Robert L. Wolpert

Redefine Statistical Significance

We propose to change the default P-value threshold for statistical significance from 0.05 to 0.005 for claims of new discoveries.

Spatial Poisson Regression for Health and Exposure Data Measured at Disparate Resolutions

Abstract Ecological regression studies are widely used to examine relationships between disease rates for small geographical areas and exposure to environmental risk factors. The raw data for such studies, including disease cases, environmental pollution concentrations, and the reference population at risk, are typically measured at various levels of spatial aggregation but are accumulated to a common geographical scale to facilitate statistical analysis. In this traditional approach, heterogeneous exposure distributions within the aggregate areas may lead to biased inference, whereas individual attributes such as age, gender, and smoking habits must either be summarized to provide area-level covariate values or used to stratify the analysis. This article presents a spatial regression analysis of the effect of traffic pollution on respiratory disorders in children. The analysis features data measured at disparate, nonnested scales, including spatially varying covariates, latent spatially varying risk factors, and case-specific individual attributes. The problem of disparate discretizations is overcome by relating all spatially varying quantities to a continuous underlying random field model. Case-specific individual attributes are accommodated by treating cases as a marked point process. Inference in these hierarchical Poisson/gamma models is based on simulated samples drawn from Bayesian posterior distributions, using Markov chain Monte Carlo methods with data augmentation.

Rapid Taste Responses in the Gustatory Cortex during Licking

Rapid tastant detection is necessary to prevent the ingestion of potentially poisonous compounds. Behavioral studies have shown that rats can identify tastants in ∼200 ms, although the electrophysiological correlates for fast tastant detection have not been identified. For this reason, we investigated whether neurons in the primary gustatory cortex (GC), a cortical area necessary for tastant identification and discrimination, contain sufficient information in a single lick cycle, or ∼150 ms, to distinguish between tastants at different concentrations. This was achieved by recording neural activity in GC while rats licked four times without a liquid reward, and then, on the fifth lick, received a tastant (FR5 schedule). We found that 34% (61 of 178) of GC units were chemosensitive. The remaining neurons were activated during some phase of the licking cycle, discriminated between reinforced and unreinforced licks, or processed task-related information. Chemosensory neurons exhibited a latency of 70–120 ms depending on concentration, and a temporally precise phasic response that returned to baseline in tens of milliseconds. Tastant-responsive neurons were broadly tuned and responded to increasing tastant concentrations by either increasing or decreasing their firing rates. In addition, some responses were only evoked at intermediate tastant concentrations. In summary, these results suggest that the gustatory cortex is capable of processing multimodal information on a rapid timescale and provide the physiological basis by which animals may discriminate between tastants during a single lick cycle.

RECONSTRUCTING PLANT ROOT AREA AND WATER UPTAKE PROFILES

A major challenge in plant ecology is quantifying how roots obtain water and nutrients from the soil. Stable-isotope analysis of hydrogen and oxygen in plant and soil water is one of the best and least destructive methods for elucidating plant–soil interactions. Plant roots obtain water from various depths in the soil and the isotopic signature of plant stem water reflects the soil water sources. Current methods for inferring plant water sources based on stable isotopes (“simple linear mixing models”) are limited. First, their formulation restricts the number of water sources to a maximum of three (e.g., surface, intermediate, deep-soil water); estimation of additional sources leads to an identifiability problem. Second, simple linear mixing models do not appropriately reflect uncertainty, and most importantly, they cannot be employed to elucidate behavior of the root system itself, such as root activity for water uptake. This study introduces the RAPID (root area profile and isotope deconvolution) algori...

Meta-Analysis of Migraine Headache Treatments: Combining Information from Heterogeneous Designs

Abstract Migraine headache is a common condition in the United States for which a wide range of drug and nondrug treatments are available. There is wide disagreement about which treatments are most effective; meta-analysis of existing clinical trials can help to bring existing evidence to bear on this question. Conducting a meta-analysis is a challenging statistical problem because of the absence of a uniform accepted definition of headache syndromes, the diversity of treatments, and the heterogeneous and incomplete nature of published information. The results of studies are summarized in various ways; most studies report continuous treatment effects for each treatment, but some report only differences in effectiveness for pairs of treatments, and others report only 2 × 2 contingency tables for dichotomized responses. In this article we present a hierarchical Bayesian grouped random-effects model for synthesizing evidence from several clinical trials comparing the effectiveness of commonly recommended pro...

Using Statistical and Computer Models to Quantify Volcanic Hazards

Risk assessment of rare natural hazards, such as large volcanic block and ash or pyroclastic flows, is addressed. Assessment is approached through a combination of computer modeling, statistical modeling, and extreme-event probability computation. A computer model of the natural hazard is used to provide the needed extrapolation to unseen parts of the hazard space. Statistical modeling of the available data is needed to determine the initializing distribution for exercising the computer model. In dealing with rare events, direct simulations involving the computer model are prohibitively expensive. The solution instead requires a combination of adaptive design of computer model approximations (emulators) and rare event simulation. The techniques that are developed for risk assessment are illustrated on a test-bed example involving volcanic flow.

Wiener path intersections and local time

Abstract We study intersection properties of Wiener processes in the plane. For each positive integer k we show that k independent Wiener processes intersect almost surely in a set of Hausdorff dimension two, and that the set of points a single process visits at least k distinct times also has dimension two. We construct a functional on configurations of k independent Wiener processes that measures the extent to which the trajectories of the k processes intersect. We prove certain L p estimates for this functional and show that it is a local time for a certain vector-valued multiparameter stochastic process.

Modeling the relationship between most probable number (MPN) and colony-forming unit (CFU) estimates of fecal coliform concentration.

Most probable number (MPN) and colony-forming-unit (CFU) estimates of fecal coliform bacteria concentration are common measures of water quality in coastal shellfish harvesting and recreational waters. Estimating procedures for MPN and CFU have intrinsic variability and are subject to additional uncertainty arising from minor variations in experimental protocol. It has been observed empirically that the standard multiple-tube fermentation (MTF) decimal dilution analysis MPN procedure is more variable than the membrane filtration CFU procedure, and that MTF-derived MPN estimates are somewhat higher on average than CFU estimates, on split samples from the same water bodies. We construct a probabilistic model that provides a clear theoretical explanation for the variability in, and discrepancy between, MPN and CFU measurements. We then compare our model to water quality samples analyzed using both MPN and CFU procedures, and find that the (often large) observed differences between MPN and CFU values for the same water body are well within the ranges predicted by our probabilistic model. Our results indicate that MPN and CFU intra-sample variability does not stem from human error or laboratory procedure variability, but is instead a simple consequence of the probabilistic basis for calculating the MPN. These results demonstrate how probabilistic models can be used to compare samples from different analytical procedures, and to determine whether transitions from one procedure to another are likely to cause a change in quality-based management decisions.

Infinite dimensional stochastic differential equation models for spatially distributed neurons

The membrane potential of spatially distributed neurons is modeled as a random field driven by a generalized Poisson process. Approximation to an Ornstein-Uhlenbeck type process is established in the sense of weak convergence of the induced measures in Skorokhod space.

Simulation of Lévy Random Fields

An efficient recently developed method, the Inverse Levy Measure (ILM) algorithm, is presented for drawing random samples from gamma, skewed stable and other nonnegative independent-increment random fields, which we call Levy random fields. The method is useful for computing posterior distributions in nonparametric hierarchical Bayesian statistical analysis. Algorithms are illustrated through prototype implementations in S-PLUS.