Prediction is the making of statements, usually probabilistic, about future events based on current information. Retrodiction statements past We present foundations quantum retrodiction and highlight its intimate connection with Bayesian interpretation probability. The close link methods enables us to explore controversies misunderstandings that have appeared in literature. To be clear, univers...

Markov categories are a recent categorical approach to the mathematical foundations of probability and statistics. Here, this is advanced by stating proving equivalent conditions for second-order stochastic dominance, widely used way comparing distributions their spread. Furthermore, we lay foundation theory statistical experiments within classical Blackwell-Sherman-Stein Theorem. Our version n...

In the present paper, we study some properties of fuzzy norm of linear operators. At first the bounded inverse theorem on fuzzy normed linear spaces is investigated. Then, we prove Hahn Banach theorem, uniform boundedness theorem and closed graph theorem on fuzzy normed linear spaces. Finally the set of all compact operators on these spaces is studied.

The apparent difficulty people have with making Bayesian inferences has been researched heavily over the past 25 years, with conflicting explanations regarding the causes of and the cures for this inadequacy. Some researchers have improved Bayesian reasoning by representing the problem visually, but usually as a tool to teach Bayesian reasoning skills. This research examines facilitating reason...

A new Bayesian algorithm for retrieving surface rain rate from Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) over the ocean is presented, along with validations against estimates from the TRMM Precipitation Radar (PR). The Bayesian approach offers a rigorous basis for optimally combining multichannel observations with prior knowledge. While other rain-rate algorithms have be...

The Condorcet Jury Theorem justifies the wisdom of crowds and lays the foundations of the ideology of the democratic regime. However, the Jury Theorem and most of its extensions focus on two alternatives and none of them quantitatively evaluate the effect of agents’ strategic behavior on the mechanism’s truth-revealing power. We initiate a research agenda of quantitatively extending the Jury Th...

When first learning Bayesian statistics, the organizational scholar may be confronted by a number of conceptual and practical challenges. The present paper seeks to minimize these by first explicating how the Bayesian process can be understood simply as the combination of two complementary sources of information: prior beliefs and data. In turn, we describe how each source is derived from Bayes...

A new proof of the class-specific feature theorem is given. The proof makes use of the observed data as opposed to the set of sufficient statistics as in the original formulation. We prove the theorem for the classical case, in which the parameter vector is deterministic and known, as well as for the Bayesian case, in which the parameter vector is modeled as a random vector with known prior pro...

1. Extensive form games with perfect information 3 1.1. Chess 3 1.2. Definition of extensive form games with perfect information 4 1.3. The ultimatum game 5 1.4. Equilibria 5 1.5. The centipede game 6 1.6. Subgames and subgame perfect equilibria 6 1.7. Backward induction, Kuhn’s Theorem and a proof of Zermelo’s Theorem 7 2. Strategic form games 10 2.1. Definition 10 2.2. Nash equilibria 10 2.3....

Existing Bayesian models, especially nonparametric Bayesian methods, rely on specially conceived priors to incorporate domain knowledge for discovering improved latent representations. While priors affect posterior distributions through Bayes’ rule, imposing posterior regularization is arguably more direct and in some cases more natural and general. In this paper, we present regularized Bayesia...