Detection Probabilities for Beta-Distributed Scattering Cross Sections

Kulp, Robert L.

doi:10.1080/02726348408908112

Cited by 2 publications

(1 citation statement)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Bayesian statisticians often use a beta density to encode prior information about a parameter (such as a binomial success parameter p) over a fixed-length interval [23]. The beta density can also model the semblance or the ratio of stacked energy to total energy across a signal array [24], fluctuations of the radar-scattering cross sections of targets [25], the self-similar process of video traffic [26], and the variation of the narrowband vector channels or spatial signature variations due to movement [27]. The Weibull probability density function has the form p͑n͒ = ͭ ␣n ␤−1 e −␣n ␤ /␤ if n ജ 0 0 otherwise ͑18͒ for positive shape parameters ␣ and ␤.…”

Section: ͑14͒mentioning

confidence: 99%

Robust stochastic resonance for simple threshold neurons

Kosko

Mitaim

2004

Phys. Rev. E

View full text Add to dashboard Cite

Simulation and theoretical results show that memoryless threshold neurons benefit from small amounts of almost all types of additive noise and so produce the stochastic-resonance or SR effect. Input-output mutual information measures the performance of such threshold systems that use subthreshold signals. The SR result holds for all possible noise probability density functions with finite variance. The only constraint is that the noise mean must fall outside a "forbidden" threshold-related interval that the user can control--a new theorem shows that this condition is also necessary. A corollary and simulations show that the SR effect occurs for right-sided beta and Weibull noise as well. These SR results further hold for the entire uncountably infinite class of alpha-stable probability density functions. Alpha-stable noise densities have infinite variance and infinite higher-order moments and often model impulsive noise environments. The stable noise densities include the special case of symmetric bell-curve densities with thick tails such as the Cauchy probability density. The SR result for alpha-stable noise densities shows that the SR effect in threshold and thresholdlike systems is robust against occasional or even frequent violent fluctuations in noise. Regression analysis reveals both an exponential relationship for the optimal noise dispersion as a function of the alpha bell-curve tail thickness and an approximate linear relationship for the SR-maximal mutual information as a function of the alpha bell-curve tail thickness.

show abstract