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On sequential Monte Carlo, partial rejection control and approximate bayesian computation

STATISTICS AND COMPUTING 2012年第6期22卷 1209-1222页

作者： Peters, G. W. Fan, Y. Sisson, S. A. Univ New S Wales Sch Math & Stat Sydney NSW Australia CSIRO Sydney N Ryde NSW 1670 Australia

We present a variant of the sequential Monte Carlo sampler by incorporating the partial rejection control mechanism of Liu (2001). We show that the resulting algorithm can be considered as a sequential Monte Carlo sampler with a modified mutation kernel. We prove that the new sampler can reduce the variance of the incremental importance weights when compared with standard sequential Monte Carlo samplers, and provide a central limit theorem. Finally, the sampler is adapted for application under the challenging approximate bayesian computation modelling framework.

关键词： Approximate bayesian computation bayesian computation Likelihood-free inference Partial rejection control Sequential Monte Carlo samplers

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Application of a predictive distribution formula to bayesian computation for incomplete data models

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STATISTICS AND COMPUTING 2005年第3期15卷 167-178页

作者： Sweeting, T Kharroubi, S UCL London WC1E 6BT England Univ Sheffield Sheffield S10 2TN S Yorkshire England

We consider exact and approximate bayesian computation in the presence of latent variables or missing data. Specifically we explore the application of a posterior predictive distribution formula derived in Sweeting and Kharroubi ( 2003), which is a particular form of Laplace approximation, both as an importance function and a proposal distribution. We show that this formula provides a stable importance function for use within poor man's data augmentation schemes and that it can also be used as a proposal distribution within a Metropolis- Hastings algorithm for models that are not analytically tractable. We illustrate both uses in the case of a censored regression model and a normal hierarchical model, with both normal and Student t distributed random effects. Although the predictive distribution formula is motivated by regular asymptotic theory, it is not necessary that the likelihood has a closed form or that it possesses a local maximum.

关键词： asymptotic approximation bayesian computation data augmentation importance sampling Laplace approximation latent variables Metropolis-Hastings missing data predictive distribution simulation

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Nested Sampling for General bayesian computation

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bayesian ANALYSIS 2006年第4期1卷 833-859页

作者： Skilling, John Maximum Entropy Data Consultants Ltd Kenmare County Kerry Ireland

Nested sampling estimates directly how the likelihood function relates to prior mass. The evidence (alternatively the marginal likelihood, marginal density of the data, or the prior predictive) is immediately obtained by summation. It is the prime result of the computation, and is accompanied by an estimate of numerical uncertainty. Samples from the posterior distribution are an optional by-product, obtainable for any temperature. The method relies on sampling within a hard constraint on likelihood value, as opposed to the softened likelihood of annealing methods. Progress depends only on the shape of the "nested" contours of likelihood, and not on the likelihood values. This invariance (over monotonic re-labelling) allows the method to deal with a class of phase-change problems which effectively defeat thermal annealing.

关键词： bayesian computation evidence marginal likelihood algorithm nest annealing phase change model selection

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Leave Pima Indians Alone: Binary Regression as a Benchmark for bayesian computation

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STATISTICAL SCIENCE 2017年第1期32卷 64-87页

作者： Chopin, Nicolas Ridgway, James ENSAE Stat 3 Ave Pierre Larousse F-92245 Malakoff France INRIA Lille Nord Europe Equipe SequeL Parc Sci Haute Borne40 Ave Halley F-59650 Villeneuve Dascq France

Whenever a new approach to perform bayesian computation is introduced, a common practice is to showcase this approach on a binary regression model and datasets of moderate size. This paper discusses to which extent this practice is sound. It also reviews the current state of the art of bayesian computation, using binary regression as a running example. Both sampling-based algorithms (importance sampling, MCMC and SMC) and fast approximations (Laplace, VB and EP) are covered. Extensive numerical results are provided, and are used to make recommendations to both end users and bayesian computation experts. Implications for other problems (variable selection) and other models are also discussed.

关键词： bayesian computation expectation propagation Markov chain Monte Carlo sequential Monte Carlo variational inference

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Inflation Rate Prediction Model Combining SMC-ABC Algorithm and BVAR

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IEEE ACCESS 2025年 13卷 45126-45141页

作者： Li, Xiang Lan, Hai Ming, Junren Wuhan Inst Technol Law & Business Sch Wuhan 430000 Hubei Peoples R China Wuhan Inst Technol Sch Marxism Wuhan 430000 Hubei Peoples R China Wuhan Inst Technol Sch Management Wuhan 430000 Hubei Peoples R China

The inflation rate is an important indicator of the economic health of a country or region. To improve the accuracy of inflation rate prediction and to fill the shortcomings of the existing inflation rate forecasting model in terms of forecasting accuracy and adaptability, the study constructed a prediction model based on the technique of bayesian vector auto-regression model. The experimental results revealed that the study's improved bayesian vector auto-regression model had a higher prediction accuracy than both the baseline and existing advanced models. Its mean absolute error and root mean square error were less than 0.001 and 0.015, respectively. In the cross-validation analysis, the generalization ability of the model was strong, with R-squared taking values of 0.962 and 0.984 for the test set and training set, respectively. In the goodness-of-fit test, the model had a significant advantage over the other models, with both Akaike information criterion and bayesian information criterion in the minimum value interval of 0.1-0.3. Anticipation Likelihood Probability converged to a maximum value of 0.973, which was the most efficient in prediction. In the applied analysis, the method was confirmed by the Diebold-Mariano test to show predictive test P-values of 2.464 per cent and 3.486 per cent, respectively. The percentage deviation analysis of the sample's percent bias had a small error, with all predictions being closest to the true value. The change trend and details of the prediction results were better grasped. The study scientifically and rationally aids policy formulation, helps to avoid the impact of inflation on the economic market, and promotes the stable and healthy development of the economy.

关键词： Predictive models Forecasting Analytical models Reactive power Economics Accuracy Bayes methods Vectors Mathematical models Adaptation models Inflation economic forecasting bayesian vector auto-regressive modeling bayesian computation sequential Monte Carlo methods

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Logit unfolding choice models for binary data

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STATISTICS AND COMPUTING 2025年第2期35卷 1-18页

作者： Lei, Rayleigh Rodriguez, Abel Univ Washington Dept Stat Padelford Hall Seattle WA 98915 USA

Discrete choice models with non-monotonic response functions are important in many areas of application, especially political sciences and marketing. This paper describes a novel unfolding model for binary data that allows for heavy-tailed shocks to the underlying utilities. One of our key contributions is a Markov chain Monte Carlo algorithm that requires little or no parameter tuning, fully explores the support of the posterior distribution, and can be used to fit various extensions of our core model that involve (bayesian) hypothesis testing on the latent construct. Our empirical evaluations of the model and the associated algorithm suggest that they provide better complexity-adjusted fit to voting data from the United States House of Representatives.

关键词： Discrete choice models bayesian computation Unfolding models Scaling

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Geographical bayesian second stage analysis for operating efficiency of Brazilian electricity distribution system operators

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ENERGY ECONOMICS 2025年 144卷

作者： Costa, Marcelo Azevedo da Silva, Aline Veronese Mineti, Leandro Brioschi Univ Fed Minas Gerais UFMG Dept Prod Engn Av Pres Antonio Carlos 6627 BR-31270901 Belo Horizonte MG Brazil Univ Estadual Campinas UNICAMP Inst Econ R Pitagoras 353 BR-13083857 Campinas SP Brazil Falconi Consulting Av Pres Juscelino Kubitschek 1327 17 Andar BR-04543011 Sao Paulo SP Brazil

Since 2011, the Brazilian electricity regulator has applied data envelopment analysis to estimate regulatory operating costs for distribution and transmission companies. Despite the availability of environmental contextual variables, second-stage analysis has been avoided, primarily due to inconsistent statistical results, including estimated coefficients contrary to technical evidence and significant changes in operating efficiencies for selected companies. Previous studies have shown that environmental adjustments are critical for companies' revenues operating in harsh environments in Brazil. Additionally, climate changes are affecting expenses varying effects nationwide. To tackle this challenge, a second-stage model in which changes in efficiencies also affected by geographical location of companies is proposed. Coefficient constraints and multiple environmental variables are applied to estimate regulatory efficiencies of Brazilian Distributor System Operators upcoming years. Results indicate maximum efficiency changes of +5.35% and an increase of 1.1% in the regulatory OPEX if the proposed second stage is applied.

关键词： Data envelopment analysis Second stage analysis bayesian computation Benchmarking analysis

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bayesian inference and cure rate modeling for event history data

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TEST 2025年第1期34卷 1-27页

作者： Papastamoulis, Panagiotis Milienos, Fotios S. Athens Univ Econ & Business Dept Stat 76 Patiss Str Athens 10434 Greece Pante Univ Social & Polit Sci Dept Sociol 136 Syngrou Ave Athens 17671 Greece

Estimating model parameters of a general family of cure models is always a challenging task mainly due to flatness and multimodality of the likelihood function. In this work, we propose a fully bayesian approach in order to overcome these issues. Posterior inference is carried out by constructing a Metropolis-coupled Markov chain Monte Carlo (MCMC) sampler, which combines Gibbs sampling for the latent cure indicators and Metropolis-Hastings steps with Langevin diffusion dynamics for parameter updates. The main MCMC algorithm is embedded within a parallel tempering scheme by considering heated versions of the target posterior distribution. It is demonstrated that along the considered simulation study the proposed algorithm freely explores the multimodal posterior distribution and produces robust point estimates, while it outperforms maximum likelihood estimation via the Expectation-Maximization algorithm. A by-product of our bayesian implementation is to control the False Discovery Rate when classifying items as cured or not. Finally, the proposed method is illustrated in a real dataset which refers to recidivism for offenders released from prison;the event of interest is whether the offender was re-incarcerated after probation or not.

关键词： MCMC bayesian computation Censored data Cured fraction

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COMPARATIVE JUDGEMENT MODELLING TO MAP FORCED MARRIAGE AT LOCAL LEVELS

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Annals of Applied Statistics 2025年第1期19卷 419-439页

作者： Seymour, Rowland Nyarko-Agyei, Albert McCabe, Helen Severn, Katie Sirl, David Kypraios, Theodore Taylor, Adam School of Mathematics University of Birmingham United Kingdom Rights Lab University of Nottingham United Kingdom School of Mathematical Sciences University of Nottingham United Kingdom Digital Research Services University of Nottingham United Kingdom

Forcing someone into marriage against their will is a violation of their human rights. In 2021, the county of Nottinghamshire, U.K., launched a strategy to tackle forced marriage and violence against women and girls. We set out to map the risk of forced marriage across the county to support the strategy and enable the development of local interventions. However, there was no centralised database for forced marriage in the county and carrying out a survey using standard survey methods was unlikely to produce robust results due to the hidden nature of this crime. Comparative judgement provides a survey design that can map the risk of forced marriage through pairwise comparisons. Current comparative judgement models require studies to have a large number of participants, so we developed a more flexible spatial modelling structure and a mechanism to schedule comparisons more effectively. The proposed modelling structure reduced the data collection burden and made a comparative judgement study feasible with a small number of participants. Underpinning this structure is a latent variable representation that improves on the scalability of inferential procedures of previous comparative judgement models. We used these methods to map the risk of forced marriage across Nottinghamshire, thereby supporting the county’s strategy for tackling violence against women and girls. © 2025, Institute of Mathematical Statistics. All rights reserved.

关键词： bayesian computation bayesian nonparametrics Bradley–Terry Model violence against women and girls

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Empirical Bayes Test of the Parameter for Exponential-Poisson Distribution with Linex Loss 24

Empirical Bayes Test of the Parameter for Exponential-Poisso...

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Proceedings of the 2024 International Conference on Mathematics and Machine Learning

作者： Guimei He Chenglong Tan Xiaolong Chai School of Statistics and Mathematics Guangdong University of Finance & Economics Guangzhou Guangdong China Institute of Artificial Intelligence and Deep Learning Guangdong University of Finance and Economics Guangzhou Guangdong China

ISBN: (纸本)9798400711657

This article explores in depth the empirical Bayes (EB) one-sided test problem for exponential Poisson distribution parameters within the Linex loss function framework. By introducing the kernel estimation method of probability density function, this paper applies an innovative empirical Bayes test function construction strategy. This method not only effectively utilizes the inherent structure of the sample data, but also significantly improves the accuracy and robustness of the test. The paper constructs an empirical bayesian algorithm with parameters to solve the empirical Bayes test problem, analyzes its asymptotic optimality, and quantifies its convergence speed. This work provides a powerful tool for solving complex statistical test problems encountered in practical applications, especially in dealing with exponential Poisson distribution parameter estimation problems with uncertain prior information, demonstrating unique value. The model and algorithm proposed in this article have certain analytical ability for analyzing models with unknown prior distributions that require estimation of multiple parameters, and have certain reference value for the application of exponential Gamma mixed models, Weibull distribution models, etc.

关键词： bayesian computation

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