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Precast segmental bridge construction in seismic zones
Published in Fabio Biondini, Dan M. Frangopol, Bridge Maintenance, Safety, Management, Resilience and Sustainability, 2012
Fabio Biondini, Dan M. Frangopol
To show the monotonicity, the First-order stochastic dominance of the posterior distribution in the Bayesian updating is first examined. First-order stochastic dominance is defined as follows: in terms of the cumulative distribution functions of the two distributions, FA(x)«FB(x) hold for all x, with strict inequality at some x. Milgrom (1981) proved that the strict monotone likelihood ratio property (MLRP) of the likelihood function is both a necessary and sufficient condition for the First-Order Stochastic Dominance of the posterior distributions in Bayesian updating. In prognosis application, if the likelihood function for the Bayesian updating as given in Eqn.
Presenting and Using Assessment Results
Published in Charles Yoe, Principles of Risk Analysis, 2019
Stochastic dominance, as used here, refers to a form of ordering for probability distributions. It is a concept developed in decision theory that sometimes enables one to call one distribution better or more desirable than another. To illustrate this concept, let us revert to some hypothetical outputs associated with two hypothetical risk management options, A and B. Let FA(x) and FB(x) be the cumulative distribution functions for these two options, and let larger values of x be preferable.
Modeling index tracking portfolio based on stochastic dominance for stock selection
Published in The Engineering Economist, 2022
Liangchuan Wu, Yuju Wang, Liang-Hong Wu
The stochastic dominance (SD) approach aims to solve portfolio selection problems similar to stock selection that returns compare point-wise cumulative distribution functions (CDFs) (Ogryczak & Ruszczyński, 1999). Based on preferred utility, investors choose a pair of uncertain alternatives to compare, then select the dominant stock in the portfolio using SD. Furthermore, the user does not entrap an explicit solution for the utility function and can identify the ordering of alternatives with first-degree stochastic dominance (FSD), second-degree stochastic dominance (SSD), and third-degree stochastic dominance (TSD). Alkhazali and Zoubi (2020) used these three orders in SD for an empirical analysis on portfolio diversification to provide information on CDF. The SD approach not only shows the dominance from one return distribution to another, but also establishes a model to prove that a given benchmark portfolio is efficiently diversified in another portfolio of all market contexts (Liesiö et al., 2020).
Image based statistical process monitoring via partial first order stochastic dominance
Published in Quality Engineering, 2022
Panagiotis Tsiamyrtzis, Marco Luigi Giuseppe Grasso, Bianca Maria Colosimo
In this study, we suggest the use of the empirical cumulative distribution function (ecdf) of pixel values of each frame, to summarize the process signature in a frame. The ecdf computation is combined with an image pre-processing operation aimed at limiting the analysis of ecdf patterns in consecutive frames to the foreground region only, where relevant process dynamics occur. Instead of deriving or modeling a reference ecdf during phase I, the proposed approach aims at estimating a benchmark that will demarcate the IC behavior. Thus, we will establish what is the region of ecdf’s IC behavior and utilize the partial first order stochastic dominance (PFOSD) properties to test (in-line during phase II) whether the process has moved from the IC to the OOC state (for an extensive bibliographic review on the concept of stochastic dominance refer to Bawa (1982)). Stochastic dominance is a form of stochastic ordering between random variables. More specifically, a random variable X is first order stochastic dominant over another random variable if its cumulative distribution function is lower than the cumulative distribution function of Y over the entire domain. PFOSD is a relaxation of the first order stochastic dominance concept as it entails a dominance over a predetermined subset of the original domain only. In our proposed approach, the random variable of interest is the pixel intensity. Comparing ecdf curves of pixel intensities corresponding to different video frames can be viewed as a PFOSD problem, where the term “partial” refers to the restriction of the range of pixel intensity values to foreground intensities only.
Risk-averse flexible policy on ambulance allocation in humanitarian operations under uncertainty
Published in International Journal of Production Research, 2021
Guodong Yu, Aijun Liu, Huiping Sun
Before presenting the risk-averse formulation, we firstly introduce the definition of FSD briefly. Stochastic dominance is based on pair-wise comparisons of random variables. There are many such stochastic dominance relations, here we focus on the notion of integral stochastic dominance (see Müller 1997). Let be a collection of functions from to . For two random variables X and Y, we define the relation via That is, when the expected value is smaller than the expected value for all . Different choices of give rise to different stochastic dominance relations. We will work with a specific choice of that has appeared earlier in Armbruster and Delage (2015) and Haskell, Shanthikumar, and Shen (2017). First, let be the set of all increasing convex functions. Second, let be a pair of random variables used to define a normalisation constraint . Finally, let be a collection of pairs of random variables indexed by the finite set K where we require for all . Then, we define It turns out that the set has special structure that makes it particularly tractable for use in optimisation, we will focus our attention on this set.