyclin B1 undergoes phosphorylation at several sites, a subset of which have been proposed to play a role in Cyclin B1 accumulation in the nucleus. Both CRM1 binding and the ability to direct nuclear export were affected by mutation of these phosphorylation sites; thus, we propose that Cyclin B1 phosphorylation at the G2/M transition prevents its interaction with CRM1, thereby reducing nuclear export and facilitating nuclear accumulation.

Outcomes After Total Ankle Replacement in Association With Ipsilateral Hindfoot Arthrodesis.

BACKGROUND: Ipsilateral hindfoot arthrodesis in combination with total ankle replacement (TAR) may diminish functional outcome and prosthesis survivorship compared to isolated TAR. We compared the outcome of isolated TAR to outcomes of TAR with ipsilateral hindfoot arthrodesis. METHODS: In a consecutive series of 404 primary TARs in 396 patients, 70 patients (17.3%) had a hindfoot fusion before, after, or at the time of TAR; the majority had either an isolated subtalar arthrodesis (n = 43, 62%) or triple arthrodesis (n = 15, 21%). The remaining 334 isolated TARs served as the control group. Mean patient follow-up was 3.2 years (range, 24-72 months). RESULTS: The SF-36 total, AOFAS Hindfoot-Ankle pain subscale, Foot and Ankle Disability Index, and Short Musculoskeletal Function Assessment scores were significantly improved from preoperative measures, with no significant differences between the hindfoot arthrodesis and control groups. The AOFAS Hindfoot-Ankle total, function, and alignment scores were significantly improved for both groups, albeit the control group demonstrated significantly higher scores in all 3 scales. Furthermore, the control group demonstrated a significantly greater improvement in VAS pain score compared to the hindfoot arthrodesis group. Walking speed, sit-to-stand time, and 4-square step test time were significantly improved for both groups at each postoperative time point; however, the hindfoot arthrodesis group completed these tests significantly slower than the control group. There was no significant difference in terms of talar component subsidence between the fusion (2.6 mm) and control groups (2.0 mm). The failure rate in the hindfoot fusion group (10.0%) was significantly higher than that in the control group (2.4%; p < 0.05). CONCLUSION: To our knowledge, this study represents the first series evaluating the clinical outcome of TARs performed with and without hindfoot fusion using implants available in the United States. At follow-up of 3.2 years, TAR performed with ipsilateral hindfoot arthrodesis resulted in significant improvements in pain and functional outcome; in contrast to prior studies, however, overall outcome was inferior to that of isolated TAR. LEVEL OF EVIDENCE: Level II, prospective comparative series.