Shrinkage Estimation in Multilevel Normal Models

This review traces the evolution of theory that started when Charles Stein in 1955 [In Proc. 3rd Berkeley Sympos. Math. Statist. Probab. I (1956) 197--206, Univ. California Press] showed that using each separate sample mean from $k\ge3$ Normal populations to estimate its own population mean $\mu_i$ can be improved upon uniformly for every possible $\mu=(\mu_1,...,\mu_k)'$. The dominating estimators, referred to here as being "Model-I minimax," can be found by shrinking the sample means toward any constant vector. Admissible minimax shrinkage estimators were derived by Stein and others as posterior means based on a random effects model, "Model-II" here, wherein the $\mu_i$ values have their own distributions. Section 2 centers on Figure 2, which organizes a wide class of priors on the unknown Level-II hyperparameters that have been proved to yield admissible Model-I minimax shrinkage estimators in the "equal variance case." Putting a flat prior on the Level-II variance is unique in this class for its scale-invariance and for its conjugacy, and it induces Stein's harmonic prior (SHP) on $\mu_i$.Comment: Published in at http://dx.doi.org/10.1214/11-STS363 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Data-Adaptive Probabilistic Likelihood Approximation for Ordinary Differential Equations

Parameter inference for ordinary differential equations (ODEs) is of fundamental importance in many scientific applications. While ODE solutions are typically approximated by deterministic algorithms, new research on probabilistic solvers indicates that they produce more reliable parameter estimates by better accounting for numerical errors. However, many ODE systems are highly sensitive to their parameter values. This produces deep local minima in the likelihood function -- a problem which existing probabilistic solvers have yet to resolve. Here, we show that a Bayesian filtering paradigm for probabilistic ODE solution can dramatically reduce sensitivity to parameters by learning from the noisy ODE observations in a data-adaptive manner. Our method is applicable to ODEs with partially unobserved components and with arbitrary non-Gaussian noise. Several examples demonstrate that it is more accurate than existing probabilistic ODE solvers, and even in some cases than the exact ODE likelihood.Comment: 9 pages, 5 figure

Diving into the consumer nutrition environment: A Bayesian spatial factor analysis of neighborhood restaurant environment

The final publication is available at Elsevier via https://dx.doi.org/10.1016/j.sste.2017.12.001 © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/Neighborhood restaurant environment (NRE) plays a vital role in shaping residents' eating behaviors. While NRE 'healthfulness' is a multi-facet concept, most studies evaluate it based only on restaurant type, thus largely ignoring variations of in-restaurant features. In the few studies that do account for such features, healthfulness scores are simply averaged over accessible restaurants, thereby concealing any uncertainty that attributed to neighborhoods' size or spatial correlation. To address these limitations, this paper presents a Bayesian Spatial Factor Analysis for assessing NRE healthfulness in the city of Kitchener, Canada. Several in-restaurant characteristics are included. By treating NRE healthfulness as a spatially correlated latent variable, the adopted modeling approach can: (i) identify specific indicators most relevant to NRE healthfulness, (ii) provide healthfulness estimates for neighborhoods without accessible restaurants, and (iii) readily quantify uncertainties in the healthfulness index. Implications of the analysis for intervention program development and community food planning are discussed. (c) 2017 Elsevier Ltd. All rights reserved

Maximum Likelihood Estimation for Single Particle, Passive Microrheology Data with Drift

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 either applied directly to determine the creep compliance [Xu et al (1998)] or transformed to determine dynamic storage and loss moduli [Mason & 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 P\'eclet 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 that simultaneously fits drift and diffusive model parameters from the path data; the MSD statistics (and consequently the compliance 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 P\'eclet 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 typical 30 second long, experimental observations of microbeads in several biological fluids. Finally, we apply and compare both methods on data from human bronchial epithelial cell culture mucus.Comment: 29 pages, 12 figure

Post-Hypoglycemic hyperglycemia are highly relevant markers for stratification of glycemic variability and partial remission status of pediatric patients with new-onset type 1 diabetes.

AimsTo evaluate whether parameters of post-hypoglycemic hyperglycemia (PHH) correlated with glucose homeostasis during the first year after type 1 diabetes onset and helped to distinguish pediatric patients undergoing partial remission or not.MethodsIn the GLUREDIA (GLUcagon Response to hypoglycemia in children and adolescents with new-onset type 1 DIAbetes) study, longitudinal values of clinical parameters, continuous glucose monitoring metrics and residual β-cell secretion from children with new-onset type 1 diabetes were analyzed during the first year after disease onset. PHH parameters were calculated using an in-house algorithm. Correlations between PHH parameters (i.e., PHH frequency, PHH duration, PHH area under the curve [PHHAUC]) and glycemic homeostasis markers were studied using adjusted mixed-effects models.ResultsPHH parameters were strong markers to differentiate remitters from non-remitters with PHH/Hyperglycemia duration ratio being the most sensitive (ratioConclusionPHH parameters are new minimal-invasive markers to discriminate remitters from non-remitters and evaluate glycemic homeostasis during the first year of type 1 diabetes. PHH parameters may also allow patient-targeted therapeutic management of hypoglycemic episodes

Molecule Microscopy

Contains research objectives, summary of research on five research projects and reports on four research projects.Joint Services Electronics Program (Contract DAAB07-74-C-0630)National Institutes of Health (Grant 1 PO1 HL14322-03)National Institutes of Health (Grant 5 SO5 RR07047-08)Environmental Measurements Project Laboratory grant from the Dean of Science, M.I.T.Boehringer Mannheim Gmb

Technological strategies to estimate and control diffusive passage times through the mucus barrier in mucosal drug delivery

The final publication is available at Elsevier via https://dx.doi.org/10.1016/j.addr.2017.12.002 © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/In mucosal drug delivery, two design goals are desirable: 1) insure drug passage through the mucosal barrier to the epithelium prior to drug removal from the respective organ via mucus clearance: and 2) design carrier particles to achieve a prescribed arrival time and drug uptake schedule at the epithelium. Both goals are achievable if one can control "one-sided" diffusive passage times of drug carrier particles: from deposition at the mucus interface, through the mucosal barrier, to the epithelium. The passage time distribution must be, with high confidence, shorter than the timescales of mucus clearance to maximize drug uptake. For 100 nm and smaller drug-loaded nanoparticulates, as well as pure drug powders or drug solutions, diffusion is normal (i.e., Brownian) and rapid, easily passing through the mucosal barrier prior to clearance. Major challenges in quantitative control over mucosal drug delivery lie with larger drug-loaded nanoparticulates that are comparable to or larger than the pores within the mucus gel network, for which diffusion is not simple Brownian motion and typically much less rapid: in these scenarios, a timescale competition ensues between particle passage through the mucus barrier and mucus clearance from the organ. In the lung, as a primary example, coordinated cilia and air drag continuously transport mucus toward the trachea, where mucus and trapped cargo are swallowed into the digestive tract. Mucus clearance times in lung airways range from minutes to hours or significantly longer depending on deposition in the upper, middle, lower airways and on lung health, giving a wide time window for drug-loaded particle design to achieve controlled delivery to the epithelium. We review the physical and chemical factors (of both particles and mucus) that dictate particle diffusion in mucus, and the technological strategies (theoretical and experimental) required to achieve the design goals. First we describe an idealized scenario - a homogeneous viscous fluid of uniform depth with a particle undergoing passive normal diffusion - where the theory of Brownian motion affords the ability to rigorously specify particle size distributions to meet a prescribed, one-sided, diffusive passage time distribution. Furthermore, we describe how the theory of Brownian motion provides the scaling of one-sided diffusive passage times with respect to mucus viscosity and layer depth, and under reasonable caveats, one can also prescribe passage time scaling due to heterogeneity in viscosity and layer depth. Small-molecule drugs and muco-inert, drug-loaded carrier particles 100 nm and smaller fall into this class of rigorously controllable passage times for drug delivery. Second we describe the prevalent scenarios in which drug-loaded carrier particles in mucus violate simple Brownian motion, instead exhibiting anomalous sub-diffusion, for which all theoretical control over diffusive passage times is lost, and experiments are prohibitive if not impossible to measure one-sided passage times. We then discuss strategies to overcome these roadblocks, requiring new particle-tracking experiments and emerging advances in theory and computation of anomalous, sub diffusive processes that are necessary to predict and control one-sided particle passage times from deposition at the mucosal interface to epithelial uptake. We highlight progress to date, remaining hurdles, and prospects for achieving the two design goals for 200 nm and larger, drug-loaded, non-dissolving, nanoparticulates.Natural Sciences and Engineering Research Council of Canada [DMS-1664645, RGPIN-2014-04255, DMS-1412844, DMS-1517274]National Science Foundation [DMS-1462992]Eshelman Institute of Innovation [DMR-1151477]National Institute of Health [R41GM123897, R56HD095629]Graduate Research Fellowship [DGE-1650116