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

Active learning of Gaussian process (GP) surrogates has been useful for optimizing experimental designs for physical/computer simulation experiments, and for steering data acquisition schemes in machine learning. In this paper, we develop a method for active learning of piecewise, Jump GP surrogates. Jump GPs are continuous within, but discontinuous across, regions of a design space, as required for applications spanning autonomous materials design, conﬁguration of smart factory systems, and many others. Although our active learning heuristics are appropriated from strategies originally designed for ordinary GPs, we demonstrate that additionally accounting for model bias, as opposed to the usual model uncertainty, is essential in the Jump GP context. Toward that end, we develop an estimator for bias and variance of Jump GP models. Illustrations, and evidence of the advantage of our proposed methods, are provided on a suite of synthetic benchmarks, and real-simulation experiments of varying complexity.

Active Learning of Piecewise Gaussian Process Surrogates

We consider large-scale industrial computer model calibration, combining multi-output simulation with limited physical observation, involved in the development of a honeycomb seal. Toward that end, we adopt a localized sampling and emulation strategy called "on-site surrogates (OSSs)", designed to cope with the amalgamated challenges of high-dimensional inputs, large-scale simulation campaigns, and nonstationary response surfaces. In previous applications, OSSs were one-at-a-time affairs for multiple outputs. We demonstrate that this leads to dissonance in calibration efforts for a common parameter set across outputs for the honeycomb. Instead, a conceptually straightforward, but implementationally intricate, principal-components representation, adapted from ordinary Gaussian process surrogate modeling to the OSS setting, can resolve this tension. With a two-pronged - optimization-based and fully Bayesian - approach, we show how pooled information across outputs can reduce uncertainty and enhance (statistical and computational) efficiency in calibrated parameters for the honeycomb relative to the previous, "data-poor" univariate analog.

Multi-output calibration of a honeycomb seal via on-site surrogates.

Bayesian Analysis of Non-Gaussian Long-Range Dependent Processes

The canonical technique for nonlinear modeling of spatial and other point-referenced data is known as kriging in the geostatistics literature, and by Gaussian Process (GP) regression in surrogate modeling and machine learning communities. There are many similarities shared between kriging and GPs, but also some important diﬀerences. One is that GPs impose a process on the data-generating mechanism that can be used to automate kernel/variogram inference, thus removing the human from the loop in a conventional semivariogram analysis. The GP framework also suggests a probabilistically valid means of scaling to handle a large corpus of training data, i.e., an alternative to so-called ordinary kriging. Finally, recent GP implementations are tailored to make the most of modern computing architectures such as multi-core workstations and multi-node supercomputers. Ultimately, we use this discussion as a springboard for an empirics-based advocacy of state-of-the-art GP technology in the geospatial modeling of a large corpus of borehole data involved in mining for gold and other minerals. Our out-of-sample validation exercise quantiﬁes how GP methods (as implemented by open source libraries) can be both more economical (fewer human and compute resources), more accurate and oﬀer better uncertainty quantiﬁcation than kriging-based alternatives. Once in the GP framework, several possible extensions beneﬁt from a fully generative modeling apparatus. In particular, we showcase a simple imputation scheme that copes with left-censoring of small measurements, which is a common feature in borehole assays.

Machine learning and geospatial methods for large-scale mining data

In forecasting problems it is important to know whether or not recent events represent a regime change (low long-term predictive potential), or rather a local manifestation of longer term eects (potentially higher predictive potential). Mathematically, a key question is about whether the underlying stochastic process exhibits \memory", and if so whether the memory is \long" in a precise sense. Being able to detect or rule out such eects can have a profound impact on speculative investment (e.g., in nancial markets) and inform public policy (e.g., characterising the size and timescales of the earth system’s response to the anthropogenic CO2 perturbation). Most previous work on inference of long memory eects is frequentist in nature. Here we provide a systematic treatment of Bayesian inference for long memory processes via the Autoregressive Fractional Integrated Moving Average (ARFIMA) model. In particular, we provide a new approximate likelihood for ecient parameter inference, and show how nuisance parameters (e.g., short memory eects) can be integrated over in order to focus on long memory parameters and hypothesis testing more directly than ever before. We illustrate our new methodology on both synthetic and observational data, with favorable comparison to the standard estimators.

Robert B. Gramacy

Papers

Active Learning of Piecewise Gaussian Process Surrogates

Multi-output calibration of a honeycomb seal via on-site surrogates.

Bayesian Analysis of Non-Gaussian Long-Range Dependent Processes

Machine learning and geospatial methods for large-scale mining data

Efficient Bayesian inference for long memory processes