Related papers: Introduction to Neutrosophic Statistics
This note introduces the concept of a partially specified prior distribution for certain post hoc inference problems, where a finite population is sampled once in order to make a decision on the presence or complete absence of some…
Estimating the size of an elusive target population is of prominent interest in many areas in the life and social sciences. Our aim is to provide an efficient and workable method to estimate the unknown population size, given the frequency…
The present communication addresses a set of observations, obeying both deterministic as well as statistical formal requirements, and serving to operate within the framework of the dynamical systems theory, with a certain emphasis placed on…
Determining the strength of non-linear statistical dependencies between two variables is a crucial matter in many research fields. The established measure for quantifying such relations is the mutual information. However, estimating mutual…
This paper gives a review of concentration inequalities which are widely employed in non-asymptotical analyses of mathematical statistics in a wide range of settings, from distribution-free to distribution-dependent, from sub-Gaussian to…
Several measures of non-convexity (departures from convexity) have been introduced in the literature, both for sets and functions. Some of them are of geometric nature, while others are more of topological nature. We address the statistical…
Data represented by probability measures arise as empirical distributions, posterior distributions, and feature-based representations of complex objects. We study heterogeneity in a population of probability measures through the expected…
Conformal prediction is a statistically rigorous method for quantifying uncertainty in models by having them output sets of predictions, with larger sets indicating more uncertainty. However, prediction sets are not inherently actionable;…
The past century has seen a steady increase in the need of estimating and predicting complex systems and making (possibly critical) decisions with limited information. Although computers have made possible the numerical evaluation of…
When a scientist performs an experiment they normally acquire a set of measurements and are expected to demonstrate that their results are "statistically significant" thus confirming whatever hypothesis they are testing. The main method for…
Probability forecasts are intended to account for the uncertainties inherent in forecasting. It is suggested that from an end-user's point of view probability is not necessarily sufficient to reflect uncertainties that are not simply the…
Various statistical tests have been developed for testing the equality of means in matched pairs with missing values. However, most existing methods are commonly based on certain distributional assumptions such as normality, 0-symmetry or…
Algorithmic statistics considers the following problem: given a binary string $x$ (e.g., some experimental data), find a "good" explanation of this data. It uses algorithmic information theory to define formally what is a good explanation.…
Sequential sampling occurs when the entire population is not known in advance and data are obtained one at a time or in groups of units. This manuscript proposes a new algorithm to sequentially select a balanced sample. The algorithm…
We develop a new approach for quantifying uncertainty in finite populations, by using design distributions to calibrate sensitivity parameters in finite population identified sets. This yields uncertainty intervals that can be interpreted…
Consider a researcher estimating the parameters of a regression function based on data for all 50 states in the United States or on data for all visits to a website. What is the interpretation of the estimated parameters and the standard…
Hierarchically-organized data arise naturally in many psychology and neuroscience studies. As the standard assumption of independent and identically distributed samples does not hold for such data, two important problems are to accurately…
Some practical results are derived for population inference based on a sample, under the two qualitative conditions of 'ignorability' and exchangeability. These are the 'Histogram Theorem', for predicting the outcome of a non-sampled member…
Existing approaches to model uncertainty typically either compare models using a quantitative model selection criterion or evaluate posterior model probabilities having set a prior. In this paper, we propose an alternative strategy which…
The issue of asymmetric uncertainties resulting from fits, nonlinear propagation and systematic effects is reviewed. It is shown that, in all cases, whenever a published result is given with asymmetric uncertainties, the value of the…