Convergence of numerical time-averaging and stationary measures via Poisson equations

Numerical approximation of the long time behavior of a stochastic di.erential equation (SDE) is considered. Error estimates for time-averaging estimators are obtained and then used to show that the stationary behavior of the numerical method converges to that of the SDE. The error analysis is based on using an associated Poisson equation for the underlying SDE. The main advantages of this approach are its simplicity and universality. It works equally well for a range of explicit and implicit schemes, including those with simple simulation of random variables, and for hypoelliptic SDEs. To simplify the exposition, we consider only the case where the state space of the SDE is a torus, and we study only smooth test functions. However, we anticipate that the approach can be applied more widely. An analogy between our approach and Stein's method is indicated. Some practical implications of the results are discussed. Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.

Assessment of LD matrix measures for the analysis of biological pathway association.

Complex diseases will have multiple functional sites, and it will be invaluable to understand the cross-locus interaction in terms of linkage disequilibrium (LD) between those sites (epistasis) in addition to the haplotype-LD effects. We investigated the statistical properties of a class of matrix-based statistics to assess this epistasis. These statistical methods include two LD contrast tests (Zaykin et al., 2006) and partial least squares regression (Wang et al., 2008). To estimate Type 1 error rates and power, we simulated multiple two-variant disease models using the SIMLA software package. SIMLA allows for the joint action of up to two disease genes in the simulated data with all possible multiplicative interaction effects between them. Our goal was to detect an interaction between multiple disease-causing variants by means of their linkage disequilibrium (LD) patterns with other markers. We measured the effects of marginal disease effect size, haplotype LD, disease prevalence and minor allele frequency have on cross-locus interaction (epistasis). In the setting of strong allele effects and strong interaction, the correlation between the two disease genes was weak (r=0.2). In a complex system with multiple correlations (both marginal and interaction), it was difficult to determine the source of a significant result. Despite these complications, the partial least squares and modified LD contrast methods maintained adequate power to detect the epistatic effects; however, for many of the analyses we often could not separate interaction from a strong marginal effect. While we did not exhaust the entire parameter space of possible models, we do provide guidance on the effects that population parameters have on cross-locus interaction.

Using Behavioral Insights For a Better Understanding of Economic Decisions (Regarding Savings, Inequality and Dishonesty)

This dissertation consists of three essays on behavioral economics, with a general aim of enriching our understanding of economic decisions using behavioral insights and experimental methodology. Each essay takes on one particular topic with this general aim.

The first chapter studies savings behavior of the poor. In this project, partnering with a savings product provider in Kenya, we tested the extent to which behavioral interventions and financial incentives can increase the saving rate of individuals with low and irregular income. Our experiment lasted for six months and included a total of twelve conditions. The control condition received weekly reminders and balance reporting via text messages. The treatment conditions received in addition one of the following interventions: (1) reminder text messages framed as if they came from the participant’s kid (2) a golden colored coin with numbers for each week of the trial, on which participants were asked to keep track of their weekly deposits (3) a match of weekly savings: The match was either 10% or 20% up to a certain amount per week. The match was either deposited at the end of each week or the highest possible match was deposited at the start of each week and was adjusted at the end. Among these interventions, by far the most effective was the coin: Those in the coin condition saved on average the highest amount and more than twice as those in the control condition. We hypothesize that being a tangible track-keeping object; the coin made subjects remember to save more often. Our results support the line of literature suggesting that saving decisions involve psychological aspects and that policy makers and product designers should take these influences into account.

The second chapter is related to views towards inequality. In this project, we investigate how the perceived fairness of income distributions depends on the beliefs about the process that generated the inequality. Specifically, we examine how two crucial features of this process affect fairness views: (1) Procedural justice - equal treatment of all, (2) Agency - one's ability to determine his/her income. We do this in a lab experiment by varying the equality of opportunity (procedural justice), and one's ability to make choices, which consequently influence subjects’ ability to influence their income (agency). We then elicit ex-post redistribution decisions of the earnings as a function of these two elements. Our results suggest both agency and procedural justice matter for fairness. Our main findings can be summarized as follows: (1) Highlighting the importance of agency, we find that inequality resulting from risk is considered to be fair only when risk is chosen freely; (2) Highlighting the importance of procedural justice, we find that introducing inequality of opportunity significantly increases redistribution, however the share of subjects redistributing none remain close to the share of subjects redistributing fully revealing an underlying heterogeneity in the population about how fairness views should account for inequality of opportunity.

The third chapter is on morality. In this project, we study whether religious rituals act as an internal reminder for basic moral principles and thus affect moral judgments. To this end, we conducted two survey experiments in Turkey and Israel to specifically test the effect of Ramadan and Yom Kippur. The results from the Turkish sample how that Ramadan has a significant effect on moral judgments to some extent for those who report to believe in God. Those who believe in God judged the moral acceptability of ten out of sixty one actions significantly differently in Ramadan, whereas those who reported not to believe in God significantly changed their judgments only for one action in Ramadan. Our results extends the hypothesis established by lab experiments that religious reminders have a significant effect on morality, by testing it in the field in the natural environment of religious rituals.

This thesis is part of a broader collaborative research agenda with both colleagues and advisors. The programming, analyses, and writing, as well as any errors in this work, are my own.

Temporal Stability of Molecular Diversity Measures in Natural Populations of Drosophila pseudoobscura and Drosophila persimilis

Many molecular ecological and evolutionary studies sample wild populations at a single point in time, failing to consider that data they collect represents genetic variation from a potentially unrepresentative snapshot in time. Variation across time in genetic parameters may occur quickly in species that produce multiple generations of offspring per year. However, many studies of rapid contemporary microevolution examine phenotypic trait divergence as opposed to molecular evolutionary divergence. Here, we compare genetic diversity in wild caught populations of Drosophila persimilis and D. pseudoobscura collected 16 years apart at the same time of year and same site at four X-linked and two mitochondrial loci to assess genetic stability. We found no major changes in nucleotide diversity in either species, but we observed a drastic shift in Tajima’s D between D. pseudoobscura timepoints at one locus associated with the increased abundance of a set of related haplotypes. Our data also suggests that D. persimilis may have recently accelerated its demographic expansion. While the changes we observed were modest, this study reinforces the importance of considering potential temporal variation in genetic parameters within single populations over short evolutionary timescales.

Participant, rater, and computer measures of coherence in posttraumatic stress disorder.

We examined the coherence of trauma memories in a trauma-exposed community sample of 30 adults with and 30 without posttraumatic stress disorder. The groups had similar categories of traumas and were matched on multiple factors that could affect the coherence of memories. We compared the transcribed oral trauma memories of participants with their most important and most positive memories. A comprehensive set of 28 measures of coherence including 3 ratings by the participants, 7 ratings by outside raters, and 18 computer-scored measures, provided a variety of approaches to defining and measuring coherence. A multivariate analysis of variance indicated differences in coherence among the trauma, important, and positive memories, but not between the diagnostic groups or their interaction with these memory types. Most differences were small in magnitude; in some cases, the trauma memories were more, rather than less, coherent than the control memories. Where differences existed, the results agreed with the existing literature, suggesting that factors other than the incoherence of trauma memories are most likely to be central to the maintenance of posttraumatic stress disorder and thus its treatment.

Accounting for Posttraumatic Stress Disorder Symptom Severity With Pre- and Posttrauma Measures: A Longitudinal Study of Older Adults.

Using data from a longitudinal study of community-dwelling older adults, we analyzed the most extensive set of known correlates of PTSD symptoms obtained from a single sample to examine the measures' independent and combined utility in accounting for PTSD symptom severity. Fifteen measures identified as PTSD risk factors in published meta-analyses and 12 theoretically and empirically supported individual difference and health-related measures were included. Individual difference measures assessed after the trauma, including insecure attachment and factors related to the current trauma memory, such as self-rated severity, event centrality, frequency of involuntary recall, and physical reactions to the memory, accounted for symptom severity better than measures of pre-trauma factors. In an analysis restricted to prospective measures assessed before the trauma, the total variance explained decreased from 56% to 16%. Results support a model of PTSD in which characteristics of the current trauma memory promote the development and maintenance of PTSD symptoms.