Browsing by Subject "Likelihood ratio"

Now showing 1 - 3 of 3

Open Access
Optimal decision rules for simple hypothesis testing under general criterion involving error probabilities
(IEEE, 2020) Dulek, B.; Öztürk, Cüneyd; Gezici, Sinan
The problem of simple M-ary hypothesis testing under a generic performance criterion that depends on arbitrary functions of error probabilities is considered. Using results from convex analysis, it is proved that an optimal decision rule can be characterized as a randomization among at most two deterministic decision rules, each of the form reminiscent to Bayes rule, if the boundary points corresponding to each rule have zero probability under each hypothesis. Otherwise, a randomization among at most M(M-1)+1 deterministic decision rules is sufficient. The form of the deterministic decision rules are explicitly specified. Likelihood ratios are shown to be sufficient statistics. Classical performance measures including Bayesian, minimax, Neyman-Pearson, generalized Neyman-Pearson, restricted Bayesian, and prospect theory based approaches are all covered under the proposed formulation. A numerical example is presented for prospect theory based binary hypothesis testing.
Open Access
Parameter identification for partially observed diffusions
(Kluwer Academic Publishers-Plenum Publishers, 1992) Dabbous, T.E.; Ahmed, N.U.
In this paper, we consider the identification problem of drift and dispersion parameters for a class of partially observed systems governed by Ito equations. Using the pathwise description of the Zakai equation, we formulate the original identification problem as a deterministic control problem in which the unnormalized conditional density (solution of the Zakai equation) is treated as the state, the unknown parameters as controls, and the likelihood ratio as the objective functional. The question of existence of elements in the parameter set that maximize the likelihood ratio is discussed. Further, using variational arguments and the Gateaux differentiability of the unnormalized density on the parameter set, we obtain the necessary conditions for optimal identification. © 1992 Plenum Publishing Corporation.
Open Access
Spectrum sensing via restricted neyman-pearson approach in the presence of non-Gaussian noise
(IEEE, 2013) Turgut, Esma; Gezici, Sinan
In this paper, spectrum sensing in cognitive radio systems is studied for non-Gaussian channels in the presence of prior distribution uncertainty. In most practical cases, some amount of prior information about signals of primary users is available to secondary users but that information is never perfect. In order to design optimal spectrum sensing algorithms in such cases, we propose to employ the restricted Neyman-Pearson (NP) approach, which maximizes the average detection probability under constraints on the worst-case detection and false-alarm probabilities. We derive a restricted NP based spectrum sensing algorithm for additive Gaussian mixture noise channels, and compare its performance against the generalized likelihood ratio test (GLRT) and the energy detector. Simulation results show that the proposed spectrum sensing algorithm provides improvements over the other approaches in terms of minimum (worst-case) and/or average detection probabilities. © 2013 IEEE.