Richard L. Tweedie

Bio: Richard L. Tweedie is an academic researcher from University of Minnesota. The author has contributed to research in topics: Markov chain & Markov process. The author has an hindex of 43, co-authored 98 publications receiving 23125 citations. Previous affiliations of Richard L. Tweedie include University of Cambridge & Colorado State University.

Trim and fill: A simple funnel-plot-based method of testing and adjusting for publication bias in meta-analysis.

Abstract: We study recently developed nonparametric methods for estimating the number of missing studies that might exist in a meta-analysis and the effect that these studies might have had on its outcome. These are simple rank-based data augmentation techniques, which formalize the use of funnel plots. We show that they provide effective and relatively powerful tests for evaluating the existence of such publication bias. After adjusting for missing studies, we find that the point estimate of the overall effect size is approximately correct and coverage of the effect size confidence intervals is substantially improved, in many cases recovering the nominal confidence levels entirely. We illustrate the trim and fill method on existing meta-analyses of studies in clinical trials and psychometrics.

Markov Chains and Stochastic Stability

Abstract: Meyn & Tweedie is back! The bible on Markov chains in general state spaces has been brought up to date to reflect developments in the field since 1996 - many of them sparked by publication of the first edition. The pursuit of more efficient simulation algorithms for complex Markovian models, or algorithms for computation of optimal policies for controlled Markov models, has opened new directions for research on Markov chains. As a result, new applications have emerged across a wide range of topics including optimisation, statistics, and economics. New commentary and an epilogue by Sean Meyn summarise recent developments and references have been fully updated. This second edition reflects the same discipline and style that marked out the original and helped it to become a classic: proofs are rigorous and concise, the range of applications is broad and knowledgeable, and key ideas are accessible to practitioners with limited mathematical background.

A Nonparametric “Trim and Fill” Method of Accounting for Publication Bias in Meta-Analysis

Abstract: Meta-analysis collects and synthesizes results from individual studies to estimate an overall effect size. If published studies are chosen, say through a literature review, then an inherent selection bias may arise, because, for example, studies may tend to be published more readily if they are statistically significant, or deemed to be more “interesting” in terms of the impact of their outcomes. We develop a simple rank-based data augmentation technique, formalizing the use of funnel plots, to estimate and adjust for the numbers and outcomes of missing studies. Several nonparametric estimators are proposed for the number of missing studies, and their properties are developed analytically and through simulations. We apply the method to simulated and epidemiological datasets and show that it is both effective and consistent with other criteria in the literature.

Exponential convergence of Langevin distributions and their discrete approximations

Abstract: In this paper we consider a continuous-time method of approximating a given distribution π using the Langevin diffusion d L t=dW t+1 2 ∇logπ(L t)dt . We find conditions under which this diffusion converges exponentially quickly to π or does not: in one dimension, these are essentially that for distributions with exponential tails of the form π (x)∝exp(-γ|x| β ) , 0 <β<∞ , exponential convergence occurs if and only if β ≥1 . We then consider conditions under which the discrete approximations to the diffusion converge. We first show that even when the diffusion itself converges, naive discretizations need not do so. We then consider a 'Metropolis-adjusted' version of the algorithm, and find conditions under which this also converges at an exponential rate: perhaps surprisingly, even the Metropolized version need not converge exponentially fast even if the diffusion does. We briefly discuss a truncated form of the algorithm which, in practice, should avoid the difficulties of the other forms.

Stability of Markovian processes III: Foster–Lyapunov criteria for continuous-time processes

Abstract: In Part I we developed stability concepts for discrete chains, together with Foster–Lyapunov criteria for them to hold. Part II was devoted to developing related stability concepts for continuous-time processes. In this paper we develop criteria for these forms of stability for continuous-parameter Markovian processes on general state spaces, based on Foster-Lyapunov inequalities for the extended generator. Such test function criteria are found for non-explosivity, non-evanescence, Harris recurrence, and positive Harris recurrence. These results are proved by systematic application of Dynkin's formula. We also strengthen known ergodic theorems, and especially exponential ergodic results, for continuous-time processes. In particular we are able to show that the test function approach provides a criterion for f-norm convergence, and bounding constants for such convergence in the exponential ergodic case. We apply the criteria to several specific processes, including linear stochastic systems under non-linear feedback, work-modulated queues, general release storage processes and risk processes.

Quantifying heterogeneity in a meta‐analysis

Abstract: The extent of heterogeneity in a meta-analysis partly determines the difficulty in drawing overall conclusions. This extent may be measured by estimating a between-study variance, but interpretation is then specific to a particular treatment effect metric. A test for the existence of heterogeneity exists, but depends on the number of studies in the meta-analysis. We develop measures of the impact of heterogeneity on a meta-analysis, from mathematical criteria, that are independent of the number of studies and the treatment effect metric. We derive and propose three suitable statistics: H is the square root of the chi2 heterogeneity statistic divided by its degrees of freedom; R is the ratio of the standard error of the underlying mean from a random effects meta-analysis to the standard error of a fixed effect meta-analytic estimate, and I2 is a transformation of (H) that describes the proportion of total variation in study estimates that is due to heterogeneity. We discuss interpretation, interval estimates and other properties of these measures and examine them in five example data sets showing different amounts of heterogeneity. We conclude that H and I2, which can usually be calculated for published meta-analyses, are particularly useful summaries of the impact of heterogeneity. One or both should be presented in published meta-analyses in preference to the test for heterogeneity.

Conducting Meta-Analyses in R with the metafor Package

Abstract: The metafor package provides functions for conducting meta-analyses in R. The package includes functions for fitting the meta-analytic fixed- and random-effects models and allows for the inclusion of moderators variables (study-level covariates) in these models. Meta-regression analyses with continuous and categorical moderators can be conducted in this way. Functions for the Mantel-Haenszel and Peto's one-step method for meta-analyses of 2 x 2 table data are also available. Finally, the package provides various plot functions (for example, for forest, funnel, and radial plots) and functions for assessing the model fit, for obtaining case diagnostics, and for tests of publication bias.

Trim and fill: A simple funnel-plot-based method of testing and adjusting for publication bias in meta-analysis.

Abstract: We study recently developed nonparametric methods for estimating the number of missing studies that might exist in a meta-analysis and the effect that these studies might have had on its outcome. These are simple rank-based data augmentation techniques, which formalize the use of funnel plots. We show that they provide effective and relatively powerful tests for evaluating the existence of such publication bias. After adjusting for missing studies, we find that the point estimate of the overall effect size is approximately correct and coverage of the effect size confidence intervals is substantially improved, in many cases recovering the nominal confidence levels entirely. We illustrate the trim and fill method on existing meta-analyses of studies in clinical trials and psychometrics.

Monte Carlo Statistical Methods

Abstract: We have sold 4300 copies worldwide of the first edition (1999). This new edition contains five completely new chapters covering new developments.