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Mendelian randomization (MR) is a natural experimental design based on the random transmission of genes from parents to offspring. However, this inferential basis is typically only implicit or used as an informal justification. As…
An important issue in survival analysis is the investigation and the modeling of hazard rates. Within a Bayesian nonparametric framework, a natural and popular approach is to model hazard rates as kernel mixtures with respect to a…
Fully Bayesian methods for Cox models specify a model for the baseline hazard function. Parametric approaches generally provide monotone estimations. Semi-parametric choices allow for more flexible patterns but they can suffer from…
This paper introduces two families of probability distributions for Bayesian analysis of hypertoroidal data. The first family consists of symmetric distributions derived from the projection of multivariate normal distributions under…
Many learning machines such as normal mixtures and layered neural networks are not regular but singular statistical models, because the map from a parameter to a probability distribution is not one-to-one. The conventional statistical…
Random matrix theory (RMT) provides a successful model for quantum systems, whose classical counterpart has a chaotic dynamics. It is based on two assumptions: (1) matrix-element independence, and (2) base invariance. Last decade witnessed…
A fundamental theoretical limitation undermines current disaster risk models: existing approaches suffer from two critical constraints. First, conventional damage prediction models remain predominantly deterministic, relying on fixed…
We study gravitational and test-field perturbations for the two possible families of spherically symmetric black-hole mimickers that smoothly interpolate between regular black holes and horizonless compact objects accordingly to the value…
The skew-normal and the skew-$t$ distributions are parametric families which are currently under intense investigation since they provide a more flexible formulation compared to the classical normal and $t$ distributions by introducing a…
Consider bivariate observations $(X_1,Y_1), \ldots, (X_n,Y_n) \in \mathbb{R}\times \mathbb{R}$ with unknown conditional distributions $Q_x$ of $Y$, given that $X = x$. The goal is to estimate these distributions under the sole assumption…
Consider a classically chaotic system which is described by a Hamiltonian H_0. At t=0 the Hamiltonian undergoes a sudden-change H_0 -> H. We consider the quantum-mechanical spreading of the evolving energy distribution, and argue that it…
Hazard rates play an important role in various areas, e.g., reliability theory, survival analysis, biostatistics, queueing theory and actuarial studies. Mixtures of distributions are also of a great preeminence in such areas as most…
The approximation ratio has become one of the dominant measures in mechanism design problems. In light of analysis of algorithms, we define the \emph{smoothed approximation ratio} to compare the performance of the optimal mechanism and a…
In this paper, we have obtained conditions on parameters that result in dispersive ordering and star ordering among two unequal sets of random variables from Proportional hazard rate and Proportional reversed hazard rate family of…
We investigate stochastic comparisons between exponential family distributions and their mixtures with respect to the usual stochastic order, the hazard rate order, the reversed hazard rate order, and the likelihood ratio order. A general…
In this paper, we discuss the ambiguous chance constrained based portfolio optimization problems, in which the perturbations associated with the input parameters are stochastic in nature, but their distributions are not known precisely. We…
We introduce a new notion of "regularity structure" that provides an algebraic framework allowing to describe functions and / or distributions via a kind of "jet" or local Taylor expansion around each point. The main novel idea is to…
Beardon and Minda gave a characterization of normal families of holomorphic and meromorphic functions in terms of a locally uniform Lipschitz condition. Here, we generalize this viewpoint to families of mappings in higher dimensions that…
The beta normal distribution is a generalization of both the normal distribution and the normal order statistics. Some of its mathematical properties and a few applications have been studied in the literature. We provide a better foundation…
A Wright function based framework is proposed to combine and extend several distribution families. The $\alpha$-stable distribution is generalized by adding the degree of freedom parameter. The PDF of this two-sided super distribution…