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STATISTICS AND COMPUTING 2025年第1期35卷 1-21页

作者： Robert, Christian P. Stoehr, Julien Univ PSL Univ Paris Dauphine CEREMADE CNRS F-75016 Paris France Univ Paris Saclay AgroParisTech INRAE UMR MIA Paris Saclay F-91120 Palaiseau France Univ Warwick Dept Stat Coventry CV4 7AL England

Simulating mixtures of distributions with both positive and negative (signed) weights proves a challenge as standard simulation algorithms prove inefficient in handling the negative weights. In particular, the natural representation of mixture random variates as being associated with latent component indicators is no longer available. We propose an exact accept-reject algorithm for the general case of finite signed mixtures that relies on optimally pairing positive and negative components and designing a stratified sampling scheme on these pairs. We analyze the performances of our approach, relative to the inverse cdf approach, since the cdf of the targeted distribution remains available for signed mixtures of common distributions.

关键词： acceptance-rejection algorithm Mixtures Signed mixtures Simulation Inverse cdf Quantile function

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Markov chain Monte Carlo and acceptance-rejection algorithms for synthesising short-term variations in the generation output of the photovoltaic system

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IET RENEWABLE POWER GENERATION 2017年第6期11卷 878-888页

作者： Kim, Insu Alabama A&M Univ Elect Engn Normal AL 35762 USA

Solar photovoltaic (PV) is fast being deployed in electric power grids. For its more reliable integration into grids, the impact of its intermittent generation on grids should be further examined. However, high-resolution solar and meteorological measurement data in 1s or 1min intervals are often not available for many areas or they are expensive to obtain. Thus, the objective of this study is to present a first-order Markov chain Monte Carlo (MCMC) method that synthesises the short-term variation, or sudden energy shortages and overages, in the power generation of a PV system in high-resolution, from low-resolution solar and meteorological data. In addition, up and down ramp rates in PV output are significant for the application of battery storage systems or grid operation. Thus, the acceptance-rejection algorithm able to limit such ramp rates is proposed. The proposed MCMC and acceptance-rejection methods are verified by comparing the statistical characteristics of the synthesised data to those of the original data. From case studies, this study found that the proposed methods could present the sufficient short-term variation in generation output of a PV system.

关键词： solar power stations photovoltaic power systems power generation reliability Monte Carlo methods Markov processes power grids battery storage plants first-order Markov chain Monte Carlo method acceptance-rejection algorithm short-term variation synthesis photovoltaic system generation output solar photovoltaic electric power grids first-order MCMC method sudden energy shortage synthesis overages synthesis low-resolution solar data meteorological data up ramp rate down ramp rate battery storage systems grid operation

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PATCHWORK rejection algorithmS

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 1990年第1期31卷 127-131页

作者： KEMP, AW UNIV ST ANDREWS INST MATHDEPT MATH SCIST ANDREWS KY16 9SSFIFESCOTLAND

New methods for implementing rejection algorithms are suggested. The objectives are to avoid the generation of unwanted envelope variates, to use fewer pseudorandom uniform variates, and to bypass as far as possible the need to decide whether to accept or to reject. Considerably fewer than two uniforms on average, per attempted output of a target random variable, can be achieved, together with an increased acceptance rate. The generation of tail variates from a normal distribution is used as illustration.

关键词： acceptance-rejection algorithm patchwork rejection unit square partition

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Rectangles algorithm for Generating Normal Variates

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NAVAL RESEARCH LOGISTICS 2012年第1期59卷 52-57页

作者： Zhang, Rui Leemis, Lawrence M. Coll William & Mary Dept Math Williamsburg VA 23187 USA Univ Maryland Robert H Smith Sch Business Dept Decis & Informat Technol College Pk MD 20742 USA

We propose an algorithm for generating normal random variates that is based on the acceptance-rejection method and uses a piecewise majorizing function. The piecewise function has 2048 equal-area pieces, 2046 of which are constant, and the two extreme pieces are curves that majorize the tails. The proposed algorithm has not only good performance from correlation induction perspective, but also works well from a speed perspective. It is faster than the inversion method by Odeh and Evans and most other methods. (C) 2011 Wiley Periodicals, Inc. Naval Research Logistics 59: 52-57, 2012

关键词： acceptance-rejection algorithm correlation induction normal distribution random variate generation

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A novel MM algorithm and the mode-sharing method in Bayesian computation for the analysis of general incomplete categorical data

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2019年 140卷 122-143页

作者： Tian, Guo-Liang Liu, Yin Tang, Man-Lai Li, Tao Southern Univ Sci & Technol Dept Math Shenzhen 518055 Guangdong Peoples R China Zhongnan Univ Econ & Law Sch Math & Stat Wuhan 430073 Hubei Peoples R China Hang Seng Univ Hong Kong Sch Decis Sci Dept Math & Stat Siu Lek YuenShatin Hong Kong Peoples R China

Incomplete categorical data often occur in the fields such as biomedicine, epidemiology, psychology, sports and so on. In this paper, we first introduce a novel minorization-maximization (MM) algorithm to calculate the maximum likelihood estimates (MLEs) of parameters and the posterior modes for the analysis of general incomplete categorical data. Although the data augmentation (DA) algorithm and Gibbs sampling as the corresponding stochastic counterparts of the expectation-maximization (EM) and ECM algorithms are developed very well, up to now, little work has been done on creating stochastic versions to the existing MM algorithms. This is the first paper to propose a mode-sharing method in Bayesian computation for general incomplete categorical data by developing a new acceptance-rejection (AR) algorithm aided with the proposed MM algorithm. The key idea is to construct a class of envelope densities indexed by a working parameter and to identify a specific envelope density which can overcome the four drawbacks associated with the traditional AR algorithm. The proposed mode-sharing based AR algorithm has three significant characteristics: (I) it can automatically establish a family of envelope densities {g(lambda)(.): lambda is an element of S-lambda} indexed by a working parameter lambda, where each member in the family shares mode with the posterior density;(II) with the onedimensional grid method searching over the finite interval S-lambda,S- it can identify an optimal working parameter lambda(opt) by maximizing the theoretical acceptance probability, yielding a best easy-sampling envelope density g lambda(opt) (.), which is more dispersive than the posterior density;(III) it can obtain the optimal envelope constant c(opt) by using the mode-sharing theorem (indicating that the high-dimensional optimization can be completely avoided) or by using the proposed MM algorithm again. Finally, a toy model and three real data sets are used to illustrate the proposed meth

关键词： acceptance-rejection algorithm Bayesian analysis General incomplete categorical data Minorization-maximization algorithm Mode-sharing method

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A gamma Bayesian exponential model for computing and updating residual life distribution of bearings

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART C-JOURNAL OF MECHANICAL ENGINEERING SCIENCE 2013年第11期227卷 2620-2633页

作者： Li, Bing Gao, Zhen Shen, ZhongJie Chen, XueFeng He, ZhengJia Xi An Jiao Tong Univ State Key Lab Mfg Syst Engn Xian 710049 Peoples R China

Residual life estimation occupies an important place in modern mechanical design and condition-based maintenance programs. Condition monitoring information can reflect the health status of the individual device, and the effective use of this information can help continuously predict the individual residual life. In this study, an exponential degradation model is developed to describe the degradation characteristics of devices for residual life estimation. This model is based on a gamma-prior Bayesian updating approach and an acceptance-rejection algorithm. With the gamma distribution representing the degradation rate differences among individuals, the real-world data can be described flexibly. By aid of Bayesian updating approach, the model can be updated with both the historical data and real-time monitoring signals. Furthermore, on the basis of the updated model and by means of acceptance-rejection algorithm, the residual life distribution can be computed without redundant computation. Consequently, the residual life can be estimated using the results of the residual life distribution. Finally, the proposed method is applied to real-world vibration-based degradation signals resulting from the accelerated fatigue testing of conical roller bearings. The results show that this method can avoid redundant computation and effectively estimate and update the bearing's residual life. Therefore, the engineering value and general application of this novel method has been validated.

关键词： Residual life estimation gamma distribution Bayesian updating approach acceptance-rejection algorithm bearing

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An efficient simulation algorithm for the generalized von Mises distribution of order two

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COMPUTATIONAL STATISTICS 2013年第1期28卷 255-268页

作者： Pfyffer, Samuel Gatto, Riccardo Univ Bern Inst Phys CH-3012 Bern Switzerland Univ Bern Inst Math Stat & Actuarial Sci CH-3012 Bern Switzerland

In this article we propose an exact efficient simulation algorithm for the generalized von Mises circular distribution of order two. It is an acceptance-rejection algorithm with a piecewise linear envelope based on the local extrema and the inflexion points of the generalized von Mises density of order two. We show that these points can be obtained from the roots of polynomials and degrees four and eight, which can be easily obtained by the methods of Ferrari and Weierstrass. A comparative study with the von Neumann acceptance-rejection, with the ratio-of-uniforms and with a Markov chain Monte Carlo algorithms shows that this new method is generally the most efficient.

关键词： acceptance-rejection algorithm Bimodality Circular distribution Markov chain Monte Carlo Methods of Ferrari and Weierstrass Piecewise linear envelope Ratio-of-uniforms algorithm

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Simulation of truncated and unimodal gamma distributions

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JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2024年第5期94卷 996-1015页

作者： Kurose, Yuta Univ Tsukuba Fac Engn Informat & Syst 1-1-1 Tennodai Tsukuba Ibaraki 3058573 Japan

An efficient random variable generator for a truncated gamma distribution with shape parameter greater than 1 is designed using an acceptance-rejection algorithm. Based on an approximation to a transformed gamma density function by the standard normal density, numerical information for the standard normal density is prepared in advance, and the calculation is performed with reference to that information. An improvement via a squeezing method is proposed to reduce the computational burden and time. The algorithm's acceptance rate for generating truncated gamma variables is very high and almost 1 when the truncated distribution is unimodal. Numerical experiments for one- and two-sided truncated domain cases are conducted to measure the execution time, including the parameter setup time. Compared with existing truncated gamma variate generators, the proposed method performs better when the distribution is unimodal and the shape parameter is equal to or greater than 3.3.

关键词： acceptance-rejection algorithm shape parameter squeezing truncated gamma distribution

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Generation of random directions from the generalized von Mises-Fisher distribution

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2024年第11期53卷 5491-5506页

作者： Salvador, Sara Gatto, Riccardo Univ Bern Inst Math Stat & Actuarial Sci Bern Switzerland Univ Bern Inst Math Stat & Actuarial Sci Alpeneggstr 22 CH-3012 Bern Switzerland

We introduce two algorithms for generating from the bimodal generalized von Mises-Fisher distribution on the sphere. This generalization of the von Mises-Fisher distribution is more flexible, in particular by allowing for multimodality, and it preserves many of the theoretical properties of the von Mises-Fisher. The first proposed generation algorithm is obtained from conditional simulation and acceptance-rejection. The second one is the Metropolis-Hastings with mixture of von Mises-Fisher as jumping or instrumental distribution. These two algorithms are compared through density estimations of generated polar angles.

关键词： acceptance-rejection algorithm Bimodal spherical distribution Conditional simulation Metropolis-Hastings algorithm Normalizing constant

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Simulating from a mixture of exponential distributions with some negatively weighted components

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Journal of Statistical Computation and Simulation 1989年第1期33卷 1-9页

作者： Elston, D.A. Glasbey, C.A. Scottish Agricultural Statistics Service University of Edinburgh King's Buildings Edinburgh EH9 3JZ United Kingdom

The acceptance-rejection algorithm is slow to simulate from mixture distributions when the acceptance probability is small. For a mixture of exponential distributions, reformulation as a mixture of general Erlang distributions may increase efficiency. The reformulation which maximises acceptance probability can be found by linear programming. An example is given in which reformulation reduces the average simulation time by a factor of 15. © 1989, Taylor & Francis Group, LLC. All rights reserved.

关键词： acceptance probability acceptance-rejection algorithm general Erlang (GE) distributions linear programming mixture-distribution reformulation Simulation

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