Instrumental Variables Estimation with Some Invalid Instruments and its Application to Mendelian Randomization

Instrumental variables have been widely used for estimating the causal effect between exposure and outcome. Conventional estimation methods require complete knowledge about all the instruments' validity; a valid instrument must not have a direct effect on the outcome and not be related to unmeasured confounders. Often, this is impractical as highlighted by Mendelian randomization studies where genetic markers are used as instruments and complete knowledge about instruments' validity is equivalent to complete knowledge about the involved genes' functions. In this paper, we propose a method for estimation of causal effects when this complete knowledge is absent. It is shown that causal effects are identified and can be estimated as long as less than $50$% of instruments are invalid, without knowing which of the instruments are invalid. We also introduce conditions for identification when the 50% threshold is violated. A fast penalized $\ell_1$ estimation method, called sisVIVE, is introduced for estimating the causal effect without knowing which instruments are valid, with theoretical guarantees on its performance. The proposed method is demonstrated on simulated data and a real Mendelian randomization study concerning the effect of body mass index on health-related quality of life index. An R package \emph{sisVIVE} is available online.Comment: 99 pages, 29 figures, 14 table

Deterministic and Stochastic Prisoner's Dilemma Games: Experiments in Interdependent Security

This paper examines experiments on interdependent security prisoner's dilemma games with repeated play. By utilizing a Bayesian hierarchical model, we examine how subjects make investment decisions as a function of their previous experience and their treatment condition. Our main findings are that individuals have differing underlying propensities to invest that vary across time, are affected by both the stochastic nature of the game and even more so by an individual's ability to learn about his or her counterpart's choices. Implications for individual decisions and the likely play of a person's counterpart are discussed in detail.

Tourist experiences of individuals with vision impairments

People with visual disabilities Travel Australia. Tourism Research Australia

Reciprocal relationships in collective flights of homing pigeons

Collective motion of bird flocks can be explained via the hypothesis of many wrongs, and/or, a structured leadership mechanism. In pigeons, previous studies have shown that there is a well-defined hierarchical structure and certain specific individuals occupy more dominant positions --- suggesting that leadership by the few individuals drives the behavior of the collective. Conversely, by analyzing the same data-sets, we uncover a more egalitarian mechanism. We show that both reciprocal relationships and a stratified hierarchical leadership are important and necessary in the collective movements of pigeon flocks. Rather than birds adopting either exclusive averaging or leadership strategies, our experimental results show that it is an integrated combination of both compromise and leadership which drives the group's movement decisions.Comment: 7 pages, 5 figure

Bayesian testing of many hypotheses ×\times many genes: A study of sleep apnea

Substantial statistical research has recently been devoted to the analysis of large-scale microarray experiments which provide a measure of the simultaneous expression of thousands of genes in a particular condition. A typical goal is the comparison of gene expression between two conditions (e.g., diseased vs. nondiseased) to detect genes which show differential expression. Classical hypothesis testing procedures have been applied to this problem and more recent work has employed sophisticated models that allow for the sharing of information across genes. However, many recent gene expression studies have an experimental design with several conditions that requires an even more involved hypothesis testing approach. In this paper, we use a hierarchical Bayesian model to address the situation where there are many hypotheses that must be simultaneously tested for each gene. In addition to having many hypotheses within each gene, our analysis also addresses the more typical multiple comparison issue of testing many genes simultaneously. We illustrate our approach with an application to a study of genes involved in obstructive sleep apnea in humans.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS241 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Gravitational Waves Probe the Coalescence Rate of Massive Black Hole Binaries

We calculate the expected nHz--$\mu$Hz gravitational wave (GW) spectrum from coalescing Massive Black Hole (MBH) binaries resulting from mergers of their host galaxies. We consider detection of this spectrum by precision pulsar timing and a future Pulsar Timing Array. The spectrum depends on the merger rate of massive galaxies, the demographics of MBHs at low and high redshift, and the dynamics of MBH binaries. We apply recent theoretical and observational work on all of these fronts. The spectrum has a characteristic strain $h_c(f)~10^{-15} (f/yr^{-1})^{-2/3}$, just below the detection limit from recent analysis of precision pulsar timing measurements. However, the amplitude of the spectrum is still very uncertain owing to approximations in the theoretical formulation of the model, to our lack of knowledge of the merger rate and MBH population at high redshift, and to the dynamical problem of removing enough angular momentum from the MBH binary to reach a GW-dominated regime.Comment: 31 Pages, 8 Figures, small changes to match the published versio