Related papers: A relation between log-likelihood and cross-valida…

Test log-likelihood is commonly used to compare different models of the same data or different approximate inference algorithms for fitting the same probabilistic model. We present simple examples demonstrating how comparisons based on test…

In Bayesian statistics, the marginal likelihood, also known as the evidence, is used to evaluate model fit as it quantifies the joint probability of the data under the prior. In contrast, non-Bayesian models are typically compared using…

The log-normal distribution is used to describe the positive data, that it has skewed distribution with small mean and large variance. This distribution has application in many sciences for example medicine, economics, biology and…

Logistic-regression calibration and fusion are potential steps in the calculation of forensic likelihood ratios. The present paper provides a tutorial on logistic-regression calibration and fusion at a practical conceptual level with…

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.

Cross validation residuals are well known for the ordinary least squares model. Here leave-M-out cross validation is extended to generalised least squares. The relationship between cross validation residuals and Cook's distance is…

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…

Cross-validation is a popular non-parametric method for evaluating the accuracy of a predictive rule. The usefulness of cross-validation depends on the task we want to employ it for. In this note, I discuss a simple non-parametric setting,…

Over the past decades, various methods for comparing the means of two log-normal have been proposed. Some of them are differing in terms of how the statistic test adjust to accept or to reject the null hypothesis. In this study, a new…

Balancing a rare and serious possibility against a more common and less serious one is a familiar problem in many situations, such as the prediction of rare diseases. The relative costs of forecasting errors can be used for any prediction…

Used to estimate the risk of an estimator or to perform model selection, cross-validation is a widespread strategy because of its simplicity and its apparent universality. Many results exist on the model selection performances of…

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…

We define the likelihood and give a number of justifications for its use as a skill measure for probabilistic forecasts. We describe a number of different scores based on the likelihood, and briefly investigate the relationships between the…

In this note, we study the relationship between the variational gap and the variance of the (log) likelihood ratio. We show that the gap can be upper bounded by some form of dispersion measure of the likelihood ratio, which suggests the…

Log-linear models are a well-established method for describing statistical dependencies among a set of n random variables. The observed frequencies of the n-tuples are explained by a joint probability such that its logarithm is a sum of…

Tests for proportional hazards assumption concerning specified covariates or groups of covariates are proposed. The class of alternatives is wide: log-hazard rates under different values of covariates may cross, approach, go away. The data…

A logic is defined that allows to express information about statistical probabilities and about degrees of belief in specific propositions. By interpreting the two types of probabilities in one common probability space, the semantics given…

The (relevance) weighted likelihood was introduced to formally embrace a variety of statistical procedures that trade bias for precision. Unlike its classical counterpart, the weighted likelihood combines all relevant information while…

Cross-validation is a widely-used technique to estimate prediction error, but its behavior is complex and not fully understood. Ideally, one would like to think that cross-validation estimates the prediction error for the model at hand, fit…

In this article, we derive concentration inequalities for the cross-validation estimate of the generalization error for subagged estimators, both for classification and regressor. General loss functions and class of predictors with both…