Related papers: A relation between log-likelihood and cross-valida…
Probability-like parameters appearing in some statistical models, and their prior distributions, are reinterpreted through the notion of `circumstance', a term which stands for any piece of knowledge that is useful in assigning a…
We study nonparametric maximum likelihood estimation of a log-concave probability density and its distribution and hazard function. Some general properties of these estimators are derived from two characterizations. It is shown that the…
The notion of belief likelihood function of repeated trials is introduced, whenever the uncertainty for individual trials is encoded by a belief measure (a finite random set). This generalises the traditional likelihood function, and…
Starting with a likelihood or preference order on worlds, we extend it to a likelihood ordering on sets of worlds in a natural way, and examine the resulting logic. Lewis earlier considered such a notion of relative likelihood in the…
For several decades, legal and scientific scholars have argued that conclusions from forensic examinations should be supported by statistical data and reported within a probabilistic framework. Multiple models have been proposed to quantify…
K-fold cross-validation is a widely used tool for assessing classifier performance. The reproducibility crisis faced by artificial intelligence partly results from the irreproducibility of reported k-fold cross-validation-based performance…
This note proposes a method, which can be applied to searches and more in general to any cross section measurement, to maximize the analysis sensitivity.
This text is a survey on cross-validation. We define all classical cross-validation procedures, and we study their properties for two different goals: estimating the risk of a given estimator, and selecting the best estimator among a given…
Recently, new methods for model assessment, based on subsampling and posterior approximations, have been proposed for scaling leave-one-out cross-validation (LOO) to large datasets. Although these methods work well for estimating predictive…
In this paper, we study stochastic comparisons of parallel systems having log-Lindley distributed components. These comparisons are carried out with respect to reversed hazard rate and likelihood ratio ordering.
For testing independence it is very popular to use either the $\chi^{2}$-statistic or $G^{2}$-statistics (mutual information). Asymptotically both are $\chi^{2}$-distributed so an obvious question is which of the two statistics that has a…
The concept of typicality refers to properties holding for the "overwhelming majority" of cases and is a fundamental idea of the qualitative approach to dynamical problems. We argue that measure-theoretical typicality would be the adequate…
Logs are semi-structured text generated by logging statements in software source code. In recent decades, software logs have become imperative in the reliability assurance mechanism of many software systems because they are often the only…
We formulate conditions on a set of log-concave sequences, under which any linear combination of those sequences is log-concave, and further, of conditions under which linear combinations of log-concave sequences that have been transformed…
In algebraic statistics, the maximum likelihood degree of a statistical model is the number of complex critical points of its log-likelihood function. A priori knowledge of this number is useful for applying techniques of numerical…
An agent often has a number of hypotheses, and must choose among them based on observations, or outcomes of experiments. Each of these observations can be viewed as providing evidence for or against various hypotheses. All the attempts to…
We prove new, general versions of Bernstein-von Mises theorem for both well-specified and misspecified models when the log-likelihood is concave in the parameter and the prior distribution is log-concave. Unlike classical versions of…
We generalize fast Gaussian process leave-one-out formulae to multiple-fold cross-validation, highlighting in turn the covariance structure of cross-validation residuals in both Simple and Universal Kriging frameworks. We illustrate how…
We show that determining the crossing number of a link is NP-hard. For some weaker notions of link equivalence, we also show NP-completeness.
In this paper, we use the method of modified signed log-likelihood ratio test for the problem of testing the equality of correlation coefficients in two independent bivariate normal distributions. We compare this method with two other…