An Approximate Method for Sampling Correlated Random Variables from Partially-Specified Distributions

Lurie, Philip M.; Goldberg, Matthew S.

doi:10.1287/mnsc.44.2.203

Cited by 111 publications

(80 citation statements)

References 12 publications

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“…One of the most common ones is to sample directly from the specified marginal distribution and correlation matrix [1]. If the marginal distribution functions are not known exactly, they could be described by their moments (mean, variance, skewness, etc.)…”

Section: Application Of Scenario Reduction To Ldc and Risk Based Genementioning

confidence: 99%

Application of scenario reduction to LDC and risk based generation expansion planning

Feng

Ryan

2012

2012 IEEE Power and Energy Society General Meeting

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Abstract--Two-stage stochastic mixed-integer programming models are formulated for minimizing expected cost or Conditional Value-at-Risk (CVaR) of a long-term power generation expansion planning problem incorporating load duration curves. The multivariate stochastic processes, such as electricity demands and fuel prices, are modeled as geometric Brownian motion (GBM) processes. Scenario paths for their future evolution are generated by statistical extrapolation of long-term historical trends. The size of the scenario set is controlled by using increasing length time periods in a tree structure. Nevertheless, some method of scenario thinning is necessary to achieve manageable solution times. To mitigate the computational complexity of the forward selection heuristic for scenario reduction, a combined heuristic scenario reduction method named Forward Selection in Wait-and-see Clusters (FSWC) is applied to the large scenario set. Numerical results for a twenty year generation expansion planning case study indicate substantial computational savings to achieve similar solutions as those obtained by forward selection alone.

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Section: Application Of Scenario Reduction To Ldc and Risk Based Genementioning

confidence: 99%

Application of scenario reduction to LDC and risk based generation expansion planning

Feng

Ryan

2012

2012 IEEE Power and Energy Society General Meeting

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“…;Decisioneering 1996;Burmaster and Udell 1990;Metzger et al 1998) and is probably the most widely used method for inducing correlations in Monte Carlo simulations. However, like the "Lurie and Goldberg (1994) described an iterative approach for obtaining a desired pattern of Pearson correlations matching specified marginal distributions, but it is essentially a trial-anderror approach that can be computationally intensive.…”

Section: Simulating Correlationsmentioning

confidence: 99%

Dependence in probabilistic modeling, Dempster-Shafer theory, and probability bounds analysis.

Oberkampf¹,

Tucker

Zhang

et al. 2004

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LIBRARY VAULTThis report summarizes methods to incorporate information (or lack of information) about inter-variable dependence into risk assessments that use Dempster-Shafer theory or probability bounds analysis to address epistemic and aleatory uncertainty. The report reviews techniques for simulating correlated variates for a given correlation measure and dependence model, computation of bounds on distribution functions under a specified dependence model, formulation of parametric and empirical dependence models, and bounding approaches that can be used when information about the intervariable dependence is incomplete. The report also reviews several of the most pervasive and dangerous myths among risk analysts about dependence in probabilistic models.*The work described in this report was performed for Sandia National Laboratories under Contract No. 19094. 3 AcknowledgmentsDiscussions with Peter Walley were helpful in elucidating the problem of representing dependence in the context of imprecise probabilities and the role of probability boxes and Dempster-Shafer structures as models of imprecise probabilities. 2.5Using inequalities in risk assessments 2.6Caveat: best-possible calculations are NP-hard 2.7Numerical example: fault tree for a pressure tank Sym b o k -Ea is distributed as is an element of is a subset of plus or minus addition, subtraction, etc. under no assumption about the dependence between the operands addition, subtraction, etc. assuming independence addition, subtraction, etc. assuming perfect dependence addition, subtraction, etc. assuming opposite dependence the empty set, i.e., the set having no members probability-box specified by a left side F(x) and a right side E(x) where E(x) I F ( x ) for all x E %, consisting of all non-decreasing functions F from the reals into [O,l] such that E(x) I F(x) I fix). {(sl,ml),. . ., (s,,m,)} an enumeration of the elements of a Dempster-Shafer structure in terms of its focal elements si and their nonzero masses mi beta (v, w) a beta distribution with shape parameters v and w convolve(X, Y,r) convolution (usually addition) assuming that X and Y have correlation r convolve(X, Y,C) convolution (usually addition) assuming the copula C describes the dependence between X and Y covariance between random variables X and Y expectation (mean) of random variable X a functionfwhose domain is the set A and whose range is the set B. In other words, for any element in A, the functionfassigns a value that is in the set B the step function that is zero for all values of x

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“…In the second group, specified (parametric) marginal distributions are sampled independently and the samples are then used along with Cholesky factorization of the covariance matrix to generate the necessary multivariate distribution. An iterative procedure of this type in described in [12], where specified marginal distributions and correlation matrix are used to produce the correlated vectors of random numbers.…”

Section: Introductionmentioning

confidence: 99%

“…The procedure has to be repeated iteratively for each marginal distribution. Similarly, the algorithm in [12] requires a non-convex optimization over the space of lower triangular matrices.…”

Section: Introductionmentioning

confidence: 99%

An algorithm for moment-matching scenario generation with application to financial portfolio optimisation

Ponomareva

Roman

Date

2015

European Journal of Operational Research

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We present an algorithm for moment-matching scenario generation. This method produces scenarios and corresponding probability weights that match exactly the given mean, the covariance matrix, the average of the marginal skewness and the average of the marginal kurtosis of each individual component of a random vector. Optimisation is not employed in the scenario generation process and thus the method is computationally more advantageous than previous approaches. The algorithm is used for generating scenarios in a mean-CVaR portfolio optimisation model. For the chosen optimization example, it is shown that desirable properties for a scenario generator are satisfied, including in-sample and out-of-sample stability. It is also shown that optimal solutions vary only marginally with increasing number of scenarios in this example; thus, good solutions can apparently be obtained with a relatively small number of scenarios. The proposed method can be used either on its own as a computationally inexpensive scenario generator or as a starting point for non-convex optimisation based scenario generators which aim to match all the third and the fourth order marginal moments (rather than average marginal moments).

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An Approximate Method for Sampling Correlated Random Variables from Partially-Specified Distributions

Cited by 111 publications

References 12 publications

Application of scenario reduction to LDC and risk based generation expansion planning

Application of scenario reduction to LDC and risk based generation expansion planning

Dependence in probabilistic modeling, Dempster-Shafer theory, and probability bounds analysis.

An algorithm for moment-matching scenario generation with application to financial portfolio optimisation

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