Related papers: The Monty Hall problem revisited
A multicomponent random process used as a model for the problem of space-time earthquake prediction; this allows us to develop consistent estimation for conditional probabilities of large earthquakes if the values of the predictor…
We describe briefly in this note a procedure for consistently estimating the marginal likelihood of a statistical model through a sample from the posterior distribution of the model parameters.
We introduce an algorithm to generate (not solve) spin-glass instances with planted solutions of arbitrary size and structure. First, a set of small problem patches with open boundaries is solved either exactly or with a heuristic, and then…
A Monte Carlo method is presented to evaluate quantum states with many particles moving in the continuum. The scattering state is generated at each time by a Monte Carlo random sampling algorithm. The same calculation are repeated until the…
We analyse the splitting algorithm performance in the estimation of rare event probabilities and this in a discrete multidimensional framework. For this we assume that each threshold is partitioned into disjoint subsets and the probability…
The information decomposition problem requires an additive decomposition of the mutual information between the input and target variables into nonnegative terms. The recently introduced solution to this problem, Information Attribution,…
By using techniques of poset representation theory, we present a formula for the number of partitions of a positive integer into three polygonal numbers.
We propose a black-box approach to reducing large semidefinite programs to a set of smaller semidefinite programs by projecting to random linear subspaces. We evaluate our method on a set of polynomial optimization problems, demonstrating…
Classical probability theory supports probability measures, assigning a fixed positive real value to each event, these measures are far from satisfactory in formulating real-life occurrences. The main innovation of this paper is the…
The utilization of model checking has been suggested as a formal verification technique for analyzing critical systems. However, the primary challenge in applying to complex systems is state space explosion problem. To address this issue,…
Value methods for solving stochastic games with partial observability model the uncertainty about states of the game as a probability distribution over possible states. The dimension of this belief space is the number of states. For many…
Within psychology, neuroscience and artificial intelligence, there has been increasing interest in the proposal that the brain builds probabilistic models of sensory and linguistic input: that is, to infer a probabilistic model from a…
We introduce a new method, combination of random testing and abstract interpretation, for the analysis of programs featuring both probabilistic and non-probabilistic nondeterminism. After introducing "ordinary" testing, we show how to…
Using the Clauser-Horne model of Bell's theorem, the locality condition is examined and it is shown the corresponding formulation is equivalent to a factorization process consisting of three stages. The first stage is introduced based on…
The notion of upper variance under multiple probabilities is defined by a corresponding minimax optimization problem. This paper proposes a simple algorithm to solve the related minimax optimization problem exactly. As an application, we…
Factor analysis, a classical multivariate statistical technique is popularly used as a fundamental tool for dimensionality reduction in statistics, econometrics and data science. Estimation is often carried out via the Maximum Likelihood…
We study the polyhedral structure of the static probabilistic lot-sizing problem and propose valid inequalities that integrate information from the chance constraint and the binary setup variables. We prove that the proposed inequalities…
The interpretation of new particle search results involves a confidence level calculation on either the discovery hypothesis or the background-only ("null") hypothesis. A typical approach uses toy Monte Carlo experiments to build an…
We study the famous mathematical puzzle of prisoners and hats. We introduce a framework in which various variants of the problem can be formalized. We examine three particular versions of the problem (each one in fact a class of problems)…
We use the idea of the broken stick problem (which goes back to Poincare) and calculate the corresponding probabilities for the cases in which the three broken part are: the medians in a triangle, the altitudes, radii of excircles, angle…