Person:

Pillai, Natesh

Approximate Bayesian computation (ABC) have become an essential tool for the analysis of complex stochastic models. Grelaud et al. [(2009) Bayesian Anal 3:427–442] advocated the use of ABC for model choice in the specific case of Gibbs random fields, relying on an intermodel sufficiency property to show that the approximation was legitimate. We implemented ABC model choice in a wide range of phylogenetic models in the Do It Yourself-ABC (DIY-ABC) software [Cornuet et al. (2008) Bioinformatics 24:2713–2719]. We now present arguments as to why the theoretical arguments for ABC model choice are missing, because the algorithm involves an unknown loss of information induced by the use of insufficient summary statistics. The approximation error of the posterior probabilities of the models under comparison may thus be unrelated with the computational effort spent in running an ABC algorithm. We then conclude that additional empirical verifications of the performances of the ABC procedure as those available in DIY-ABC are necessary to conduct model choice.

Two common concerns raised in analyses of randomized experiments are (i) appropriately handling issues of non-compliance, and (ii) appropriately adjusting for multiple tests (e.g., on multiple outcomes or subgroups). Although simple intention-to-treat (ITT) and Bonferroni methods are valid in terms of type I error, they can each lead to a substantial loss of power; when employing both simultaneously, the total loss may be severe. Alternatives exist to address each concern. Here we propose an analysis method for experiments involving both features that merges posterior predictive p-values for complier causal effects with randomization-based multiple comparisons adjustments; the results are valid familywise tests that are doubly advantageous: more powerful than both those based on standard ITT statistics and those using traditional multiple comparison adjustments. The operating characteristics and advantages of our method are demonstrated through a series of simulated experiments and an analysis of the United States Job Training Partnership Act (JTPA) Study, where our methods lead to different conclusions regarding the significance of estimated JTPA effects.

Determining the mixing time of Kac's random walk on the sphere Sn−1 is a long-standing open problem. We show that the total variation mixing time of Kac's walk on Sn−1 is between 12nlog(n) and 200nlog(n). Our bound is thus optimal up to a constant factor, improving on the best-known upper bound of O(n5log(n)2) due to Jiang. Our main tool is a `non-Markovian' coupling recently introduced by the second author for obtaining the convergence rates of certain high dimensional Gibbs samplers in continuous state spaces.

We analyze the computational efficiency of approximate Bayesian computation (ABC), which approximates a likelihood function by drawing pseudo-samples from the associated model. For the rejection sampling version of ABC, it is known that multiple pseudo-samples cannot substantially increase (and can substantially decrease) the efficiency of the algorithm as compared to employing a high-variance estimate based on a single pseudo-sample. We show that this conclusion also holds for a Markov chain Monte Carlo version of ABC, implying that it is unnecessary to tune the number of pseudo-samples used in ABC-MCMC. This conclusion is in contrast to particle MCMC methods, for which increasing the number of particles can provide large gains in computational efficiency.

State-of-the-art techniques in passive particle-tracking microscopy provide high-resolution path trajectories of diverse foreign particles in biological fluids. For particles on the order of 1 μm diameter, these paths are generally inconsistent with simple Brownian motion. Yet, despite an abundance of data confirming these findings and their wide-ranging scientific implications, stochastic modeling of the complex particle motion has received comparatively little attention. Even among posited models, there is virtually no literature on likelihood-based inference, model comparisons, and other quantitative assessments. In this article, we develop a rigorous and computationally efficient Bayesian methodology to address this gap. We analyze two of the most prevalent candidate models for 30-sec paths of 1 μm diameter tracer particles in human lung mucus: fractional Brownian motion (fBM) and a Generalized Langevin Equation (GLE) consistent with viscoelastic theory. Our model comparisons distinctly favor GLE over fBM, with the former describing the data remarkably well up to the timescales for which we have reliable information. Supplementary materials for this article are available online.

Understanding the response of agriculture to heat and moisture stress is essential to adapt food systems under climate change. Although evidence of crop yield loss with extreme temperature is abundant, disentangling the roles of temperature and moisture in determining yield has proven challenging, largely due to the limited soil moisture data and the tight coupling between moisture and temperature at the land surface. Here, using well-resolved observations of soil moisture from the recently launched Soil Moisture Active Passive satellite, we quantified the contribution of imbalances between atmospheric evaporative demand and soil moisture to maize yield damages in the U.S. Midwest. We show that retrospective yield predictions based on the interactions between atmospheric demand and soil moisture significantly outperform those using temperature and precipitation singly or together. The importance of accounting for this water balance is highlighted by the fact that climate simulations uniformly predict increases in atmospheric demand during the growing season but root-zone soils that are variously drier or wetter. A damage estimate conditioned only on simulated changes in atmospheric demand, as opposed to also accounting for changes in soil-moisture, would erroneously indicate approximately twice the damage. This research demonstrates that more accurate predictions of maize yield can be achieved by using soil moisture data and indicates that accurate estimates of how climate change will influence crop yields requires explicitly accounting for variations in water availability.

Volume limitations and low yield thresholds of biological fluids have led to widespread use of passive microparticle rheology. The mean-squared-displacement (MSD) statistics of bead position time series (bead paths) are transformed to determine dynamic storage and loss moduli [Mason and Weitz (1995)]. A prevalent hurdle arises when there is a non-diffusive experimental drift in the data. Commensurate with the magnitude of drift relative to diffusive mobility, quantified by a Péclet number, the MSD statistics are distorted, and thus the path data must be “corrected” for drift. The standard approach is to estimate and subtract the drift from particle paths, and then calculate MSD statistics. We present an alternative, parametric approach using maximum likelihood estimation (MLE) that simultaneously fits drift and diffusive model parameters from the path data; the MSD statistics (and dynamic moduli) then follow directly from the best-fit model. We illustrate and compare both methods on simulated path data over a range of Péclet numbers, where exact answers are known. We choose fractional Brownian motion as the numerical model because it affords tunable, sub-diffusive MSD statistics consistent with several biological fluids. Finally, we apply and compare both methods on data from human bronchial epithelial cell culture mucus.

Many finite-state reversible Markov chains can be naturally decomposed into “projection” and “restriction” chains. In this paper we provide bounds on the total variation mixing times of the original chain in terms of the mixing properties of these related chains. This paper is in the tradition of existing bounds on Poincar ́e and log-Sobolev constants of Markov chains in terms of similar decompositions [JSTV04, MR02, MR06, MY09]. Our proofs are simple, relying largely on recent results relating hitting and mixing times of reversible Markov chains [PS13, Oli12]. We describe situations in which our results give substantially better bounds than those obtained by applying existing decomposition results and provide examples for illustration.

It has historically been a challenge to perform Bayesian inference in a design-based survey context. The present paper develops a Bayesian model for sampling inference in the presence of inverse-probability weights. We use a hierar- chical approach in which we model the distribution of the weights of the nonsam- pled units in the population and simultaneously include them as predictors in a nonparametric Gaussian process regression. We use simulation studies to evaluate the performance of our procedure and compare it to the classical design-based es- timator. We apply our method to the Fragile Family and Child Wellbeing Study. Our studies find the Bayesian nonparametric finite population estimator to be more robust than the classical design-based estimator without loss in efficiency, which works because we induce regularization for small cells and thus this is a way of automatically smoothing the highly variable weights.