Probabilistic Optimal Design Using Successive Surrogate Probability Density Functions

1993 ◽  
Vol 115 (3) ◽  
pp. 385-391 ◽  
Author(s):  
R. J. Eggert ◽  
R. W. Mayne
Keyword(s):  
Probability Density ◽  
Optimization Method ◽  
Probability Density Functions ◽  
Density Functions ◽  
Matching Method ◽  
Design Constraint ◽  
New Approach ◽  
Function Formulation ◽  
The Moment ◽  
Theoretical Considerations

Probabilistic optimization using the moment matching method and the simulation optimization method are discussed and compared to conventional deterministic optimization. A new approach based on successively approximating probability density functions, using recursive quadratic programming for the optimization process, is described. This approach incorporates the speed and robustness of analytical probability density functions and improves accuracy by considering simulation results. Theoretical considerations and an example problem illustrate the features of the approach. The paper closes with a discussion of an objective function formulation which includes the expected cost of design constraint failure.

Probabilistic Optimal Design Using Successive Surrogate Probability Density Functions

1990 ◽  
Author(s):  
R. J. Eggert ◽  
R. W. Mayne
Keyword(s):  
Probability Density ◽  
Optimization Method ◽  
Probability Density Functions ◽  
Density Functions ◽  
Matching Method ◽  
Design Constraint ◽  
New Approach ◽  
Function Formulation ◽  
The Moment ◽  
Theoretical Considerations

Abstract Probabilistic optimization using the moment matching method and the simulation optimization method are discussed and compared to conventional deterministic optimization. A new approach based on successively approximating probability density functions, using recursive quadratic programming for the optimization process, is described. This approach incorporates the speed and robustness of analytical probability density functions and improves accuracy by considering simulation results. Theoretical considerations and an example problem illustrate the features of the approach. The paper closes with a discussion of an objective function formulation which includes the expected cost of design constraint failure.

A New Approach to Probability in Engineering Design and Optimization

1984 ◽  
Vol 106 (1) ◽  
pp. 5-10 ◽  
Author(s):  
J. N. Siddall
Keyword(s):  
Probability Density ◽  
Engineering Design ◽  
Probability Distributions ◽  
Probability Density Functions ◽  
Density Functions ◽  
New Approach ◽  
Design And Optimization ◽  
Evolutionary Technique ◽  
Probability And Statistics

The anomalous position of probability and statistics in both mathematics and engineering is discussed, showing that there is little consensus on concepts and methods. For application in engineering design, probability is defined as strictly subjective in nature. It is argued that the use of classical methods of statistics to generate probability density functions by estimating parameters for assumed theoretical distributions should be used with caution, and that the use of confidence limits is not really meaningful in a design context. Preferred methods are described, and a new evolutionary technique for developing probability distributions of new random variables is proposed. Although Bayesian methods are commonly considered to be subjective, it is argued that, in the engineering sense, they are really not. A general formulation of the probabilistic optimization problem is described, including the role of subjective probability density functions.

scholarly journals EXTREMAL STATISTICS OF STORM SURGES BY TYPHOON

1984 ◽  
Vol 1 (19) ◽  
pp. 8
Author(s):  
Yoshito Tsuchiya ◽  
Yoshiaki Kawata
Keyword(s):  
Probability Density ◽  
Return Period ◽  
Storm Surges ◽  
Probability Density Functions ◽  
Density Functions ◽  
Tidal Variation ◽  
New Approach ◽  
Probability Of Occurrence ◽  
Typhoon Track ◽  
Tidal Data

The objective of this paper is to propose a new approach based on the direction of the typhoon track for determining the probability of occurrence of extremal tides due to storm surges, as well as their return period. The study includes the effects of periods in tidal data and of tidal variation stemming from extensive reclamation along coasts on the fitness of the extremal data to probability density functions. The method is justified by application to an analysis of the probability of occurrence of storm surges in Osaka bay.

NEARLY EXACT OPTION PRICE SIMULATION USING CHARACTERISTIC FUNCTIONS

2012 ◽  
Vol 15 (07) ◽  
pp. 1250047 ◽  
Author(s):  
CAROLE BERNARD ◽  
ZHENYU CUI ◽  
DON MCLEISH
Keyword(s):  
Characteristic Function ◽  
Probability Density ◽  
Option Price ◽  
Probability Density Functions ◽  
Heston Model ◽  
Characteristic Functions ◽  
Density Functions ◽  
New Approach ◽  
Black Scholes ◽  
Unbiased Estimates

This paper presents a new approach to perform a nearly unbiased simulation using inversion of the characteristic function. As an application we are able to give unbiased estimates of the price of forward starting options in the Heston model and of continuously monitored Parisian options in the Black-Scholes framework. This method of simulation can be applied to problems for which the characteristic functions are easily evaluated but the corresponding probability density functions are complicated.

Feedback Control of Stochastic Systems to Track Prespecified Probability Density Functions

2005 ◽  
Author(s):  
Ozer Elbeyli ◽  
J. Q. Sun
Keyword(s):  
Probability Density ◽  
Stochastic Systems ◽  
Control Design ◽  
Probability Density Functions ◽  
Density Functions ◽  
Moment Equations ◽  
Feedback Controls ◽  
The Moment ◽  
Non Gaussian ◽  
Probability Density Function Pdf

We present a study of feedback controls of stochastic systems to track a prespecified probability density function (PDF). The moment equations of the response are used in the control design to illustrate the underlining issues. A hierarchical approach is proposed to design the control for tracking Gaussian and non-Gaussian PDFs. The control design approach is demonstrated with a simple example.

POINT SHAVING IN THE NFL GAMBLING MARKET: A BOOTSTRAP INVESTIGATION

2012 ◽  
Vol 3 (3) ◽  
pp. 13-31 ◽  
Author(s):  
George Diemer
Keyword(s):  
Probability Density ◽  
Hypothesis Test ◽  
Probability Density Functions ◽  
Density Functions ◽  
New Approach ◽  
Point Spread ◽  
Game Outcome ◽  
Gambling Market

Recent research has examined a statistical phenomenon sometimes associated with point shaving in the NCAA Basketball gambling market.  In a similar fashion, this study examines the NFL gambling market based on 3,641 games over the years 1993-2007.   This research uses a new approach: a bootstrap hypothesis test of equality in the game outcome distributions for large favorites vs. small favorites.  Probability density functions of large favorites vs. small favorites are constructed and compared.  The results are consistent with studies that suggest point shaving exists, and they counter recent claims that the statistical phenomenon are of a more innocent nature.  This research leads to the rejection of the null of no point shaving in the NFL point spread gambling market.

scholarly journals On the extraction of the power-law parts of probability density functions in star-forming clouds

2019 ◽  
Vol 489 (1) ◽  
pp. 788-801 ◽  
Author(s):  
Todor V Veltchev ◽  
Philipp Girichidis ◽  
Sava Donkov ◽  
Nicola Schneider ◽  
Orlin Stanchev ◽  
...  
Keyword(s):  
Probability Density ◽  
Power Law ◽  
Column Density ◽  
Probability Density Functions ◽  
Arbitrary Distribution ◽  
Density Functions ◽  
Theoretical Studies ◽  
Applied Statistics ◽  
New Approach ◽  
Star Forming

ABSTRACT We present a new approach to extract the power-law part of a density/column-density probability density function (ρ-pdf/N-pdf) in star-forming clouds. This approach is based on the mathematical method bPlfit of Virkar & Clauset (2014, Annals of Applied Statistics, 8, 89) and it assesses the power-law part of an arbitrary distribution, without any assumptions about the other parts of this distribution. The slope and deviation point are derived as averaged values as the number of bins is varied. Neither parameter is sensitive to spikes and other local features of the tail. This adapted bPlfit method is applied to two different sets of data from numerical simulations of star-forming clouds at scales 0.5 and 500 pc, and it displays ρ-pdf and N-pdf evolution in agreement with a number of numerical and theoretical studies. Applied to Herschel data on the regions Aquila and Rosette, the method extracts pronounced power-law tails, consistent with those seen in simulations of evolved clouds.

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