Related papers: Understanding parameter differences between analys…

Bayesian analyses require that all variable model parameters are given a prior probability distribution. This can pose a challenge for analyses where multiple experiments are combined if these experiments use different parametrisations for…

Traditionally regression analysis answers questions about the relationships among variables based on the assumption that the observation values of variables are precise numbers. It has long been dominated by least squares techniques, mostly…

Being able to interpret, or explain, the predictions made by a machine learning model is of fundamental importance. This is especially true when there is interest in deploying data-driven models to make high-stakes decisions, e.g. in…

Reasoning about unpredicted change consists in explaining observations by events; we propose here an approach for explaining time-stamped observations by surprises, which are simple events consisting in the change of the truth value of a…

Estimating and quantifying uncertainty in unknown system parameters from limited data remains a challenging inverse problem in a variety of real-world applications. While many approaches focus on estimating constant parameters, a subset of…

Change-point analysis is a flexible and computationally tractable tool for the analysis of times series data from systems that transition between discrete states and whose observables are corrupted by noise. The change-point algorithm is…

Suppose data are fitted to some parametric model but that the true model happens to be one with an additional parameter. When a parameter is to be estimated one can use likelihood estimation in the wider model or in the narrow model.…

There are two distinct definitions of 'P-value' for evaluating a proposed hypothesis or model for the process generating an observed dataset. The original definition starts with a measure of the divergence of the dataset from what was…

We study the problem of parameter estimation for time-series possessing two, widely separated, characteristic time scales. The aim is to understand situations where it is desirable to fit a homogenized singlescale model to such multiscale…

Bifurcation theory is the usual analytic approach to study the parameter space of a dynamical system. Despite the great power of prediction of these techniques, fundamental limitations appear during the study of a given problem. Nonlinear…

For data sets with similar features, for example highly correlated features, most existing stability measures behave in an undesired way: They consider features that are almost identical but have different identifiers as different features.…

The uncertainty or the variability of the data may be treated by considering, rather than a single value for each data, the interval of values in which it may fall. This paper studies the derivation of basic description statistics for…

A common problem in data analysis is that the functional form, as well as the parameter values, of the underlying model which should describe a dataset is not known a priori. In these cases some extra uncertainty must be assigned to the…

Recently, many regularized procedures have been proposed for variable selection in linear regression, but their performance depends on the tuning parameter selection. Here a criterion for the tuning parameter selection is proposed, which…

Measuring the distance between data points is fundamental to many statistical techniques, such as dimension reduction or clustering algorithms. However, improvements in data collection technologies has led to a growing versatility of…

The estimation of static parameters in dynamical systems and control theory has been extensively studied, with significant progress made in estimating varying parameters in specific system types. Suppose, in the general case, we have data…

In this article, we introduce a procedure for selecting variables in principal components analysis. The procedure was developed to identify a small subset of the original variables that best explain the principal components through…

Measuring inter-dataset similarity is an important task in machine learning and data mining with various use cases and applications. Existing methods for measuring inter-dataset similarity are computationally expensive, limited, or…

Data values in a dataset can be missing or anomalous due to mishandling or human error. Analysing data with missing values can create bias and affect the inferences. Several analysis methods, such as principle components analysis or…

The explanations of large language models have recently been shown to be sensitive to the randomness used for their training, creating a need to characterize this sensitivity. In this paper, we propose a characterization that questions the…