Related papers: Solution to Banff 2 Challenge Based on Likelihood …
In this paper, we present a possible theoretical explanation for benford's law. We develop a recursive relation between the probabilities, using simple intuitive ideas. We first use numerical solutions of this recursion and verify that the…
Likelihood ratio tests are intuitively appealing. Nevertheless, a number of examples are known in which they perform very poorly. The present paper discusses a large class of situations in which this is the case, and analyzes just how…
Various problems in Engineering and Statistics require the computation of the likelihood ratio function of two probability densities. In classical approaches the two densities are assumed known or to belong to some known parametric family.…
This paper presents a derivation of the Two-Way Likelihood Ratio (G) Test and Comparison to the Two-Way Chi Squared Test
In this paper we provide a provably convergent algorithm for the multivariate Gaussian Maximum Likelihood version of the Behrens--Fisher Problem. Our work builds upon a formulation of the log-likelihood function proposed by Buot and…
A two--step Christoffel function based solution is proposed to distribution regression problem. On the first step, to model distribution of observations inside a bag, build Christoffel function for each bag of observations. Then, on the…
Let $\mu$ be a $p$-dimensional vector, and let $\Sigma_1$ and $\Sigma_2$ be $p \times p$ positive definite covariance matrices. On being given random samples of sizes $N_1$ and $N_2$ from independent multivariate normal populations…
In this work, we explore the application of likelihood ratio as a forensic evidence assessment tool to evaluate the causal mechanism of a bloodstain pattern. It is assumed that there are two competing hypotheses regarding the cause of a…
A risk-aware decision-making problem can be formulated as a chance-constrained linear program in probability measure space. Chance-constrained linear program in probability measure space is intractable, and no numerical method exists to…
Particle physics experiments such as those run in the Large Hadron Collider result in huge quantities of data, which are boiled down to a few numbers from which it is hoped that a signal will be detected. We discuss a simple probability…
We present a positive solution to the so-called Bernoulli Conjecture concerning the characterization of sample boundedness of Bernoulli processes. We also discuss some applications and related open problems.
Two variational formulas for the power of the binary hypothesis testing problem are derived. The first is given as the Legendre transform of a certain function and the second, induced from the first, is given in terms of the Cumulative…
In this work we introduce a novel approach, based on sampling, for finding assignments that are likely to be solutions to stochastic constraint satisfaction problems and constraint optimisation problems. Our approach reduces the size of the…
When presenting forensic evidence, such as a DNA match, experts often use the Likelihood ratio (LR) to explain the impact of evidence . The LR measures the probative value of the evidence with respect to a single hypothesis such as 'DNA…
The problem of pattern selection arises when the evolution equations have many solutions, whereas observed patterns constitute a much more restricted set. An approach is advanced for treating the problem of pattern selection by defining the…
In the Bayesian paradigm for presenting forensic evidence to court, it is recommended that the weight of the evidence be summarized as a likelihood ratio (LR) between two opposing hypotheses of how the evidence could have been produced.…
We propose a new approach to solve an NP complete problem by means of stochastic limit.
The Monty Hall puzzle has been solved and dissected in many ways, but always using probabilistic arguments, so it is considered a probability puzzle. In this paper the puzzle is set up as an orthodox statistical problem involving an unknown…
We describe a statistical hypothesis test for the presence of a signal based on the likelihood ratio statistic. We derive the test for a case of interest and also show that for that case the test works very well, even far out in the tails…
The present paper answers the following questions related with high-dimensional manova: (i) is it possible to develop a likelihood ratio test for high-dimensional manova? (ii) would such test perform well? (iii) would it be able to…