Related papers: Solution to Banff 2 Challenge Based on Likelihood …
We discuss the history of attempts to solve the Pell equation using certain auxiliary equations that correspond, in modern terminology, to a second 2-descent.
Works, briefly surveyed here, are concerned with two basic methods: Maximum Probability and Bayesian Maximum Probability; as well as with their asymptotic instances: Relative Entropy Maximization and Maximum Non-parametric Likelihood.…
We provide a method for approximating Bayesian inference using rejection sampling. We not only make the process efficient, but also dramatically reduce the memory required relative to conventional methods by combining rejection sampling…
We give a simple statistical proof of a binomial identity, by evaluating the Laplace transform of the maximum of n independent exponential random variables in two different ways. As a by product, we obtain a simple proof of an interesting…
Several authors have explained that the likelihood ratio measures the strength of the evidence represented by observations in statistical problems. This idea works fine when the goal is to evaluate the strength of the available evidence for…
The "rare type match problem" is the situation in which the suspect's DNA profile, matching the DNA profile of the crime stain, is not in the database of reference. The evaluation of this match in the light of the two competing hypotheses…
We give an algorithm A which assigns probabilities to logical sentences. For any simple infinite sequence of sentences whose truth-values appear indistinguishable from a biased coin that outputs "true" with probability p, we have that the…
We address the issue of performing inference on the parameters that index a bimodal extension of the Birnbaum-Saunders distribution (BS). We show that maximum likelihood point estimation can be problematic since the standard nonlinear…
We study linear chance-constrained problems where the coefficients follow a Gaussian mixture distribution. We provide mixed-binary quadratic programs that give inner and outer approximations of the chance constraint based on piecewise…
A linearized version of Heisenberg's fundamental equation is solved, and the solutions satisfy the axioms of a relativistic quantum field theory with a fundamental length.
The likelihood ratio (LR) measures the relative weight of forensic data regarding two hypotheses. Several levels of uncertainty arise if frequentist methods are chosen for its assessment: the assumed population model only approximates the…
We consider the issue of performing accurate small-sample testing inference in beta regression models, which are useful for modeling continuous variates that assume values in $(0,1)$, such as rates and proportions. We derive the Bartlett…
We consider whether the asymptotic distributions for the log-likelihood ratio test statistic are expected to be Gaussian or chi-squared. Two straightforward examples provide insight on the difference.
In this paper we study the continuous dependence with respect to obstacles for obstacle problems with measure data. This is deeply investigated introducing a suitable type of convergence, which gives stability under very general hypotheses.…
As a natural approach to modeling system safety conditions, chance constraint (CC) seeks to satisfy a set of uncertain inequalities individually or jointly with high probability. Although a joint CC offers stronger reliability certificate,…
After Abel Ruffini theorem and Galois Theory the search for a method or formula to solve quintic equation ends. This paper discuss about the radical solution of quintic equation using a method that could be proved in some simple steps. A…
Parametric inference posits a statistical model that is a specified family of probability distributions. Restricted inference, e.g., restricted likelihood ratio testing, attempts to exploit the structure of a statistical submodel that is a…
It is well known that there is no direct one-to-one relation between $p$-values and likelihood ratios or Bayes factors, since their relation crucially involves the sample size $n$. We investigate their (asymptotic) relation in a…
In this paper,we consider the solutions of the elliptic double obstacle problems with Orlicz growth involving measure data. Some pointwise estimates for the approximable solutions to these problems are obtained in terms of fractional…
The On-Off problem, aka. Li-Ma problem, is a statistical problem where a measured rate is the sum of two parts. The first is due to a signal and the second due to a background, both of which are unknown. Mostly frequentist solutions are…