In light of the information measures introduced in Part I, a generalized version of the Asymp-totic Equipartition Property (AEP) is proved. General xed-length data compaction and data compression (source coding) theorems for arbitrary nite-alphabet sources are also established. Finally, the general expression of the Neyman-Pearson type-II error exponent subject to upper bounds on the type-I err...

PHYSTAT2003 brought statisticians together with particle physicists, astrophysicists, and cosmologists. This paper, which is taken from the text of the keynote address, concerns the uneasy relationship between Bayesian and frequentist statistics, with particular attention to the “neutrino problem”: how to set confidence limits for a parameter known to be non-negative. Model selection, an object...

Binary decision theory has been applied to the general interferometric problem. Optimal detection scheme|according to the Neyman-Pearson criterion|has been considered for di erent phase-enhanced states of radiation eld, and the corresponding bounds on minimum detectable phase shift has been evaluated. A general bound on interferometric precision has been also obtained in terms of photon number ...

Noise enhanced hypothesis-testing is studied according to the restricted Neyman-Pearson (NP) criterion. First, a problem formulation is presented for obtaining the optimal probability distribution of additive noise in the restricted NP framework. Then, sufficient conditions for improvability and nonimprovability are derived in order to specify if additive noise can or cannot improve detection p...

This paper is concerned with hypothesis tests for g-probabilities, a class of nonlinear probability measures. The problem is shown to be a special case of a general stochastic optimization problem where the objective is to choose the terminal state of certain backward stochastic differential equations so as to minimize a g-expectation. The latter is solved with a stochastic maximum principle ap...