Bayesian model averaging (BMA) is an effective technique for addressing model uncertainty in variable selection problems. However, current BMA approaches have computational difficulty dealing with data in which there are many more measurements (variables) than samples. This paper presents a method for combining l(1) regularization and Markov chain Monte Carlo model composition techniques for BMA. By treating the l(1) regularization path as a model space, we propose a method to resolve the model uncertainty issues arising in model averaging from solution path point selection. We show that this method is computationally and empirically effective for regression and classification in high-dimensional data sets. We apply our technique in simulations, as well as to some applications that arise in genomics.

This article describes two R packages for probabilistic weather forecasting, ensem-bleBMA, which offers ensemble postprocessing via Bayesian model averaging (BMA), and Prob-ForecastGOP, which implements the geostatistical output perturbation (GOP) method.BMA forecasting models use mixture distributions, in which each component corresponds to an ensemble member, and the form of the component distribution depends on the weather parameter (temperature, quantitative precipitation or wind speed).The model parameters are estimated from training data.The GOP technique uses geostatistical methods to produce probabilistic forecasts of entire weather fields for temperature or pressure, based on a single numerical forecast on a spatial grid.Both packages include functions for evaluating predictive performance, in addition to model fitting and forecasting.

Bayesian model averaging (BMA) is a statistical postprocessing technique that generates calibrated and sharp predictive probability density functions (PDFs) from forecast ensembles. It represents the predictive PDF as a weighted average of PDFs centered on the bias-corrected ensemble members, where the weights reflect the relative skill of the individual members over a training period. This work adapts the BMA approach to situations that arise frequently in practice; namely, when one or more of the member forecasts are exchangeable, and when there are missing ensemble members. Exchangeable members differ in random perturbations only, such as the members of bred ensembles, singular vector ensembles, or ensemble Kalman filter systems. Accounting for exchangeability simplifies the BMA approach, in that the BMA weights and the parameters of the component PDFs can be assumed to be equal within each exchangeable group. With these adaptations, BMA can be applied to postprocess multimodel ensembles of any composition. In experiments with surface temperature and quantitative precipitation forecasts from the University of Washington mesoscale ensemble and ensemble Kalman filter systems over the Pacific Northwest, the proposed extensions yield good results. The BMA method is robust to exchangeability assumptions, and the BMA postprocessed combined ensemble shows better verification results than any of the individual, raw, or BMA postprocessed ensemble systems. These results suggest that statistically postprocessed multimodel ensembles can outperform individual ensemble systems, even in cases in which one of the constituent systems is superior to the others.

Least angle regression and LASSO (ℓ 1 ‐penalized regression) offer a number of advantages in variable selection applications over procedures such as stepwise or ridge regression, including prediction accuracy, stability, and interpretability. We discuss formulations of these algorithms that extend to datasets in which the number of observations could be so large that it would not be possible to access the matrix of predictors as a unit in computations. Our methods require a single pass through the data for orthogonal transformation, effectively reducing the dimension of the computations required to obtain the regression coefficients and residual sum of squares to the number of predictors, rather than the number of observations. Copyright © 2009 Wiley Periodicals, Inc. Statistical Analysis and Data Mining 1: 000‐000, 2009

This paper describes the University of Washington Probability Forecast (PROBCAST), a Web-based portal to probabilistic weather predictions over the Pacific Northwest. PROBCAST products are derived from the output of a mesoscale ensemble system run at the University of Washington, with the fields being postprocessed using Bayesian model averaging to produce sharp and reliable probabilistic predictions of temperature and precipitation. Based on research by University of Washington psychologists and human-interface specialists, a Web site has been constructed that allows for access to key elements of the probabilistic information produced by the system. The design approach of the PROBCAST system is explained in this paper as well as some of the challenges for future development. PROBCAST is intended to be a prototype for the kind of probabilistic forecast interface that could be used throughout the nation.

Least Angle Regression is a promising technique for variable selection applications, offering a nice alternative to stepwise regression. It provides an explanation for the similar behavior of LASSO (L1-penalized regression) and forward stagewise regression, and provides a fast implementation of both. The idea has caught on rapidly, and sparked a great deal of research interest. In this paper, we give an overview of Least Angle Regression and the current state of related research. AMS 2000 subject classifications: Primary 62J07; secondary 69J99.

Least Angle Regression is a promising technique for variable selection applications, offering a nice alternative to stepwise regression. It provides an explanation for the similar behavior of LASSO (l(1)-penalized regression) and forward stagewise regression, and provides a fast implementation of both. The idea has caught on rapidly, and sparked a great deal of research interest. In this paper, we give an overview of Least Angle Regression and the current state of related research.

ensembleBMA is a contributed R package for probabilistic forecasting using ensemble post- processing via Bayesian Model Averaging. It provides functions for modeling and forecast- ing with data that may include missing ensemble member forecasts. The modeling can also account for exchangeable ensemble members. The modeling functions estimate model pa- rameters from training data via the EM algorithm for normal mixture models (appropriate for temperature or pressure), mixtures of gamma distributions (appropriate for maximum wind speed), and mixtures of gamma distributions with a point mass at 0 (appropriate for quantitative precipitation). Also included are functions for forecasting from these models, as well as functions for verification to assess forecasting performance.

Due to recent advances in methods and software for model-based clustering, and to the interpretability of the results, clustering procedures based on probability models are increasingly preferred over heuristic methods. The clustering process estimates a model for the data that allows for overlapping clusters, producing a probabilistic clustering that quantifies the uncertainty of observations belonging to components of the mixture. The resulting clustering model can also be used for some other important problems in multivariate analysis, including density estimation and discriminant analysis. Examples of the use of model-based clustering and classification techniques in chemometric studies include multivariate image analysis, magnetic resonance imaging, microarray image segmentation, statistical process control, and food authenticity. We review model-based clustering and related methods for density estimation and discriminant analysis, and show how the R package mclust can be applied in each instance.

ensembleBMA is a contributed R package for probabilistic forecasting using ensemble postprocessing via Bayesian Model Averaging. It provides functions for modeling and forecasting with data that may include missing ensemble member forecasts. The modeling can also account for exchangeable ensemble members. The modeling functions estimate model parameters from training data via the EM algorithm for normal mixture models (appropriate for temperature or pressure), mixtures of gamma distributions (appropriate for maximum wind speed), and mixtures of gamma distributions with a point mass at 0 (appropriate for quantitative precipitation). Also included are functions for forecasting from these models, as well as functions for verication to assess forecasting performance.