Related papers: Indeterminate Probability Theory
Traditional neural network regression models provide only point estimates, failing to capture predictive uncertainty. Probabilistic neural networks (PNNs) address this limitation by producing output distributions, enabling the construction…
Univariate and multivariate normal probability distributions are widely used when modeling decisions under uncertainty. Computing the performance of such models requires integrating these distributions over specific domains, which can vary…
This article is devoted to providing a review of mathematical formulations in which Polynomial Chaos Theory (PCT) has been incorporated into stochastic model predictive control (SMPC). In the past decade, PCT has been shown to provide a…
Constructing prediction sets with coverage guarantees for unobserved outcomes is a core problem in modern statistics. Methods for predictive inference have been developed for a wide range of settings, but usually only consider test data…
Quantifying the uncertainty of predictions is a core problem in modern statistics. Methods for predictive inference have been developed under a variety of assumptions, often -- for instance, in standard conformal prediction -- relying on…
We study an information analogue of infinitely divisible probability distributions, where the i.i.d. sum is replaced by the joint distribution of an i.i.d. sequence. A random variable $X$ is called informationally infinitely divisible if,…
This short study presents an opportunistic approach to a (more) reliable validation method for prediction uncertainty average calibration. Considering that variance-based calibration metrics (ZMS, NLL, RCE...) are quite sensitive to the…
A general piecewise (including pointwise) probability distribution with space-saving notation and its hierarchical particular cases are considered. The explicit closed-form normalization, expectation, and variance formulas along with the…
Introduction: Joint models are increasingly used in clinical trials. An important part of model building is to properly assess the descriptive and predictive ability of these models. Normalised prediction discrepancies (npd) and normalised…
The likelihood function plays a pivotal role in statistical inference; it is adaptable to a wide range of models and the resultant estimators are known to have good properties. However, these results hinge on correct specification of the…
Model-based testing (MBT) is a well-known technology, which allows for automatic test case generation, execution and evaluation. To test non-functional properties, a number of test MBT frameworks have been developed to test systems with…
Many supervised machine learning tasks, such as future state prediction in dynamical systems, require precise modeling of a forecast's uncertainty. The Multiple Hypotheses Prediction (MHP) approach addresses this problem by providing…
Distribution-free prediction sets play a pivotal role in uncertainty quantification for complex statistical models. Their validity hinges on reliable calibration data, which may not be readily available as real-world environments often…
Copulas are a powerful tool for modeling multivariate distributions as they allow to separately estimate the univariate marginal distributions and the joint dependency structure. However, known parametric copulas offer limited flexibility…
The analysis of practical probabilistic models on the computer demands a convenient representation for the available knowledge and an efficient algorithm to perform inference. An appealing representation is the influence diagram, a network…
Maximum entropy principle (MEP) offers an effective and unbiased approach to inferring unknown probability distributions when faced with incomplete information, while neural networks provide the flexibility to learn complex distributions…
Probabilistic forecasting of irregularly sampled multivariate time series with missing values is an important problem in many fields, including health care, astronomy, and climate. State-of-the-art methods for the task estimate only…
Motivated by recently emerging problems in machine learning and statistics, we propose data models which relax the familiar i.i.d. assumption. In essence, we seek to understand what it means for data to come from a set of probability…
Evaluating joint probabilities of potential outcomes and observed variables, and their linear combinations, is a fundamental challenge in causal inference. This paper addresses the bounding and identification of these probabilities in…
We propose two classes of nonparametric point estimators of $\theta=P(X<Y)$ in the case where $(X,Y)$ are paired, possibly dependent, absolutely continuous random variables. The proposed estimators are based on nonparametric estimators of…