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Extensions of linear models are very commonly used in the analysis of biological data. Whereas goodness of fit measures such as the coefficient of determination (R2) or the adjusted R2 are well established for linear models, it is not…

A goodness-of-fit test for the fitting of a parametric model to data obtained from a detector with finite resolution and limited acceptance is proposed. The parameters of the model are found by minimization of a statistic that is used for…

Recently several more efficient versions of quantum state tomography have been proposed, with the purpose of making tomography feasible even for many-qubit states. The number of state parameters to be estimated is reduced by tentatively…

The semiparametric linear hazard regression model introduced by McKeague and Sasieni (1994) is an extension of the linear hazard regression model developed by Aalen (1980). Methods of model selection for this type of model are still…

Conformal prediction, which makes no distributional assumptions about the data, has emerged as a powerful and reliable approach to uncertainty quantification in practical applications. The nonconformity measure used in conformal prediction…

The feature space (including both input and output variables) characterises a data mining problem. In predictive (supervised) problems, the quality and availability of features determines the predictability of the dependent variable, and…

Explicitly accounting for all applicable independent variables, even when the model being tested does not, is critical in testing goodness-of-fit for logistic regression. This can increase statistical power by orders of magnitude.

Many analyses require linking records from two databases comprising overlapping sets of individuals. In the absence of unique identifiers, the linkage procedure often involves matching on a set of categorical variables, such as…

This paper presents a Bayesian framework for assessing the adequacy of a model without the necessity of explicitly enumerating a specific alternate model. A test statistic is developed for tracking the performance of the model across…

This paper applies the minimum message length principle to inference of linear regression models with Student-t errors. A new criterion for variable selection and parameter estimation in Student-t regression is proposed. By exploiting…

Modern foundation models rely heavily on using scaling laws to guide crucial training decisions. Researchers often extrapolate the optimal architecture and hyper parameters settings from smaller training runs by describing the relationship…

In a statistical analysis in Particle Physics, nuisance parameters can be introduced to take into account various types of systematic uncertainties. The best estimate of such a parameter is often modeled as a Gaussian distributed variable…

We consider the problem of goodness-of-fit testing for a model that has at least one unknown parameter that cannot be eliminated by transformation. Examples of such problems can be as simple as testing whether a sample consists of…

In this work, we propose a modified Bayesian Information Criterion (BIC) specifically designed for mixture models and hierarchical structures. This criterion incorporates the determinant of the Hessian matrix of the log-likelihood function,…

In this paper we give a short theoretical description of the general predictive adaptive arithmetic coding technique. The links between this technique and the works of J. Rissanen in the 80's, in particular the BIC information criterion…

We propose two methods to evaluate the conditional Akaike information (cAI) for nonlinear mixed-effects models with no restriction on cluster size. Method 1 is designed for continuous data and includes formulae for the derivatives of fixed…

Many real-world classification problems are significantly class-imbalanced to detriment of the class of interest. The standard set of proper evaluation metrics is well-known but the usual assumption is that the test dataset imbalance equals…

Logistic regression is an important statistical tool for assessing the probability of an outcome based upon some predictive variables. Standard methods can only deal with precisely known data, however many datasets have uncertainties which…

First, we analyze the variance of the Cross Validation (CV)-based estimators used for estimating the performance of classification rules. Second, we propose a novel estimator to estimate this variance using the Influence Function (IF)…

Bayesian model selection is a tool to decide whether the introduction of a new parameter is warranted by data. I argue that the usual sampling statistic significance tests for a null hypothesis can be misleading, since they do not take into…