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OPTIMIZING STATISTICAL DECISIONS
BY ADDING NOISE
by
Ashok Patel
A Thesis Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
MASTER OF ARTS
(APPLIED MATHEMATICS)
May 2008
Copyright 2008 Ashok Patel
Object Description
| Title | Optimizing statistical decisions by adding noise |
| Author | Patel, Ashok |
| Author email | ashokpat@usc.edu |
| Degree | Master of Arts |
| Document type | Thesis |
| Degree program | Applied Mathematics |
| School | College of Letters, Arts and Sciences |
| Date defended/completed | 2008-03-14 |
| Date submitted | 2008 |
| Restricted until | Unrestricted |
| Date published | 2008-04-28 |
| Advisor (committee chair) | Mikulevicius, Remijius |
| Advisor (committee member) |
Lototsky, Sergey Kosko, Bart |
| Abstract | This thesis presents an algorithm to find near-optimal "stochastic resonance" (SR) noise to maximize the expected payoff in statistical decision problems subject to a single inequality constraint on the expected cost. The SR effect or noise benefit occurs when the expected cost satisfies the inequality constraint while the expected payoff in the presence of a noise or randomization is larger than in the case without noise. The payoff and cost functions are real-valued bounded nonnegative Borel-measurable functions on a finite-dimensional noise space N. We show that the optimal SR noise is just the randomization of two noise realizations if the statistical decision problem is subject only to a single inequality constraint and if the optimal noise exists. We give necessary and sufficient conditions for the existence of such optimal noise. If the optimal noise does not exist then there exists a sequence of noise random variables such that the limit of the respective expected-payoff sequence is optimal. We develop an algorithm that finds an SR noise ~N' from a finite set of noise realizations ~N subset N. This noise ~N' is nearly optimal if the payoff function on the actual noise space N is sufficiently close to its restriction to ~N. An upper bound limits the number of iterations that the algorithm requires to find such near-optimal SR noise. Two applications demonstrate the SR noise algorithm. The first application finds a near-optimal SR noise for a suboptimal one-sample Neyman-Pearson hypothesis test of variance. The second application gives a near-optimal signal power randomization for an average-power-constrained anti-podal signal transmitter in the presence of additive Gaussian-mixture channel noise where the receiver uses a maximum a posteriori (MAP) method for optimal signal detection. These applications show that the algorithm finds near-optimal noise or random |
| Keyword | optimization; statistical decisions; stochastic resonance; SR noise algorithm |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Type | texts |
| Legacy record ID | usctheses-m1191 |
| Rights | Patel, Ashok |
| Repository name | Libraries, University of Southern California |
| Repository address | Los Angeles, California |
| Repository email | http://www.usc.edu/isd/libraries/services/ask_a_librarian/email/ |
| Filename | etd-Ashok-20080428 |
| Archival file | uscthesesreloadpub_Volume40/etd-Ashok-20080428.pdf |
Description
| Title | Page 1 |
| Full text | OPTIMIZING STATISTICAL DECISIONS BY ADDING NOISE by Ashok Patel A Thesis Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree MASTER OF ARTS (APPLIED MATHEMATICS) May 2008 Copyright 2008 Ashok Patel |
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