Related papers: Posterior Probabilities: Dominance and Optimism
The computational costs of inference and planning have confined Bayesian model-based reinforcement learning to one of two dismal fates: powerful Bayes-adaptive planning but only for simplistic models, or powerful, Bayesian non-parametric…
Whether the fate of our species can be forecast from its past has been the topic of considerable controversy. One refutation of the so-called Doomsday Argument is based on the premise that we are more likely to exist in a universe…
The laws of chance are often subtle and deceptive. This is why games of chance work. People are convinced that they obey seemingly intuitive laws, while the underlying mathematical structure reveals a different and more complex reality.…
We propose a new method for conducting Bayesian prediction that delivers accurate predictions without correctly specifying the unknown true data generating process. A prior is defined over a class of plausible predictive models. After…
Modus ponens (\emph{from $A$ and "if $A$ then $C$" infer $C$}, short: MP) is one of the most basic inference rules. The probabilistic MP allows for managing uncertainty by transmitting assigned uncertainties from the premises to the…
The main object of Bayesian statistical inference is the determination of posterior distributions. Sometimes these laws are given for quantities devoid of empirical value. This serious drawback vanishes when one confines oneself to…
We develop a systematic approach to quantum probability as a theory of rational betting in quantum gambles. In these games of chance the agent is betting in advance on the outcomes of several (finitely many) incompatible measurements. One…
Measures of association in contingency tables, such as odds ratios and their generalizations, are often studied under different sampling schemes that either fix or leave random the margins of the table. While classical results show that…
Stochastic kinetic models are often used to describe complex biological processes. Typically these models are analytically intractable and have unknown parameters which need to be estimated from observed data. Ideally we would have…
In any probabilistic theory, we may say a bipartite state on a composite system AB steers its marginal state (on, say, system B) if, for any decomposition of the marginal as a mixture, with probabilities p_i, of states b_i of B, there…
We consider Bayesian sample size determination using a criterion that utilizes the first two moments of the expected posterior variance. We study the resulting sample size in dependence on the chosen prior and explore the success rate for…
Clustering is widely studied in statistics and machine learning, with applications in a variety of fields. As opposed to classical algorithms which return a single clustering solution, Bayesian nonparametric models provide a posterior over…
In the following we revisit the frequency interpretation of probability of Richard von Mises, in order to bring the essential implicit notions in focus. Following von Mises, we argue that probability can only be defined for events that can…
Within classical propositional logic, assigning probabilities to formulas is shown to be equivalent to assigning probabilities to valuations. A novel notion of probabilistic entailment enjoying desirable properties of logical consequence is…
General Probabilistic Theories provide the most general mathematical framework for the theory of probability in an operationally natural manner, and generalize classical and quantum theories. In this article, we study state-discrimination…
A spectral approach to Bayesian inference is presented. It pursues the emulation of the posterior probability density. The starting point is a series expansion of the likelihood function in terms of orthogonal polynomials. From this…
We calculate survival probability of a special state which couples randomly to a regular or chaotic environment. The environment is modelled by a suitably chosen random matrix ensemble. The exact results exhibit non--perturbative features…
Bayesian optimization is a coherent, ubiquitous approach to decision-making under uncertainty, with applications including multi-arm bandits, active learning, and black-box optimization. Bayesian optimization selects decisions (i.e.…
Many formalisms combining ontology languages with uncertainty, usually in the form of probabilities, have been studied over the years. Most of these formalisms, however, assume that the probabilistic structure of the knowledge remains…
Education in statistics, the application of statistics in scientific research, and statistics itself as a scientific discipline are in crisis. Within science, the main cause of the crisis is the insufficiently clarified concept of…