Related papers: What is the likelihood function, and how is it use…
There are important problems in physics related to the concept of probability. One of these problems is related to negative probabilities used in physics from 1930s. In spite of many demonstrations of usefulness of negative probabilities,…
Probability metrics constitute an important tool in probability theory and statistics \cite{DKS91}, \cite{R91}, \cite{Z83} as they are specific metrics on spaces of random variables which, by satisfying an extra condition, concord well with…
Motivated by real-world situations found in high energy particle physics, we consider a generalisation of the likelihood-ratio estimation task to a quasiprobabilistic setting where probability densities can be negative. By extension, this…
Although the likelihood function is normalizeable with respect to the data there is no guarantee that the same holds with respect to the model parameters. This may lead to singularities in the expectation value integral of these parameters,…
The likelihood calculation of a vast number of particles is the computational bottleneck for the particle filter in applications where the observation information is rich. For fast computing the likelihood of particles, a numerical fitting…
Likelihood profiling is an efficient and powerful frequentist approach for parameter estimation, uncertainty quantification and practical identifiablity analysis. Unfortunately, these methods cannot be easily applied for stochastic models…
The Wigner function of quantum systems is an effective instrument to construct the approximate classical description of the systems for which the classical approximation is possible. During the last time, the Wigner function formalism is…
Likelihood ratios are used for a variety of applications in particle physics data analysis, including parameter estimation, unfolding, and anomaly detection. When the data are high-dimensional, neural networks provide an effective tools for…
Identifying the effects of causes and causes of effects is vital in virtually every scientific field. Often, however, the needed probabilities may not be fully identifiable from the data sources available. This paper shows how partial…
In quantum mechanics, not everything that can be observed can be observed simultaneously. Observational data exhibits \emph{contextuality} -- a generalisation of nonlocality -- if the result of an observation is necessarily dependent on…
This study has the purpose of addressing four questions that lie at the base of the probability theory and statistics, and includes two main steps. As first, we conduct the textual analysis of the most significant works written by eminent…
Testing hypotheses is an issue of primary importance in the scientific research, as well as in many other human activities. Much clarification about it can be achieved if the process of learning from data is framed in a stochastic model of…
The process of doing Science in condition of uncertainty is illustrated with a toy experiment in which the inferential and the forecasting aspects are both present. The fundamental aspects of probabilistic reasoning, also relevant in real…
The notion of probability density for a random function is not as straightforward as in finite-dimensional cases. While a probability density function generally does not exist for functional data, we show that it is possible to develop the…
Challenging research in various fields has driven a wide range of methodological advances in variable selection for regression models with high-dimensional predictors. In comparison, selection of nonlinear functions in models with additive…
A probabilistic interpretation of one-particle relativistic quantum mechanics is proposed. Quantum Action Principle formulated earlier is used for to make the dynamics of the Minkowsky time variable of a particle to be classical. After…
The likelihood function represents statistical evidence in the context of data and a probability model. Considerable theory has demonstrated that evidence strength for different parameter values can be interpreted from the ratio of…
Bayesian probability theory is used to analyze the oft-made assumption that humans are typical observers in the universe. Some theoretical calculations make the {\it selection fallacy} that we are randomly chosen from a class of objects by…
This chapter presents probability logic as a rationality framework for human reasoning under uncertainty. Selected formal-normative aspects of probability logic are discussed in the light of experimental evidence. Specifically, probability…
The familiar theories of physics have the feature that the application of the theory to make predictions in specific circumstances can be done by means of an algorithm. We propose a more precise formulation of this feature --- one based on…