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A random phenomenon may have two sources of random variation: an unstable identity and a set of external variation-generating factors. When only a single source is active, two mutually exclusive extreme scenarios may ensue that result in…
Direct measurements of Gini coefficients by conventional arithmetic calculations are a poor estimator, even if paradoxically, they include the entire population, as because of super-additivity they cannot lend themselves to comparisons…
Diagnostic testing is germane to a variety of scenarios in medicine, pandemic tracking, threat detection, and signal processing. This is an expository paper with some original results. Here we first set up a mathematical architecture for…
Socio-economic inequality is measured using various indices. The Gini ($g$) index, giving the overall inequality is the most commonly used, while the recently introduced Kolkata ($k$) index gives a measure of $1-k$ fraction of population…
In this note, an alternative for presenting the distribution of `significant' events in searches for new phenomena is described. The alternative is based on probability density functions used in the evaluation of the `significance' of an…
We study the problems related to the estimation of the Gini index in presence of a fat-tailed data generating process, i.e. one in the stable distribution class with finite mean but infinite variance (i.e. with tail index $\alpha\in(1,2)$).…
Extensions of linear models are very commonly used in the analysis of biological data. Whereas goodness of fit measures such as the coefficient of determination (R2) or the adjusted R2 are well established for linear models, it is not…
This paper develops some objective priors for certain parameters of the bivariate normal distribution. The parameters considered are the regression coefficient, the generalized variance, and the ratio of the conditional variance of one…
The concepts of variability and uncertainty, both epistemic and alleatory, came from experience and coexist with different connotations. Therefore this article attempts to express their relation by analytic means firstly setting sights on…
We study distributional similarity measures for the purpose of improving probability estimation for unseen cooccurrences. Our contributions are three-fold: an empirical comparison of a broad range of measures; a classification of similarity…
Hypoelliptic diffusion processes can be used to model a variety of phenomena in applications ranging from molecular dynamics to audio signal analysis. We study parameter estimation for such processes in situations where we observe some…
Estimating prevalence, the fraction of a population with a certain medical condition, is fundamental to epidemiology. Traditional methods rely on classification of test samples taken at random from a population. Such approaches to…
The classical Lorenz curve is often used to depict inequality in a population of incomes, and the associated Gini coefficient is relied upon to make comparisons between different countries and other groups. The sample estimates of these…
The negative binomial distribution has been widely used as a more flexible model than the Poisson distribution for count data. However, when the true data-generating process is Poisson, it is often challenging to distinguish it from a…
This paper proposes the k-generalized distribution as a model for describing the distribution and dispersion of income within a population. Formulas for the shape, moments and standard tools for inequality measurement - such as the Lorenz…
Propensity score weighting is widely used to improve the representativeness and correct the selection bias in the voluntary sample. The propensity score is often developed using a model for the sampling probability, which can be subject to…
Propensity score plays a central role in causal inference, but its use is not limited to causal comparisons. As a covariate balancing tool, propensity score can be used for controlled descriptive comparisons between groups whose memberships…
An important challenge in statistical analysis lies in controlling the estimation bias when handling the ever-increasing data size and model complexity of modern data settings. In this paper, we propose a reliable estimation and inference…
This article examines the application of a popular measure of sparsity, Gini Index, on network graphs. A wide variety of network graphs happen to be sparse. But the index with which sparsity is commonly measured in network graphs is edge…
Probabilistic modeling is cyclical: we specify a model, infer its posterior, and evaluate its performance. Evaluation drives the cycle, as we revise our model based on how it performs. This requires a metric. Traditionally, predictive…