Statistics for Spatial Data.

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Convex Analysisの二,三の進展について

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Modern Applied Statistics With S

Big Data applications are typically associated with systems involving large numbers of users, massive complex software systems, and large-scale heterogeneous computing and storage architectures. The construction of such systems involves many distributed design choices. The end products (e.g., recommendation systems, medical analysis tools, real-time game engines, speech recognizers) thus involve many tunable configuration parameters. These parameters are often specified and hard-coded into the software by various developers or teams. If optimized jointly, these parameters can result in significant improvements. Bayesian optimization is a powerful tool for the joint optimization of design choices that is gaining great popularity in recent years. It promises greater automation so as to increase both product quality and human productivity. This review paper introduces Bayesian optimization, highlights some of its methodological aspects, and showcases a wide range of applications.

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Taking the Human Out of the Loop: A Review of Bayesian Optimization

Foreword Stephen P. Brooks, Andrew Gelman, Galin L. Jones, and Xiao-Li Meng Introduction to MCMC, Charles J. Geyer A short history of Markov chain Monte Carlo: Subjective recollections from in-complete data, Christian Robert and George Casella Reversible jump Markov chain Monte Carlo, Yanan Fan and Scott A. Sisson Optimal proposal distributions and adaptive MCMC, Jeffrey S. Rosenthal MCMC using Hamiltonian dynamics, Radford M. Neal Inference and Monitoring Convergence, Andrew Gelman and Kenneth Shirley Implementing MCMC: Estimating with confidence, James M. Flegal and Galin L. Jones Perfection within reach: Exact MCMC sampling, Radu V. Craiu and Xiao-Li Meng Spatial point processes, Mark Huber The data augmentation algorithm: Theory and methodology, James P. Hobert Importance sampling, simulated tempering and umbrella sampling, Charles J.Geyer Likelihood-free Markov chain Monte Carlo, Scott A. Sisson and Yanan Fan MCMC in the analysis of genetic data on related individuals, Elizabeth Thompson A Markov chain Monte Carlo based analysis of a multilevel model for functional MRI data, Brian Caffo, DuBois Bowman, Lynn Eberly, and Susan Spear Bassett Partially collapsed Gibbs sampling & path-adaptive Metropolis-Hastings in high-energy astrophysics, David van Dyk and Taeyoung Park Posterior exploration for computationally intensive forward models, Dave Higdon, C. Shane Reese, J. David Moulton, Jasper A. Vrugt and Colin Fox Statistical ecology, Ruth King Gaussian random field models for spatial data, Murali Haran Modeling preference changes via a hidden Markov item response theory model, Jong Hee Park Parallel Bayesian MCMC imputation for multiple distributed lag models: A case study in environmental epidemiology, Brian Caffo, Roger Peng, Francesca Dominici, Thomas A. Louis, and Scott Zeger MCMC for state space models, Paul Fearnhead MCMC in educational research, Roy Levy, Robert J. Mislevy, and John T. Behrens Applications of MCMC in fisheries science, Russell B. Millar Model comparison and simulation for hierarchical models: analyzing rural-urban migration in Thailand, Filiz Garip and Bruce Western

Handbook of Markov Chain Monte Carlo

Long memory plays an important role in many fields by determining the behaviour and predictability of systems; for instance, climate, hydrology, finance, networks and DNA sequencing. In particular, it is important to test if a process is exhibiting long memory since that impacts the accuracy and confidence with which one may predict future events on the basis of a small amount of historical data. A major force in the development and study of long memory was the late Benoit B. Mandelbrot. Here we discuss the original motivation of the development of long memory and Mandelbrot's influence on this fascinating field. We will also elucidate the sometimes contrasting approaches to long memory in different scientific communities

A brief history of long memory: Hurst, Mandelbrot and the road to ARFIMA

We investigate the merits of replication, and provide methods for optimal design (including replicates), with the goal of obtaining globally accurate emulation of noisy computer simulation experime...

Replication or Exploration? Sequential Design for Stochastic Simulation Experiments

A single-index model (SIM) provides for parsimonious multidimensional nonlinear regression by combining parametric (linear) projection with univariate nonparametric (nonlinear) regression models. We show that a particular Gaussian process (GP) formulation is simple to work with and ideal as an emulator for some types of computer experiment as it can outperform the canonical separable GP regression model commonly used in this setting. Our contribution focuses on drastically simplifying, reinterpreting, and then generalizing a recently proposed fully Bayesian GP-SIM combination. Favorable performance is illustrated on synthetic data and a real-data computer experiment. Two R packages, both released on CRAN, have been augmented to facilitate inference under our proposed model(s).

Gaussian Process Single-Index Models as Emulators for Computer Experiments.

In this paper, we develop a simulation-based framework for regu- larized logistic regression, exploiting two novel results for scale mixtures of nor- mals. By carefully choosing a hierarchical model for the likelihood by one type of mixture, and implementing regularization with another, we obtain new MCMC schemes with varying e-ciency depending on the data type (binary v. binomial, say) and the desired estimator (maximum likelihood, maximum a posteriori, poste- rior mean). Advantages of our omnibus approach include ∞exibility, computational e-ciency, applicability in p ? n settings, uncertainty estimates, variable selection, and assessing the optimal degree of regularization. We compare our methodology to modern alternatives on both synthetic and real data. An R package called reglogit is available on CRAN.

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Simulation-based Regularized Logistic Regression

Simulated tempering (ST) is an established Markov chain Monte Carlo (MCMC) method for sampling from a multimodal density ?(?). Typically, ST involves introducing an auxiliary variable k taking values in a finite subset of [0,1] and indexing a set of tempered distributions, say ? k (?)? ?(?) k . In this case, small values of k encourage better mixing, but samples from ? are only obtained when the joint chain for (?,k) reaches k=1. However, the entire chain can be used to estimate expectations under ? of functions of interest, provided that importance sampling (IS) weights are calculated. Unfortunately this method, which we call importance tempering (IT), can disappoint. This is partly because the most immediately obvious implementation is naive and can lead to high variance estimators. We derive a new optimal method for combining multiple IS estimators and prove that the resulting estimator has a highly desirable property related to the notion of effective sample size. We briefly report on the success of the optimal combination in two modelling scenarios requiring reversible-jump MCMC, where the naive approach fails.

Robert B. Gramacy

Papers

A brief history of long memory: Hurst, Mandelbrot and the road to ARFIMA

Replication or Exploration? Sequential Design for Stochastic Simulation Experiments

Gaussian Process Single-Index Models as Emulators for Computer Experiments.

Simulation-based Regularized Logistic Regression

Importance tempering