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A composite likelihood is an inference function derived by multiplying a set of likelihood components. This approach provides a flexible framework for drawing inference when the likelihood function of a statistical model is computationally…
This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a…
Over the past two decades, several consistent procedures have been designed to infer causal conclusions from observational data. We prove that if the true causal network might be an arbitrary, linear Gaussian network or a discrete Bayes…
We derive a parallel sampling algorithm for computational inverse problems that present an unknown linear forcing term and a vector of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of…
The log-transform is a common tool in statistical analysis, reducing the impact of extreme values, compressing the range of reported values for improved visualization, enabling the usage of parametric statistical tests requiring normally…
Statistical analysis is an important tool to distinguish systematic from chance findings. Current statistical analyses rely on distributional assumptions reflecting the structure of some underlying model, which if not met lead to problems…
A method is developed for calculating effective sums of divergent series. This approach is a variant of the self-similar approximation theory. The novelty here is in using an algebraic transformation with a power providing the maximal…
In this article we will propose a completely new point of view for solving one of the most important paradoxes concerning game theory. The solution develop shifts the focus from the result to the strategy s ability to operate in a cognitive…
Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions…
The two envelopes paradox is discussed. By calculating the conditional probability, we arrive at a conditional expectations which differs from existing results.
Decomposition methods are often used for producing counterfactual predictions in non-strategic settings. When the outcome of interest arises from a game-theoretic setting where agents are better off by deviating from their strategies after…
We study how the divide and conquer principle --- partition the available data into subsamples, compute an estimate from each subsample and combine these appropriately to form the final estimator --- works in non-standard problems where…
The Jensen inequality is a widely used tool in a multitude of fields, such as for example information theory and machine learning. It can be also used to derive other standard inequalities such as the inequality of arithmetic and geometric…
The number of inversions is a statistic on permutation groups measuring the degree to which the entries of a permutation are out of order. We provide a generalization of that statistic by introducing the statistic number of pseudoinversions…
In this paper we study the inverse of so-called unfair permutations, and explore various properties of them. Our investigation begins with comparing this class of permutations with uniformly random permutations, and showing that they behave…
We propose an approach for testing the hypothesis that two realizations of the random variables in the form of histograms are taken from the same statistical population (i.e. that two histograms are drawn from the same distribution). The…
In statistical mechanics, the generally called Stirling approximation is actually an approximation of Stirling's formula. In this article, it is shown that the term that is dropped is in fact the one that takes fluctuations into account.…
In this work, we develop a method named Twinning, for partitioning a dataset into statistically similar twin sets. Twinning is based on SPlit, a recently proposed model-independent method for optimally splitting a dataset into training and…
Statistical hypothesis testing serves as statistical evidence for scientific innovation. However, if the reported results are intentionally biased, hypothesis testing no longer controls the rate of false discovery. In particular, we study…
In the context of big data analysis, the divide-and-conquer methodology refers to a multiple-step process: first splitting a data set into several smaller ones; then analyzing each set separately; finally combining results from each…