Related papers: What is the likelihood function, and how is it use…
Within quantum mechanics it is possible to assign a probability to the chance that a measurement has been made at a specific time t. However, the interpretation of such a probability is far from clear. We argue that a recent measuring…
Belief functions are a powerful and popular framework for the mathematical characterisation of uncertainty, in particular in situations in which lack of data renders learning a probability distribution for the problem impractical. The first…
The forensic science community has increasingly sought quantitative methods for conveying the weight of evidence. Experts from many forensic laboratories summarize their findings in terms of a likelihood ratio. Several proponents of this…
Bayesian probability theory is used as a framework to develop a formalism for the scientific method based on principles of inductive reasoning. The formalism allows for precise definitions of the key concepts in theories of physics and also…
The intuitive reasoning of physicists in conditions of uncertainty is closer to the Bayesian approach than to the frequentist ideas taught at University and which are considered the reference framework for handling statistical problems. The…
Energy-based probabilistic models learned by maximizing the likelihood of the data are limited by the intractability of the partition function. A widely used workaround is to maximize the pseudo-likelihood, which replaces the global…
Here the probability density of relativistic particles coordinates, satisfying the formal conditions of the quantum mechanics and the special relativity, is determined (under textbooks view, such density does not exist). It is specified for…
The ability to calculate precise likelihood ratios is fundamental to many STEM areas, such as decision-making theory, biomedical science, and engineering. However, there is no assumption-free statistical methodology to achieve this. For…
Estimations of physical parameters using data usually involve non-uniform experimental efficiencies. In this article, a method of maximum likelihood fit is introduced using the efficiency as a weight, while the probability distribution…
We propose an integration of possibility theory into non-classical logics. We obtain many formal results that generalize the case where possibility and necessity functions are based on classical logic. We show how useful such an approach is…
The Jeffreys-Lindley paradox displays how the use of a p-value (or number of standard deviations z) in a frequentist hypothesis test can lead to an inference that is radically different from that of a Bayesian hypothesis test in the form…
We give a extensive account of a recent new way of applying the Dirichlet form theory to random Poisson measures. The main application is to obtain existence of density for thelaws of random functionals of L\'evy processes or solutions of…
Probability interference is a fundamental characteristic of quantum mechanics. In this paper we attempt to show with the help of some examples, where this fundamental trait of quantum physics can be found back in a social science…
The path probability of a particle undergoing stochastic motion is studied by the use of functional technique, and the general formula is derived for the path probability distribution functional. The probability of finding paths inside a…
This note is sketching a simple and natural mathematical construction for explaining the probabilistic nature of quantum mechanics. It employs nonstandard analysis and is based on Feynman's interpretation of the Heisenberg uncertainty…
Randomness is a central concept to statistics and physics. Here, a statistical analysis shows experimental evidence that tossing coins and finding last digits of prime numbers are identical regarding statistics for equally likely outcomes.…
Likelihood ratio tests are a widely used method in global analyses in particle physics. The computation of the statistical significance (p-value) of these tests is usually done with a simple formula that relies on Wilks' theorem. There are,…
Physics is based on probabilities as fundamental entities of a mathematical description. Expectation values of observables are computed according to the classical statistical rule. The overall probability distribution for one world covers…
Considering a discrete and finite statistical model of a general position we introduce an exact expression for the partition function in terms of a finite series. The leading term in the series is the Bethe-Peierls (Belief Propagation)-BP…
The propositional logic is generalized on the real numbers field. The logical analog of the Bernoulli independent tests scheme is constructed. The variant of the nonstandard analysis is adopted for the definition of the logical function,…