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Improving the data augmentation algorithm in the Two-Block Setup

JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2015年第4期24卷 1114-1133页

作者： Pal, Subhadip Khare, Kshitij Hobert, James P. Univ Florida Dept Stat Gainesville FL 32611 USA

The data augmentation (DA) approach to approximate sampling from an intractable probability density f(X) is based on the construction of a joint density, f(X, Y), whose conditional densities, f(X|Y) and f(Y|X), can be straightforwardly sampled. However, many applications of the DA algorithm do not fall in this single-block setup. In these applications, X is partitioned into two components, X = (U, V), in such a way that it is easy to sample from f(Y|X), f(U|V, Y), and f(V|U, Y). We refer to this alternative version of DA, which is effectively a three-variable Gibbs sampler, as two-block DA. We develop two methods to improve the performance of the DA algorithm in the two-block setup. These methods are motivated by the Haar PX-DA algorithm, which has been developed in previous literature to improve the performance of the single-block DA algorithm. The Haar PX-DA algorithm, which adds a computationally inexpensive extra step in each iteration of the DA algorithm while preserving the stationary density, has been shown to be optimal among similar techniques. However, as we illustrate, the Haar PX-DA algorithm does not lead to the required stationary density f(X) in the two-block setup. Our methods incorporate suitable generalizations and modifications to this approach, and work in the two-block setup. A theoretical comparison of our methods to the two-block DA algorithm, a much harder task than the single-block setup due to nonreversibility and structural complexities, is provided. We successfully apply our methods to applications of the two-block DA algorithm in Bayesian robit regression and Bayesian quantile regression. Supplementary materials for this article are available online.

关键词： data augmentation algorithm Group action Haar measure Sandwich algorithm Two-block DA algorithm

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Modified Polya-Gamma data augmentation for Bayesian analysis of directional data

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JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2022年第16期92卷 3430-3451页

作者： Pal, Subhadip Gaskins, Jeremy Univ Louisville Dept Bioinformat & Biostat Louisville KY 40292 USA

In this work, we develop new data augmentation algorithms for Bayesian analysis of directional data using the von Mises-Fisher distribution in arbitrary dimensions. The approach leads to a new class of distributions, called the Modified Polya-Gamma distribution, which we construct in detail. The proposed data augmentation strategies circumvent the need for analytic approximations to integration, numerical integration, or Metropolis-Hastings for the corresponding posterior inference. Simulations and real data examples are presented to demonstrate the applicability and to apprise the performance of the proposed procedures.

关键词： data augmentation algorithm directional data von Mises-Fisher distribution latent variables Modified-Half-Normal Modified Polya-Gamma infinite convolutions of exponential distributions

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A novel load allocation strategy based on the adaptive chiller model with data augmentation

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ENERGY 2024年 309卷

作者： Jia, Zhiyang Jin, Xinqiao Lyu, Yuan Xue, Qi Du, Zhimin Shanghai Jiao Tong Univ Sch Mech Engn Shanghai 200240 Peoples R China

Model-based load allocation strategy is an impactful solution to enhance energy efficiency of multiple-chiller system. Its performance is heavily dependent on the accuracy of chiller model. data-driven model is a prettygood solution. However, in real multiple-chiller system, the range of operation condition in historical data is commonly narrow, so it is challenging to develop an accurate data-driven model of chiller throughout full range of operation condition. In this paper, data augmentation algorithm is presented to generate the data outside of historical data, which is based on conditional generative adversarial network (CGAN) and elastic weight consolidation algorithm (EWC). Combined historical data and generated data, augmented training dataset is set up and updated by online operation data. Trained by online updated augmented training dataset periodically, adaptive chiller model is set up. Based on adaptive chiller model, a novel load allocation strategy presented for multiple-chiller system. The proposed strategy is verified by field test in multiple-chiller system. The results show that adaptive chiller model, with the aid of data augmentation algorithm, is more accurate. The proposed strategy can achieve 5.03 % energy saving compared with fixed set-point strategy, and the EER of proposed strategy is 6.27 % higher than that of fixed set-point strategy.

关键词： Model-based load allocation strategy Adaptive chiller model Conditional generative adversarial network data augmentation algorithm Multiple-chiller system

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Application of gamma process to two-agent combinations with delayed toxicity

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2021年第1期50卷 153-163页

作者： Yada, Shinjo Hamada, Chikuma A2 Healthcare Dev Strategy Div Biostat Dept Tokyo Japan Tokyo Univ Sci Dept Informat & Comp Technol Tokyo Japan

Phase I trials investigate the drugs used on humans for the first time. In cancer treatment, drug safety is examined based on the toxicity. Herein, we propose a dose-finding method for oncological phase I drug combinations with delayed toxicity. The toxicity data of the patients who do not complete the follow-up period and do not experience toxicity are considered missing data. We use data augmentation to impute missing data while modeling the time required to experience toxicity using a hazard function, modeled using a gamma process. Simulation results demonstrate that the proposed method shortens trial durations without affecting performance.

关键词： Missing data data augmentation algorithm Gamma process Delayed toxicity Phase I clinical trial

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Efficient Bayesian metamodeling for fine-grained and robust fragility analysis of buildings at a regional scale

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STRUCTURAL SAFETY 2023年第1期102卷

作者： Su, Peiyang Xiong, Feng Lu, Yang Hu, Qidan Zhang, Bowen Sichuan Univ Key Lab Deep Underground Sci & Engn Minist Educ Coll Architecture & Environm 24 South Sect 1Yihuan Rd Chengdu Peoples R China Hong Kong Polytech Univ Dept Bldg & Real Estate Hong Kong Peoples R China Sichuan Univ 24 South Sect 1Yihuan Rd Chengdu 610065 Sichuan Peoples R China

A fine-grained seismic fragility analysis of regional buildings considering 'Soil-Structure-Cluster Interaction' (SSCI) effect faces a dilemma between accuracy and efficiency. In the present study, a Bayesian Neural Network (BNN) model is adopted to address this problem. Specifically, the conventional neural network (NN) algorithm and a Bayesian inference are integrated into one approach, where the NN predicts the structural responses of buildings and the Bayesian inference quantifies the epistemic uncertainty of fragility estimations arising from limited response data due to the high computational cost of the structural analysis. Moreover, the Gaussian kernel function-based data augmentation (KDA) algorithm is proposed to sample the simulated structural response data for BNN model training. The proposed framework is implemented on the regional buildings of Sichuan University as a case study. The results show that the BNN can make accurate and robust fragility esti-mations with high modeling efficiency.

关键词： Regional seismic fragility assessment Site-city interaction effect Bayesian neural network data augmentation algorithm

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A new multivariate zero-adjusted Poisson model with applications to biomedicine

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BIOMETRICAL JOURNAL 2019年第6期61卷 1340-1370页

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

Recently, although advances were made on modeling multivariate count data, existing models really has several limitations: (i) The multivariate Poisson log-normal model (Aitchison and Ho, 1989) cannot be used to fit multivariate count data with excess zero-vectors;(ii) The multivariate zero-inflated Poisson (ZIP) distribution (Li et al., 1999) cannot be used to model zero-truncated/deflated count data and it is difficult to apply to high-dimensional cases;(iii) The Type I multivariate zero-adjusted Poisson (ZAP) distribution (Tian et al., 2017) could only model multivariate count data with a special correlation structure for random components that are all positive or negative. In this paper, we first introduce a new multivariate ZAP distribution, based on a multivariate Poisson distribution, which allows the correlations between components with a more flexible dependency structure, that is some of the correlation coefficients could be positive while others could be negative. We then develop its important distributional properties, and provide efficient statistical inference methods for multivariate ZAP model with or without covariates. Two real data examples in biomedicine are used to illustrate the proposed methods.

关键词： data augmentation algorithm expectation-maximization algorithm hypothesis testing multivariate zero-adjusted Poisson stochastic representation

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Estimating the spectral gap of a trace-class Markov operator

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ELECTRONIC JOURNAL OF STATISTICS 2019年第1期13卷 1790-1822页

作者： Qin, Qian Hobert, James P. Khare, Kshitij Univ Florida Dept Stat Gainesville FL 32611 USA

The utility of a Markov chain Monte Carlo algorithm is, in large part, determined by the size of the spectral gap of the corresponding Markov operator. However, calculating (and even approximating) the spectral gaps of practical Monte Carlo Markov chains in statistics has proven to be an extremely difficult and often insurmountable task, especially when these chains move on continuous state spaces. In this paper, a method for accurate estimation of the spectral gap is developed for general state space Markov chains whose operators are non-negative and trace-class. The method is based on the fact that the second largest eigenvalue (and hence the spectral gap) of such operators can be bounded above and below by simple functions of the power sums of the eigenvalues. These power sums often have nice integral representations. A classical Monte Carlo method is proposed to estimate these integrals, and a simple sufficient condition for finite variance is provided. This leads to asymptotically valid confidence intervals for the second largest eigenvalue (and the spectral gap) of the Markov operator. In contrast with previously existing techniques, our method is not based on a near-stationary version of the Markov chain, which, paradoxically, cannot be obtained in a principled manner without bounds on the spectral gap. On the other hand, it can be quite expensive from a computational standpoint. The efficiency of the method is studied both theoretically and empirically.

关键词： data augmentation algorithm eigenvalues Hilbert-Schmidt operator Markov chain Monte Carlo

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A note on the convergence rate of MCMC for robust Bayesian multivariate linear regression with proper priors

COMPUTATIONAL AND MATHEMATICAL METHODS

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COMPUTATIONAL AND MATHEMATICAL METHODS 2020年第3期2卷

作者： Backlund, Grant Hobert, James P. Univ Florida Dept Stat Gainesville FL 32611 USA

The multivariate linear regression model with errors from a scale mixture of Gaussian densities yields a complex likelihood function. Combining this likelihood with any nontrivial prior distribution leads to a highly intractable posterior density. If a conditionally conjugate prior is used, then there is a well known and easy-to-implement data augmentation (DA) algorithm available for exploring the posterior. Hobert et al recently showed that, under an improper conditionally conjugate prior (and weak regularity conditions), the Markov chain that drives the DA algorithm converges at a geometric rate. Unfortunately, the model studied by Hobert et al can only be used in situations where the X matrix has full column rank. In this note, analogous convergence rate results are established for a proper conditionally conjugate prior. An important advantage of using a proper prior is that, not only is the X matrix allowed to be column rank deficient, but it can also have more columns than rows, that is, our model is applicable in cases where p > n. This is an important extension in the era of big data.

关键词： data augmentation algorithm drift condition geometric ergodicity heavy-tailed distribution scale mixture

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A comparison theorem for data augmentation algorithms with applications

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ELECTRONIC JOURNAL OF STATISTICS 2016年第1期10卷 308-329页

作者： Choi, Hee Min Hobert, James P. Univ Calif Davis Dept Stat Davis CA 95616 USA Univ Florida Dept Stat Gainesville FL 32611 USA

The data augmentation (DA) algorithm is considered a useful Markov chain Monte Carlo algorithm that sometimes suffers from slow convergence. It is often possible to convert a DA algorithm into a sandwich algorithm that is computationally equivalent to the DA algorithm, but converges much faster. Theoretically, the reversible Markov chain that drives the sandwich algorithm is at least as good as the corresponding DA chain in terms of performance in the central limit theorem and in the operator norm sense. In this paper, we use the sandwich machinery to compare two DA algorithms. In particular, we provide conditions under which one DA chain can be represented as a sandwich version of the other. Our results are used to extend Hobert and Marchev's (2008) results on the Haar PX-DA algorithm and to improve the collapsing theorem of Liu et al. (1994) and Liu (1994). We also illustrate our results using Brownlee's (1965) stack loss data.

关键词： data augmentation algorithm sandwich algorithm central limit theorem convergence rate operator norm

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Trace-class Monte Carlo Markov chains for Bayesian multivariate linear regression with non-Gaussian errors

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JOURNAL OF MULTIVARIATE ANALYSIS 2018年 166卷 335-345页

作者： Qin, Qian Hobert, James P. Univ Florida Dept Stat Gainesville FL 32611 USA

Let pi denote the intractable posterior density that results when the likelihood from a multivariate linear regression model with errors from a scale mixture of normals is combined with the standard non-informative prior. There is a simple data augmentation algorithm (based on latent data from the mixing density) that can be used to explore pi. Let h and d denote the mixing density and the dimension of the regression model, respectively. Hobert et al. (2018) have recently shown that, if h converges to 0 at the origin at an appropriate rate, and integral(infinity)(0) u(d/2) h(u) du < infinity, then the Markov chains underlying the data augmentation (DA) algorithm and an alternative Haar parameter expanded DA (PX-DA) algorithm are both geometrically ergodic. Their results are established using probabilistic techniques based on drift and minorization conditions. In this paper, spectral analytic techniques are used to establish that something much stronger than geometric ergodicity often holds. In particular, it is shown that, under simple conditions on h, the Markov operators defined by the DA and Haar PX-DA Markov chains are trace-class, i.e., compact with summable eigenvalues. Many standard mixing densities satisfy the conditions developed in this paper. Indeed, the new results imply that the DA and Haar PX-DA Markov operators are trace-class whenever the mixing density is generalized inverse Gaussian, log-normal, Frechet (with shape parameter larger than d/2), or inverted Gamma (with shape parameter larger than d/2). (C) 2018 Elsevier Inc. All rights reserved.

关键词： Compact operator data augmentation algorithm Haar PX-DA algorithm Heavy-tailed distribution Scale mixture Markov operator Trace-class operator

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