Browsing by Subject "Bayes risk"

Now showing 1 - 5 of 5

Open Access
Noise enhanced M-ary composite hypothesis-testing in the presence of partial prior information
(IEEE, 2010-12-06) Bayram, S.; Gezici, Sinan
In this correspondence, noise enhanced detection is studied for M-ary composite hypothesis-testing problems in the presence of partial prior information. Optimal additive noise is obtained according to two criteria, which assume a uniform distribution (Criterion 1) or the least-favorable distribution (Criterion 2) for the unknown priors. The statistical characterization of the optimal noise is obtained for each criterion. Specifically, it is shown that the optimal noise can be represented by a constant signal level or by a randomization of a finite number of signal levels according to Criterion 1 and Criterion 2, respectively. In addition, the cases of unknown parameter distributions under some composite hypotheses are considered, and upper bounds on the risks are obtained. Finally, a detection example is provided in order to investigate the theoretical results.
Open Access
Optimal cost allocation in centralized and decentralized detection problems
(IEEE, 2016) Laz, Eray; Gezici, Sinan
The optimal cost allocation problem is proposed for centralized and decentralized detection systems in the presence of cost constrained measurements, where the aim is to minimize the probability of error of a given detection system under a total cost constraint. The probability of error expressions are obtained for centralized and decentralized detection systems, and the optimal cost allocation strategies are provided. In addition, special cases are investigated in the presence of Gaussian observations and measurement noise. The solutions of the proposed problems specify the optimal allocation of the cost budget among various measurement devices (sensors) to achieve the optimum detection performance. Numerical examples are presented to discuss the implications of the results.
Open Access
Optimal stochastic design for multi-parameter estimation problems
(IEEE, 2014- 05) Soğancı, Hamza; Gezici, Sinan; Arıkan, Orhan
In this study, we consider performance improvement of an array of fixed estimators by using stochastic design techniques. The optimal design is investigated both in the absence and presence of an average power constraint. Two different performance criteria are considered; the average Bayes risk and the maximum Bayes risk. It is shown that the optimal stochastic parameter design results in a randomization between different numbers of parameter values depending on the type of the performance criterion. © 2014 IEEE.
Open Access
Optimal stochastic parameter design for estimation problems
(Institute of Electrical and Electronics Engineers, 2012) Soganci, H.; Gezici, Sinan; Arıkan, Orhan
In this study, the aim is to perform optimal stochastic parameter design in order to minimize the cost of a given estimator. Optimal probability distributions of signals corresponding to different parameters are obtained in the presence and absence of an average power constraint. It is shown that the optimal parameter design results in either a deterministic signal or a randomization between two different signal levels. In addition, sufficient conditions are obtained to specify the cases in which improvements over the deterministic parameter design can or cannot be achieved via the stochastic parameter design. Numerical examples are presented in order to provide illustrations of theoretical results.
Open Access
Optimal time sharing strategies for parameter estimation and channel switching problems
(2014) Soğancı, Hamza
Time sharing (randomization) can offer considerable amount of performance improvement in various detection and estimation problems and communication systems. In the first three chapters of this dissertation, time sharing among different signal levels is considered for parametric estimation problems. In the final chapter, time sharing among different channels is investigated for an average power constrained communication system. In the first chapter, the aim is to improve the performance of a single fixed estimator by the optimal stochastic design of signal values corresponding to parameters. It is obtained that the optimal parameter design corresponds to time sharing between at most two different signal values. In the second chapter, the problem in the first chapter is generalized to a scenario where there are multiple parameters and multiple estimators. In this scenario, two different cost functions are considered. The first cost function is the total risk of all the estimators. The optimal solution for this case is time sharing between at most two different signal values. The second cost function is the maximum risk of all the estimators. For this case, it is shown that the optimal parameter design is time sharing among at most three different signal values. In the third chapter, the linear minimum mean squared error (LMMSE) estimator is considered. It is observed that time sharing is not needed for the LMMSE estimator, but still the performance can be improved by modifying the signal level. In the final chapter, the optimal channel switching problem is studied for Gaussian channels, and the optimal channel switching strategy is determined in the presence of average power and average cost constraints. It is shown that the optimal channel switching strategy is to switch among at most three channels.