منابع مشابه
Quantum Bayes rule
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 ...
متن کاملKernel Bayes' Rule
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...
متن کاملProbability Theory without Bayes' Rule
Within the Kolmogorov theory of probability, Bayes’ rule allows one to perform statistical inference by relating conditional probabilities to unconditional probabilities. As we show here, however, there is a continuous set of alternative inference rules that yield the same results, and that may have computational or practical advantages for certain problems. We formulate generalized axioms for ...
متن کاملTeaching Bayes ' Rule : A Data
There is a current emphasis on making the introductory statistics class more dataoriented. Data distributions are used to motivate probability distributions, such as the normal, and sampling distributions. However, di culties remain in communicating the basic tenets of traditional statistical procedures such as con dence intervals and hypothesis tests. It is shown that skills in understanding r...
متن کاملBayes + Hilbert = Quantum Mechanics
Quantum mechanics (QM) is based on four main axioms, which were derived after a long process of trial and error. The motivations for the axioms are not always clear and even to experts the basic axioms of QM often appear counter-intuitive. In a recent paper [1], we have shown that: ◦ It is possible to derive quantum mechanics from a single principle of self-consistency or, in other words, that ...
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ژورنال
عنوان ژورنال: Physical Review A
سال: 2001
ISSN: 1050-2947,1094-1622
DOI: 10.1103/physreva.64.014305