We state a quantum version of Bayes’s rule for statistical inference and give a simple general derivation within the framework of generalized measurements. The rule can be applied to measurements on N copies of a system if the initial state of the N copies is exchangeable. As an illustration, we apply the rule to N qubits. Finally, we show that quantum state estimates derived via the principle ...

A nonparametric kernel-based method for realizing Bayes’ rule is proposed, based on kernel representations of probabilities in reproducing kernel Hilbert spaces. The prior and conditional probabilities are expressed as empirical kernel mean and covariance operators, respectively, and the kernel mean of the posterior distribution is computed in the form of a weighted sample. The kernel Bayes’ ru...

The justification of Bayes' rule by cognitive rationality principles is undertaken by extending the propositional axiom systems usually proposed in two contexts of belief change: revising and updating. Probabilistic belief change axioms are introduced, either by direct transcription of the set-theoretic ones, or in a stronger way nevertheless in the spirit of the underlying propositional princi...

We present a general framework for representing belief-revision rules and use it to characterize Bayes’s rule as a classical example and Je¤rey’s rule as a non-classical one. In Je¤rey’s rule, the input to a belief revision is not simply the information that some event has occurred, as in Bayes’s rule, but a new assignment of probabilities to some events. Despite their di¤erences, Bayes’s and J...

We present a general framework for representing belief-revision rules and use it to characterize Bayes’s rule as a classical example and Je¤rey’s rule as a non-classical one. In Je¤rey’s rule, the input to a belief revision is not simply the information that some event has occurred, as in Bayes’s rule, but a new assignment of probabilities to some events. Despite their di¤erences, Bayes’s and J...

Starting from first principles, we re-visit the statistical approach and study two forms of the Bayes decision rule: the common rule for minimizing the number of string errors and a novel rule for minimizing the number of symbols errors. The Bayes decision rule for minimizing the number of string errors is widely used, e.g. in speech recognition, POS tagging and machine translation, but its jus...

An allocation rule is called Bayes-Nash incentive compatible, if there exists a payment rule, such that truthful reports of agents’ types form a Bayes-Nash equilibrium in the direct revelation mechanism consisting of the allocation rule and the payment rule. This paper provides a characterization of Bayes-Nash incentive compatible allocation rules in social choice settings where agents have mul...

This paper concerns a relationship between Bayes’ inference rule and decision rules from the rough set perspective. In statistical inference based on the Bayes’ rule it is assumed that some prior knowledge (prior probability) about some parameters without knowledge about the data is given first. Next the posterior probability is computed by employing the available data. The posterior probabilit...