Application of Threshold-Accepting to the Evaluation of the Discrepancy of a Set of Points

Winker, Peter; Fang, Kai‐Tai

doi:10.1137/s0036142995286076

Cited by 123 publications

(68 citation statements)

References 14 publications

(24 reference statements)

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“…[7,21,22,23] and the literature mentioned therein. In fact, it has been shown recently in [23] that the decision problem whether an arbitrary point set has discrepancy smaller than ε is (if suitably posed) N P -complete.…”

Section: Resultsmentioning

confidence: 99%

Component-by-component construction of low-discrepancy point sets of small size

Doerr

Gnewuch²,

Kritzer³

et al. 2008

McMa

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Abstract. We investigate the problem of constructing small point sets with low star discrepancy in the s-dimensional unit cube. The size of the point set shall always be polynomial in the dimension s. Our particular focus is on extending the dimension of a given low-discrepancy point set.This results in a deterministic algorithm that constructs N -point sets with small discrepancy in a component-by-component fashion. The algorithm also provides the exact star discrepancy of the output set. Its run-time considerably improves on the run-times of the currently known deterministic algorithms that generate low-discrepancy point sets of comparable quality.We also study infinite sequences of points with infinitely many components such that all initial subsegments projected down to all finite dimensions have low discrepancy. To this end, we introduce the inverse of the star discrepancy of such a sequence, and derive upper bounds for it as well as for the star discrepancy of the projections of finite subsequences with explicitly given constants. In particular, we establish the existence of sequences whose inverse of the star discrepancy depends linearly on the dimension.

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Section: Resultsmentioning

confidence: 99%

Component-by-component construction of low-discrepancy point sets of small size

Doerr

Gnewuch²,

Kritzer³

et al. 2008

McMa

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“…Of course, the threshold decreases gradually to zero which means that in the final steps only solutions which improve the objective functions are accepted. A data driven procedure determines the threshold sequence as described by Winker and Fang (1997) and adapted by Gilli et al (2006). This algorithm as a whole has proven its effectiveness to find an acceptable optimum.…”

Section: Hydropower Plant Managementmentioning

confidence: 99%

Long-term Uncertainty of Hydropower Revenue Due to Climate Change and Electricity Prices

Gaudard

Gabbi²,

Bauder³

et al. 2016

Water Resour Manage

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Hydropower represents the world's largest renewable energy source. As a flexible technology, it enhances reliability and security of the electricity system. However, climate change and market liberalization may hinder investment due to the evolution of water runoffs and electricity prices. Both alter expected revenue and bring uncertainty. It increases risk and deters investment. Our research assesses how climate change and market fluctuation affect annual revenue. But this paper focuses on the uncertainty, rather than on forecasting. This transdisciplinary topic is investigated by means of a mixed method, i.e. both quantitative and qualitative. The quantitative approach uses established models in natural sciences and economics. The uncertainty is accounted for by applying various scenarios and various datasets coming from different models. Based on those results, uncertainty is discussed through an analysis discerning three dimensions of uncertainty. Uncertainty analysis requires the assessment of a large panel of models and data sets. It is therefore rarely carried out. The originality of the paper also lies on the combination of quantitative established models with a qualitative analysis. The results surprisingly show that the greenhouse gas scenarios may in fact represent a low source of uncertainty, unlike electricity prices. Like forecasting, the main uncertainties are actually case study related and depend on the investigated variables. It is also shown that the nature of uncertainty evolves. Runoff uncertainty goes from variability, i.e. inherent randomness, to epistemic, i.e. limitation of science. The reverse situation occurs with the electricity price. The implications for scientists and policy makers are discussed.

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“…The threshold sequence which is used for the acceptance decision gets linearly lowered to zero within 80% of the iterations. It is based on a data-driven threshold sequence which is endogenously generated from the sample (see Winker and Fang (1997) for details). 7 Line 2 shows the initialization of the (equation-specific) parameters of the transition speed and location parameter.…”

Section: Threshold Acceptingmentioning

confidence: 99%

Finding Starting-Values for Maximum Likelihood Estimation of Vector STAR Models

Schleer

2013

SSRN Journal

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Die Dis cus si on Pape rs die nen einer mög lichst schnel len Ver brei tung von neue ren For schungs arbei ten des ZEW. Die Bei trä ge lie gen in allei ni ger Ver ant wor tung der Auto ren und stel len nicht not wen di ger wei se die Mei nung des ZEW dar.Dis cus si on Papers are inten ded to make results of ZEW research prompt ly avai la ble to other eco no mists in order to encou ra ge dis cus si on and sug gesti ons for revi si ons. The aut hors are sole ly respon si ble for the con tents which do not neces sa ri ly repre sent the opi ni on of the ZEW. Abstract This paper focuses on finding starting-values for maximum likelihood estimation of Vector STAR models. Based on a Monte Carlo exercise, different procedures are evaluated. Their performance is assessed w.r.t. model fit and computational effort. I employ i) grid search algorithms, and ii) heuristic optimization procedures, namely, differential evolution, threshold accepting, and simulated annealing. In the equation-by-equation starting-value search approach the procedures achieve equally good results. Unless the errors are cross-correlated, equation-by-equation search followed by a derivative-based algorithm can handle such an optimization problem sufficiently well. This result holds also for higher-dimensional VSTAR models with a slight edge for the heuristic methods. Being faced with more complex Vector STAR models for which a multivariate search approach is required, simulated annealing and differential evolution outperform threshold accepting and the grid with a zoom.JEL classification: C32, C61, C63

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Application of Threshold-Accepting to the Evaluation of the Discrepancy of a Set of Points

Cited by 123 publications

References 14 publications

Component-by-component construction of low-discrepancy point sets of small size

Component-by-component construction of low-discrepancy point sets of small size

Long-term Uncertainty of Hydropower Revenue Due to Climate Change and Electricity Prices

Finding Starting-Values for Maximum Likelihood Estimation of Vector STAR Models

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