Ramalingam Shanmugam

Errors, Bias and Uncertainties in Astronomy.

A statistical analysis of the increasing inflow of data with which astronomers are confronted from different modern facilities. This book stems from a meeting held in September 1989 at the International Stellar Data Centre in Strasbourg.

Plantar Fasciopathy Treated with Dynamic Splinting A Randomized Controlled Trial

BACKGROUND Plantar fasciopathy (or plantar fasciitis) is considered to be one of the most common foot abnormalities, affecting up to 2 million Americans each year, and the chief complaint is acute heel pain. Therapeutic protocols for this condition have included stretching exercises, corticosteroid injections, physical therapy, and foot orthoses, but a single modality has not been found to be universally effective. We sought to determine the efficacy of stretching with dynamic splinting for the treatment of plantar fasciitis. METHODS Sixty patients (76 feet) were enrolled in this 12-week study from four different clinics across the United States. Patients were randomly categorized into experimental and control groups. All of the patients received nonsteroidal anti-inflammatory drugs, orthoses, and corticosteroid injections if needed. Thirty experimental patients also received dynamic splinting for nightly wear to obtain a low-load, prolonged-duration stretch with dynamic tension. The dependent variable was change from baseline in Plantar Fasciopathy Pain/Disability Scale score, and the independent variable was group (experimental versus control). RESULTS Two-sample t tests were calculated, and there was a significant difference in the mean change scores of experimental versus control patients (-33 versus -2 points, P < .0001). CONCLUSIONS Dynamic splinting was effective for reducing the pain of plantar fasciopathy, and this modality should be included in the standard of care for treating plantar fasciopathy.

Encyclopedia of statistics in behavioural science

With the cooperative efforts of 16 internationally known behavioural scientists in the editorial board, the two editors Brian S. Everitt and David C. Howell composed these four volumes for applied statisticians and behavioural science researchers. The entries are alphabetically arranged. The contributors are experts in these topics. Volume 1 covers topics including A priori versus post hoc testing through dummy variables. A wide range of topics starting at ecological fallacy through Lord’s paradox is addressed in Volume 2. Volume 3 contains entries from M estimators of location through to Quetelet. In Volume 4, topics from R & Q analysis through to z scores are illustrated. All the entries are superbly selected. Among them, my favourites are adaptive sampling, analysis of covariance, area sampling, bagging, Bayes, biplot, boosting, case studies, catalogue of parametric tests, catastrophe theory, censored observations, clinical psychology, cluster analysis, computer based testing, correspondence analysis, data mining, design effects, discriminant analysis, epistasis, event history analysis, external validity, facet theory, factor analysis, fuzzy cluster analysis, game theory, gene-environment interaction, graphical methods, growth curve, heritability, hierarchical models, history of behavioural statistics, information theory, intervention analysis, item analysis, latent transition models, linkage analysis, longitudinal designs, Mahalanobis distance, mail surveys, matching, mathematical psychology, meta analysis, missing data, Monte Carlo simulation, multiple testing, multivariate outliers, neural networks, nonlinear models, non-random samples, number needed to treat, odds and odds ratios, optimal scaling, optimization methods, paradoxes, pattern recognition, power, principal component analysis, probability models, proximity measures, randomization, rater agreement, recursive models, residuals, robustness, sensitivity analysis, signal detection, statistical models, structural equations, survival analysis, symmetry plot, time series analysis, utility theory, variance components, and Walsh averages. The biographical notes of a limited number of heroes in statistics are given. Some of these heroes are Bruno de Finneti, Abraham de Moivre, R. A. Fisher, Howard Hotelling, Karl Pearson, Henry Scheffe, Frank Wilcoxon, Frank Yates, and G. U. Yule. Several graphical techniques are superbly illustrated. The abbreviations and acronyms in each volume are very helpful to allow readers to read and comprehend the material. The theory and formulas are downplayed. The concepts and applications are more emphasized. I enjoyed

Generalized exponential and logarithmic polynomials with statistical applications

In many statistical discussions, especially in data analysis, the idea of polynomials plays a key role. For example, Dwyer [1] employed polynomials to express factorial moments of discrete distribution in terms of cumulative totals. Traditionally, polynomials are derived using the difference operator method (see [2], p. 134]). In this article, using the differential equation approach as an alternative method, we obtain generalized exponential and logarithmic polynomials, and find their special cases appearing in statistical signal‐noise models.

Encyclopedia of Environmetrics Volume 2

In this review, I comment on the contents [starting at E to L] of only volume 2. There are four volumes with titles ranging from A to Z that are useful in the study of environmetrics. There are twelve sections covering Chemometrics, Ecological Statistics, Environmental Health, Environmental Policy and Regulations, Extremes and Environmental Risk, Natural Resources and Agriculture, Hydrological and Physical Processes, Spatial=Temporal Modeling and Analysis, Statistical and Numerical Computing, Stochastic Modeling and Environmental Change, and Statistical Theory and Methods. In a remarkable manner, the editors have assembled in these volumes expert’s opinion and explanation of useful concepts and techniques. ‘‘Environmetrics’’ is an emerging discipline of the twenty-first century. The environmental studies end up in data analysis. What makes the data analyses in environmetrics unique is their large database. The powerful and efficient computing algorithms combined with novel statistical concepts are necessary to do the environmental data analyses. Hence, environmental studies remain more interdisciplinary attracting computational experts, model builders, and multivariate statisticians. As the editors express, the word environmetrics grew from an obscure word to be a significant word of the International Environmetrics Society with thousands of members. The articles focus on computer intensive statistical techniques, and challenges in spatial= temporal modeling and risk analysis. The coverage is very in-depth. The volumes have cross references for the readers to catch up with related ideas and tools. The acronyms and abbreviations in the front of the volume offer a great help for the confused readers. Some of noteworthy topics in volume 2 are Echelon analysis, ecological statistics, ecological economics, ecosystems, edge effect, effluent, electromagnetic field, elicitation, EM algorithm, emissions, empirical Bayes, encounter data, epidemic models, escape trajectory, estimation, exceedance probability, exposures, extreme values, factor analysis, familial correlations, fertility studies, Fieller’s theorem, forestry, frontier models, fuzzy regression, gamma and Gaussian processes, generalized additive models, generalized p-values, genetic algorithms, geographic information systems, Gibbs sampling, Global issues, ground water studies, hazards, heritability, hierarchical models, hormesis, Hotelling T, hydrological models, image analysis, importance sampling, incomplete block designs, influence diagrams, informatics, intercropping, inverted distributions, jackknifing, kernel estimation, kriging, Kronecker products, lakes, landscapes, laws and environmental statistics, least squares,

PREDICTING A “SUCCESSFUL” PREVENTION OF AN EPIDEMIC

The usual practice is that a “successful” medical intervention (due to the severity of the epidemic to the public health) takes place in the middle of the data collection period with an aim to reduce the incidence. However, not all situations might be clear on whether such an intervention even took place. Of interest to governing agencies is the prevalence of such a “successful” medical intervention. This article makes use of ideas on the characterization of probability distributions to address the likelihood for the prevalence of a “successful” intervention in an epidemic outbreak. The methodology is illustrated using plague data of two villages in India.

A tutorial about diagnostic methodology with dementia data

The purpose of the diagnostic methodology is to discuss, estimate and interpret medical parameters such as sensitivity, specificity and prevalence of a diseased population in the chosen community for the research study. However, this statistical methodology is not fully and correctly comprehended by all in the medical professions although everyone admits to its high importance and use. This article is therefore carefully prepared to alleviate commonly experienced conceptual confusions. To ease the comprehension of difficult material, real-life data of 135 participants with dementia illness are considered, analysed and interpreted. Consequently, even less technically oriented medical professionals can learn how to interpret the results from the diagnostic methodology. Critical comments with discussions in the end help to appreciate the operational procedure of the diagnostic methodology.

Advocacy for automated statistical systems

In this robotic age of intelligent manufacturing, what is needed is a well-planned built-in automated statistical systems (AASS) which would by itself intelligently and timely figure out the need for a statistical study including statistical planning of either observational or experimental nature and also carry out a statistical expert systems analysis. This AASS is indispensable so far as saving time and reducing different complexities in a manufacturing process. This article examines impediments in establishing AASS from engineering and statistical viewpoints. The potential benefits of AASS are pointed out. It is time to think about AASS loud and clear.

Asymptotic homogeneity tests for mean exponential family distributions

Abstract A new class of distributions is defined, called the Mean Exponential Family (MEF). An asymptotic test statistic is derived to examine the homogeneity of a sample from the MEF, and then, expressions are obtained for binomial, Poisson, negative biomial, beta, gamma, normal, Pareto, Laplace, and Raleigh distributions as special cases. As the results confirm a known underlying distribution for many data in the literature, there are advantages in the presented approach.

On the Stirling Distribution of the First Kind

A distribution of probabilities at positive integers t = n, n+1, …, proportional to F(t , n) θt/t!, 0 < θ < 1, is called the Stirling distribution of the first kind (SDFK) with parameters n and θ. The distribution is so named because it depends upon F(t , n), the Stirling numbers of the first kind. Patil and Wani (1965) have shown that the SDFK is the distribution of the sum of n independent and identically distributed random variables following the logarithmic series distribution. In this paper, some alternative derivations of the Patil and Wani’s result are given to further study the probabilistic structure of the SDFK. We show that with respect to the parameter n, the convolution of two independent SDFK’s is again a SDFK. Exact as well as approximate expressions of the distribution function of the SDFK are derived. Recurrence relations among the moments and the cumulants of the SDFK follow easily once we recognize that the distribution is a member of the class of power series distributions. Also, the minimum variance unbiased estimator of the probability function at any given point is derived. Several results of Patil and Wani (1965) follow as particular cases of ours when n = 1. If only θ is to be estimated, an easy graphical method is sketched to estimate it.