Search

The climate change projections of the Intergovernmental Panel on Climate Change are based on scenarios for future emissions, but these are not statistically-based and do not have a full probabilistic interpretation. Raftery et al. (Nat Clim Change 7:637–641, 2017) and Liu and Raftery (Commun Earth Environ 2:1–10, 2021) developed probabilistic forecasts for global average temperature change to 2100, but these do not give forecasts for specific parts of the globe. Here we develop a method for probabilistic long-term spatial forecasts of local average annual temperature change, combining the probabilistic global method with a pattern scaling approach. This yields a probability distribution for temperature in any year and any part of the globe in the future. Out-of-sample predictive validation experiments show the method to be well calibrated. Consistent with previous studies, we find that for long-term temperature changes, high latitudes warm more than low latitudes, continents more than oceans, and the Northern Hemisphere more than the Southern Hemisphere, except for the North Atlantic. There is a 5% chance that the temperature change for the Arctic would reach 16 ∘ C. With probability 95%, the temperature of North Africa, West Asia and most of Europe will increase by at least 2 ∘ C. We find that natural variability is a large part of the uncertainty in early years, but this declines so that by 2100 most of the overall uncertainty comes from model uncertainty and uncertainty about future emissions. [ABSTRACT FROM AUTHOR]

We propose a method for forecasting global human migration flows. A Bayesian hierarchical model is used to make probabilistic projections of the 39,800 bilateral migration flows among the 200 most populous countries. We generate out-of-sample forecasts for all bilateral flows for the 2015 to 2020 period, using models fitted to bilateral migration flows for five 5-y periods from 1990 to 1995 through 2010 to 2015. We find that the model produces well-calibrated out-of-sample forecasts of bilateral flows, as well as total country-level inflows, outflows, and net flows. The mean absolute error decreased by 61% using our method, compared to a leading model of international migration. Out-of-sample analysis indicated that simple methods for forecasting migration flows offered accurate projections of bilateral migration flows in the near term. Our method matched or improved on the out-of-sample performance using these simple deterministic alternatives, while also accurately assessing uncertainty. We integrate the migration flow forecasting model into a fully probabilistic population projection model to generate bilateral migration flow forecasts by age and sex for all flows from 2020 to 2025 through 2040 to 2045. [ABSTRACT FROM AUTHOR]

Probability models are used for many statistical tasks, notably parameter estimation, interval estimation, inference about model parameters, point prediction, and interval prediction. Thus, choosing a statistical model and accounting for uncertainty about this choice are important parts of the scientific process. Here we focus on one such choice, that of variables to include in a linear regression model. Many methods have been proposed, including Bayesian and penalized likelihood methods, and it is unclear which one to use. We compared 21 of the most popular methods by carrying out an extensive set of simulation studies based closely on real datasets that span a range of situations encountered in practical data analysis. Three adaptive Bayesian model averaging (BMA) methods performed best across all statistical tasks. These used adaptive versions of Zellner's g-prior for the parameters, where the prior variance parameter g is a function of sample size or is estimated fromthe data. We found that forBMAmethods implemented with Markov chain Monte Carlo, 10,000 iterations were enough. Computationally, we found two of the three best methods (BMA with g = n and empirical Bayes-local) to be competitive with the least absolute shrinkage and selection operator (LASSO), which is often preferred as a variable selection technique because of its computational efficiency. BMA performed better than Bayesian model selection (in which just one model is selected). [ABSTRACT FROM AUTHOR]

There is a growing expectation that data collected by government-funded studies should be openly available to ensure research reproducibility, which also increases concerns about data privacy. A strategy to protect individuals' identity is to release multiply imputed (MI) synthetic datasets with masked sensitivity values. However, information loss or incorrectly specified imputation models can weaken or invalidate the inferences obtained from the MI-datasets. We propose a new masking framework with a data-augmentation (DA) component and a tuning mechanism that balances protecting identity disclosure against preserving data utility. Applying it to a restricted-use Canadian Scleroderma Research Group (CSRG) dataset, we found that this DA-MI strategy achieved a 0% identity disclosure risk and preserved all inferential conclusions. It yielded 95% confidence intervals (CIs) that had overlaps of 98.5% (95.5%) on average with the CIs constructed using the full, unmasked CSRG dataset in a work-disability (interstitial lung disease) study. The CI-overlaps were lower for several other methods considered, ranging from 73.9% to 91.9% on average with the lowest value being 28.1%; such low CI-overlaps further led to some incorrect inferential conclusions. These findings indicate that the DA-MI masking framework facilitates sharing of useful research data while protecting participants' identities. for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement. [ABSTRACT FROM AUTHOR]

We describe the vote package in R, which implements the plurality (or first-past-the-post), two-round runoff, score, approval, and Single Transferable Vote (STV) electoral systems, as well as methods for selecting the Condorcet winner and loser. We emphasize the STV system, which we have found to work well in practice for multi-winner elections with small electorates, such as committee and council elections, and the selection of multiple job candidates. For single-winner elections, STV is also called Instant Runoff Voting (IRV), Ranked Choice Voting (RCV), or the alternative vote (AV) system. The package also implements the STV system with equal preferences, for the first time in a software package, to our knowledge. It also implements a new variant of STV, in which a minimum number of candidates from a specified group are required to be elected. We illustrate the package with several real examples. [ABSTRACT FROM AUTHOR]

Projecting mortality for subnational units, or regions, is of great interest to practicing demographers. We seek a probabilistic method for projecting subnational life expectancy that is based on the national Bayesian hierarchical model used by the United Nations, and at the same time is easy to use. We propose three methods of this kind. Two of them are variants of simple scaling methods. The third method models life expectancy for a region as equal to national life expectancy plus a region-specific stochastic process which is a heteroskedastic first-order autoregressive process (AR(1)), with a variance that declines to a constant as life expectancy increases. We apply our models to data from 29 countries. In an out-of-sample comparison, the proposed methods outperformed other comparative methods and were well calibrated for individual regions. The AR (1) method performed best in terms of crossover patterns between regions. Although the methods work well for individual regions, there are some limitations when evaluating within-country variation. We identified four countries for which the AR(1) method either underestimated or overestimated the predictive between-region within-country standard deviation. However, none of the competing methods work better in this regard than the AR(1) method. In addition to providing the full distribution of subnational life expectancy, the methods can be used to obtain probabilistic forecasts of age-specific mortality rates. [ABSTRACT FROM AUTHOR]

There are multiple sources of data giving information about the number of SARS-CoV-2 infections in the population, but all have major drawbacks, including biases and delayed reporting. For example, the number of confirmed cases largely underestimates the number of infections, and deaths lag infections substantially, while test positivity rates tend to greatly overestimate prevalence. Representative random prevalence surveys, the only putatively unbiased source, are sparse in time and space, and the results can come with big delays. Reliable estimates of population prevalence are necessary for understanding the spread of the virus and the effectiveness of mitigation strategies. We develop a simple Bayesian framework to estimate viral prevalence by combining several of the main available data sources. It is based on a discrete-time Susceptible-Infected-Removed (SIR) model with time-varying reproductive parameter. Our model includes likelihood components that incorporate data on deaths due to the virus, confirmed cases, and the number of tests administered on each day. We anchor our inference with data from randomsample testing surveys in Indiana and Ohio. We use the results from these two states to calibrate the model on positive test counts and proceed to estimate the infection fatality rate and the number of new infections on each day in each state in the United States. We estimate the extent to which reported COVID cases have underestimated true infection counts, which was large, especially in the first months of the pandemic. We explore the implications of our results for progress toward herd immunity. [ABSTRACT FROM AUTHOR]

Education and family planning can both be influenced by policy and are thought to accelerate fertility decline. However, questions remain about the nature of these effects. Does the effect of education operate through increasing educational attainment of women or educational enrollment of children? At which educational level is the effect strongest? Does the effect of family planning operate through increasing contraceptive prevalence or reducing unmet need? Is education or family planning more important? We assessed the quantitative impact of education and family planning in high‐fertility settings using a regression framework inspired by Granger causality. We found that women's attainment of lower secondary education is key to accelerating fertility decline and found an accelerating effect of contraceptive prevalence for modern methods. We found the impact of contraceptive prevalence to be substantially larger than that of education. These accelerating effects hold in sub‐Saharan Africa, but with smaller effect sizes there than elsewhere. [ABSTRACT FROM AUTHOR]

We propose a method for estimating migration flows between all pairs of countries that allows for decomposition of migration into emigration, return, and transit components. Current state-of-theart estimates of bilateral migration flows rely on the assumption that the number of global migrants is as small as possible. We relax this assumption, producing complete estimates of all betweencountry migration flows with genuine estimates of total global migration. We find that the total number of individuals migrating internationally has oscillated between 1.13 and 1.29% of the global population per 5-year period since 1990. Return migration and transit migration are big parts of total migration; roughly one of four migration events is a return to an individual's country of birth. In the most recent time period, we estimate particularly large return migration flows fromthe United States to Central and South America and from the Persian Gulf to south Asia. [ABSTRACT FROM AUTHOR]

Summary: Professor Adrian E. Raftery is the Boeing International Professor of Statistics and Sociology and an adjunct professor of Atmospheric Sciences at the University of Washington in Seattle. He was born in Dublin, Ireland, and obtained a BA in Mathematics (1976) and an MSc in Statistics and Operations Research (1977) at Trinity College Dublin. He obtained a doctorate in mathematical statistics in 1980 from the Université Pierre et Marie Curie in Paris, France, under the supervision of Paul Deheuvels. He was a lecturer in statistics at Trinity College Dublin from 1980 to 1986, and then an associate (1986–1990) and full (1990‐present) professor of statistics and sociology at the University of Washington. He was the founding Director of the Center for Statistics and Social Sciences (1999–2009). Professor Raftery has published over 200 articles in peer‐reviewed statistical, sociological and other journals. His research focuses on Bayesian model selection and Bayesian model averaging, model‐based clustering, inference for deterministic simulation models, and the development of new statistical methods for demography, sociology, and the environmental and health sciences. He is a member of the United States National Academy of Sciences, a Fellow of the American Academy of Arts and Sciences, an Honorary Member of the Royal Irish Academy, a member of the Washington State Academy of Sciences, a Fellow of the American Statistical Association, a Fellow of the Institute of Mathematical Statistics, and an elected Member of the Sociological Research Association. He has won the Population Association of America's Clifford C. Clogg Award, the American Sociological Association's Paul F. Lazarsfeld Award for Distinguished Contribution to Knowledge, the Jerome Sacks Award for Outstanding Cross‐Disciplinary Research from the National Institute of Statistical Sciences, the Parzen Prize for Statistical Innovation, and the Science Foundation Ireland St. Patrick's Day Medal. He is also a former Coordinating and Applications Editor of the Journal of the American Statistical Association and a former Editor of Sociological Methodology. He was identified as the world's most cited researcher in mathematics for the decade 1995–2005 by Thomson‐ISI. Thirty‐three students have obtained PhD's working under Raftery's supervision, of whom 21 hold or have held tenure‐track university faculty positions. He has over 150 academic descendants. This interview took place over two sessions in March 2023. [ABSTRACT FROM AUTHOR]

A new method, called contour shifting, is proposed for correcting the bias in forecasts of contours such as sea ice concentration above certain thresholds. Retrospective comparisons of observations and dynamical model forecasts are used to build a statistical spatiotemporal model of how predicted contours typically differ from observed contours. Forecasted contours from a dynamical model are then adjusted to correct for expected errors in their location. The statistical model changes over time to reflect the changing error patterns that result from reducing sea ice cover in the satellite era in both models and observations. For an evaluation period from 2001 to 2013, these bias-corrected forecasts are on average more accurate than the unadjusted dynamical model forecasts for all forecast months in the year at four different lead times. The total area, which is incorrectly categorized as containing sea ice or not, is reduced by 3.3 × 105 km2 (or 21.3%) on average. The root-mean-square error of forecasts of total sea ice area is also reduced for all lead times. [ABSTRACT FROM AUTHOR]

The article offers the observation of the author on the study carried out by researches on the topic of latent position for networks. It mentions the use of Bayesian formula and stochastic block model. The article discusses topics including social networks, computation of simulations and replicate networks.

Probabilistic forecasts are becoming more and more available. How should they be used and communicated? What are the obstacles to their use in practice? We review experience with five problems where probabilistic forecasting played an important role. This leads us to identify five types of potential users: low stakes users, who do not need probabilistic forecasts; general assessors, who need an overall idea of the uncertainty in the forecast; change assessors, who need to know if a change is out of line with expectations; risk avoiders, who wish to limit the risk of an adverse outcome; and decision theorists, who quantify their loss function and perform the decision-theoretic calculations. This suggests that it is important to interact with users and consider their goals. Cognitive research tells us that calibration is important for trust in probability forecasts and that it is important to match the verbal expression with the task. The cognitive load should be minimized, reducing the probabilistic forecast to a single percentile if appropriate. Probabilities of adverse events and percentiles of the predictive distribution of quantities of interest often seem to be the best way to summarize probabilistic forecasts. Formal decision theory has an important role but in a limited range of applications. © 2016 Wiley Periodicals, Inc. Statistical Analysis and Data Mining: The ASA Data Science Journal, 2016 [ABSTRACT FROM AUTHOR]

We show that Bayesian population reconstruction, a recent method for estimating past populations by age, works for data of widely varying quality. Bayesian reconstruction simultaneously estimates age-specific population counts, fertility rates, mortality rates, and net international migration flows from fragmentary data, while formally accounting for measurement error. As inputs, Bayesian reconstruction uses initial bias-reduced estimates of standard demographic variables. We reconstruct the female populations of three countries: Laos, a country with little vital registration data where population estimation depends largely on surveys; Sri Lanka, a country with some vital registration data; and New Zealand, a country with a highly developed statistical system and good quality vital registration data. In addition, we extend the method to countries without censuses at regular intervals. We also use it to assess the consistency of results between model life tables and available census data, and hence to compare different model life table systems. [ABSTRACT FROM PUBLISHER]

Background: Inference of gene networks from expression data is an important problem in computational biology. Many algorithms have been proposed for solving the problem efficiently. However, many of the available implementations are programming libraries that require users to write code, which limits their accessibility. Results: We have developed a tool called CyNetworkBMA for inferring gene networks from expression data that integrates with Cytoscape. Our application offers a graphical user interface for networkBMA, an efficient implementation of Bayesian Model Averaging methods for network construction. The client-server architecture of CyNetworkBMA makes it possible to distribute or centralize computation depending on user needs. Conclusions: CyNetworkBMA is an easy-to-use tool that makes network inference accessible to non-programmers through seamless integration with Cytoscape. CyNetworkBMA is available on the Cytoscape App Store at http://apps. cytoscape.org/apps/cynetworkbma. [ABSTRACT FROM AUTHOR]

The United Nations (UN) recently released population projections based on data until 2012 and a Bayesian probabilistic methodology. Analysis of these data reveals that, contrary to previous literature, the world population is unlikely to stop growing this century. There is an 80% probability that world population, now 7.2 billion people, will increase to between 9.6 billion and 12.3 billion in 2100. This uncertainty is much smaller than the range from the traditional UN high and low variants. Much of the increase is expected to happen in Africa, in part due to higher fertility rates and a recent slowdown in the pace of fertility decline. Also, the ratio of working-age people to older people is likely to decline substantially in all countries, even those that currently have young populations. [ABSTRACT FROM AUTHOR]

Background Genome-wide time-series data provide a rich set of information for discovering gene regulatory relationships. As genome-wide data for mammalian systems are being generated, it is critical to develop network inference methods that can handle tens of thousands of genes efficiently, provide a systematic framework for the integration of multiple data sources, yield robust, accurate and compact gene-togene relationships. Results We developed and applied ScanBMA, a Bayesian inference method that incorporates external information to improve the accuracy of the inferred network. In particular, we developed a new strategy to efficiently search the model space, applied data transformations to reduce the effect of spurious relationships, and adopted the g-prior to guide the search for candidate regulators. Our method is highly computationally efficient, thus addressing the scalability issue with network inference. The method is implemented as the ScanBMA function in the networkBMA Bioconductor software package. Conclusions We compared ScanBMA to other popular methods using time series yeast data as well as time-series simulated data from the DREAM competition. We found that ScanBMA produced more compact networks with a greater proportion of true positives than the competing methods. Specifically, ScanBMA generally produced more favorable areas under the Receiver-Operating Characteristic and Precision- Recall curves than other regression-based methods and mutual-information based methods. In addition, ScanBMA is competitive with other network inference methods in terms of running time. [ABSTRACT FROM AUTHOR]

Projections of countries' future populations, broken down by age and sex, are widely used for planning and research. They are mostly done deterministically, but there is a widespread need for probabilistic projections. We propose a Bayesian method for probabilistic population projections for all countries. The total fertility rate and female and male life expectancies at birth are projected probabilistically using Bayesian hierarchical models estimated via Markov chain Monte Carlo using United Nations population data for all countries. These are then converted to age-specific rates and combined with a cohort component projection model. This yields probabilistic projections of any population quantity of interest. The method is illustrated for five countries of different demographic stages, continents and sizes. The method is validated by an out of sample experiment in which data from 1950-1990 are used for estimation, and applied to predict 1990-2010. The method appears reasonably accurate and well calibrated for this period. The results suggest that the current United Nations high and low variants greatly underestimate uncertainty about the number of oldest old from about 2050 and that they underestimate uncertainty for high fertility countries and overstate uncertainty for countries that have completed the demographic transition and whose fertility has started to recover towards replacement level, mostly in Europe. The results also indicate that the potential support ratio (persons aged 20-64 per person aged 65+) will almost certainly decline dramatically in most countries over the coming decades. [ABSTRACT FROM AUTHOR]

Summary We propose an online binary classification procedure for cases when there is uncertainty about the model to use and parameters within a model change over time. We account for model uncertainty through dynamic model averaging, a dynamic extension of Bayesian model averaging in which posterior model probabilities may also change with time. We apply a state-space model to the parameters of each model and we allow the data-generating model to change over time according to a Markov chain. Calibrating a 'forgetting' factor accommodates different levels of change in the data-generating mechanism. We propose an algorithm that adjusts the level of forgetting in an online fashion using the posterior predictive distribution, and so accommodates various levels of change at different times. We apply our method to data from children with appendicitis who receive either a traditional (open) appendectomy or a laparoscopic procedure. Factors associated with which children receive a particular type of procedure changed substantially over the 7 years of data collection, a feature that is not captured using standard regression modeling. Because our procedure can be implemented completely online, future data collection for similar studies would require storing sensitive patient information only temporarily, reducing the risk of a breach of confidentiality. [ABSTRACT FROM AUTHOR]

Background: Inference about regulatory networks from high-throughput genomics data is of great interest in systems biology. We present a Bayesian approach to infer gene regulatory networks from time series expression data by integrating various types of biological knowledge. Results: We formulate network construction as a series of variable selection problems and use linear regression to model the data. Our method summarizes additional data sources with an informative prior probability distribution over candidate regression models. We extend the Bayesian model averaging (BMA) variable selection method to select regulators in the regression framework. We summarize the external biological knowledge by an informative prior probability distribution over the candidate regression models. Conclusions: We demonstrate our method on simulated data and a set of time-series microarray experiments measuring the effect of a drug perturbation on gene expression levels, and show that it outperforms leading regression-based methods in the literature. [ABSTRACT FROM AUTHOR]

The authors introduce two ways to produce locally calibrated grid-based probabilistic forecasts of temperature. Both start from the Global Bayesian model averaging (Global BMA) statistical postprocessing method, which has constant predictive bias and variance across the domain, and modify it to make it local. The first local method, geostatistical model averaging (GMA), computes the predictive bias and variance at observation stations and interpolates them using a geostatistical model. The second approach, Local BMA, estimates the parameters of BMA at a grid point from stations that are close to the grid point and similar to it in elevation and land use. The results of these two methods applied to the eight-member University of Washington Mesoscale Ensemble (UWME) are given for the 2006 calendar year. GMA was calibrated and sharper than Global BMA, with prediction intervals that were 8%% narrower than Global BMA on average. Examples using sparse and dense training networks of stations are shown. The sparse network experiment illustrates the ability of GMA to draw information from the entire training network. The performance of Local BMA was not statistically different from Global BMA in the dense network experiment, and was superior to both GMA and Global BMA in areas with sufficient nearby training data. [ABSTRACT FROM AUTHOR]

Abstract: Uncertainty is inherent in major infrastructure projects, but public decision-making for such projects ignores it. We investigate the uncertainty about the future effects of tearing down the Alaskan Way Viaduct in downtown Seattle, using an integrated model of housing, jobs, land use and transportation, on outcomes including average commute times. Our methodology combines the urban simulation model UrbanSim with the regional transportation model. We assess uncertainty using Bayesian melding, yielding a full predictive distribution of average commute times on 22 different routes in 2020. Of these routes, 14 do not include the viaduct and eight do. For the 14 base routes that do not include the viaduct, the predictive distributions overlap substantially, and so there is no indication that removing the viaduct would increase commute times for these routes. For each of the eight routes that do include the viaduct, the 95% predictive interval for the difference in average travel times between the two scenarios includes zero, so there is not strong statistical support for the conclusion that removing the viaduct would lead to any increase in travel times. However, the median predicted increase is positive for each of these routes, with an average of 6min, suggesting that there may be some measurable increase in travel time for drivers that use the viaduct as a core component of their commute. [Copyright &y& Elsevier]

Bayesian model averaging (BMA) is a statistical postprocessing technique that has been used in probabilistic weather forecasting to calibrate forecast ensembles and generate predictive probability density functions (PDFs) for weather quantities. The authors apply BMA to probabilistic visibility forecasting using a predictive PDF that is a mixture of discrete point mass and beta distribution components. Three approaches to developing predictive PDFs for visibility are developed, each using BMA to postprocess an ensemble of visibility forecasts. In the first approach, the ensemble is generated by a translation algorithm that converts predicted concentrations of hydrometeorological variables into visibility. The second approach augments the raw ensemble visibility forecasts with model forecasts of relative humidity and quantitative precipitation. In the third approach, the ensemble members are generated from relative humidity and precipitation alone. These methods are applied to 12-h ensemble forecasts from 2007 to 2008 and are tested against verifying observations recorded at Automated Surface Observing Stations in the Pacific Northwest. Each of the three methods produces predictive PDFs that are calibrated and sharp with respect to both climatology and the raw ensemble. [ABSTRACT FROM AUTHOR]

The Joint United Nations Programme on HIV/AIDS (UNAIDS) has decided to use Bayesian melding as the basis for its probabilistic projections of HIV prevalence in countries with generalized epidemics. This combines a mechanistic epidemiological model, prevalence data, and expert opinion. Initially, the posterior distribution was approximated by sampling-importance-resampling, which is simple to implement, easy to interpret, transparent to users, and gave acceptable results for most countries. For some countries, however, this is not computationally efficient because the posterior distribution tends to be concentrated around nonlinear ridges and can also be multimodal. We propose instead incremental mixture importance sampling (IMIS), which iteratively builds up a better importance sampling function. This retains the simplicity and transparency of sampling importance resampling, but is much more efficient computationally. It also leads to a simple estimator of the integrated likelihood that is the basis for Bayesian model comparison and model averaging. In simulation experiments and on real data, it outperformed both sampling importance resampling and three publicly available generic Markov chain Monte Carlo algorithms for this kind of problem. [ABSTRACT FROM AUTHOR]

Background Every 2 years, the Joint United Nations Programme on HIV/AIDS (UNAIDS) produces probabilistic estimates and projections of HIV prevalence rates for countries with generalised HIV/AIDS epidemics. To do this they use a simple epidemiological model and data from antenatal clinics and household surveys. The estimates are made using the Bayesian melding method, implemented by the incremental mixture importance sampling technique. This methodology is referred to as the ‘estimation and projection package (EPP) model’. This has worked well for estimating and projecting prevalence in most countries. However, there has recently been an ‘uptick’ in prevalence in Uganda after a long sustained decline, which the EPP model does not predict. Methods To address this problem, a modification of the EPP model, called the ‘r stochastic model’ is proposed, in which the infection rate is allowed to vary randomly in time and is applied to the entire non-infected population. Results The resulting method yielded similar estimates of past prevalence to the EPP model for four countries and also similar median (‘best’) projections, but produced prediction intervals whose widths increased over time and that allowed for the possibility of an uptick after a decline. This seems more realistic given the recent Ugandan experience. [ABSTRACT FROM PUBLISHER]

Winter road maintenance is one of the main tasks for the Washington State Department of Transportation. Anti-icing, that is, the preemptive application of chemicals, is often used to keep the roadways free of ice. Given the preventive nature of anti-icing, accurate predictions of road ice are needed. Currently, anti-icing decisions are usually based on deterministic weather forecasts. However, the costs of the two kinds of errors are highly asymmetric because the cost of a road closure due to ice is much greater than that of taking anti-icing measures. As a result, probabilistic forecasts are needed to optimize decision making. We propose two methods for forecasting the probability of ice formation. Starting with deterministic numerical weather predictions, we model temperature and precipitation using distributions centered around the bias-corrected forecasts. This produces a joint predictive probability distribution of temperature and precipitation, which then yields the probability of ice formation, defined here as the occurrence of precipitation when the temperature is below freezing. The first method assumes that temperatures, as well as precipitation, at different spatial locations are conditionally independent given the numerical weather predictions. The second method models the spatial dependence between forecast errors at different locations. The model parameters are estimated using a Bayesian approach via Markov chain Monte Carlo. We evaluate both methods by comparing their probabilistic forecasts with observations of ice formation for Interstate Highway 90 in Washington State for the 2003–2004 and 2004–2005 winter seasons. The use of the probabilistic forecasts reduces costs by about 50% when compared to deterministic forecasts. The spatial method improves the reliability of the forecasts, but does not result in further cost reduction when compared to the first method. [ABSTRACT FROM AUTHOR]

We propose a method for selecting variables in latent class analysis, which is the most common model-based clustering method for discrete data. The method assesses a variable’s usefulness for clustering by comparing two models, given the clustering variables already selected. In one model the variable contributes information about cluster allocation beyond that contained in the already selected variables, and in the other model it does not. A headlong search algorithm is used to explore the model space and select clustering variables. In simulated datasets we found that the method selected the correct clustering variables, and also led to improvements in classification performance and in accuracy of the choice of the number of classes. In two real datasets, our method discovered the same group structure with fewer variables. In a dataset from the International HapMap Project consisting of 639 single nucleotide polymorphisms (SNPs) from 210 members of different groups, our method discovered the same group structure with a much smaller number of SNPs. [ABSTRACT FROM AUTHOR]

We consider the problem of online prediction when it is uncertain what the best prediction model to use is. We develop a method called Dynamic Model Averaging (DMA) in which a state space model for the parameters of each model is combined with a Markov chain model for the correct model. This allows the "correct" model to vary over time. The state space and Markov chain models are both specified in terms of forgetting, leading to a highly parsimonious representation. As a special case, when the model and parameters do not change, DMA is a recursive implementation of standard Bayesian model averaging, which we call recursive model averaging (RMA). The method is applied to the problem of predicting the output strip thickness for a cold rolling mill, where the output is measured with a time delay. We found that when only a small number of physically motivated models were considered and one was clearly best, the method quickly converged to the best model, and the cost of model uncertainty was small; indeed DMA performed slightly better than the best physical model. When model uncertainty and the number of models considered were large, our method ensured that the penalty for model uncertainty was small. At the beginning of the process, when control is most difficult, we found that DMA over a large model space led to better predictions than the single best performing physically motivated model. We also applied the method to several simulated examples, and found that it recovered both constant and time-varying regression parameters and model specifications quite well. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Markov chain Monte Carlo (MCMC) methods for Bayesian computation are mostly used when the dominating measure is the Lebesgue measure, the counting measure, or a product of these. Many Bayesian problems give rise to distributions that are not dominated by the Lebesgue measure or the counting measure alone. In this article we introduce a simple framework for using MCMC algorithms in Bayesian computation with mixtures of mutually singular distributions. The idea is to find a common dominating measure that allows the use of traditional Metropolis--Hastings algorithms. In particular, using our formulation, the Gibbs sampler can be used whenever the full conditionals are available. We compare our formulation with the reversible jump approach and show that the two are closely related. We give results for three examples, involving testing a normal mean, variable selection in regression, and hypothesis testing for differential gene expression under multiple conditions. This allows us to compare the three methods considered: Metropolis--Hastings with mutually singular distributions, Gibbs sampler with mutually singular distributions, and reversible jump. In our examples, we found the Gibbs sampler to be more precise and to need considerably less computer time than the other methods. In addition, the full conditionals used in the Gibbs sampler can be used to further improve the estimates of the model posterior probabilities via Rao--Blackwellization, at no extra cost. [ABSTRACT FROM AUTHOR]

A Bayesian model-based clustering method is proposed for clustering objects on the basis of dissimilarites. This combines two basic ideas. The first is that the objects have latent positions in a Euclidean space, and that the observed dissimilarities are measurements of the Euclidean distances with error. The second idea is that the latent positions are generated from a mixture of multivariate normal distributions, each one corresponding to a cluster. We estimate the resulting model in a Bayesian way using Markov chain Monte Carlo. The method carries out multidimensional scaling and model-based clustering simultaneously, and yields good object configurations and good clustering results with reasonable measures of clustering uncertainties. In the examples we study, the clustering results based on low-dimensional configurations were almost as good as those based on high-dimensional ones. Thus, the method can be used as a tool for dimension reduction when clustering high-dimensional objects, which may be useful especially for visual inspection of clusters. We also propose a Bayesian criterion for choosing the dimension of the object configuration and the number of clusters simultaneously. This is easy to compute and works reasonably well in simulations and real examples. [ABSTRACT FROM AUTHOR]

Bayesian model averaging (BMA) is a statistical way of postprocessing forecast ensembles to create predictive probability density functions (PDFs) for weather quantities. It represents the predictive PDF as a weighted average of PDFs centered on the individual bias-corrected forecasts, where the weights are posterior probabilities of the models generating the forecasts and reflect the forecasts’ relative contributions to predictive skill over a training period. It was developed initially for quantities whose PDFs can be approximated by normal distributions, such as temperature and sea level pressure. BMA does not apply in its original form to precipitation, because the predictive PDF of precipitation is nonnormal in two major ways: it has a positive probability of being equal to zero, and it is skewed. In this study BMA is extended to probabilistic quantitative precipitation forecasting. The predictive PDF corresponding to one ensemble member is a mixture of a discrete component at zero and a gamma distribution. Unlike methods that predict the probability of exceeding a threshold, BMA gives a full probability distribution for future precipitation. The method was applied to daily 48-h forecasts of 24-h accumulated precipitation in the North American Pacific Northwest in 2003–04 using the University of Washington mesoscale ensemble. It yielded predictive distributions that were calibrated and sharp. It also gave probability of precipitation forecasts that were much better calibrated than those based on consensus voting of the ensemble members. It gave better estimates of the probability of high-precipitation events than logistic regression on the cube root of the ensemble mean. [ABSTRACT FROM AUTHOR]

Normal mixture models are widely used for statistical modeling of data, including cluster analysis. However maximum likelihood estimation (MLE) for normal mixtures using the EM algorithm may fail as the result of singularities or degeneracies. To avoid this, we propose replacing the MLE by a maximum a posteriori (MAP) estimator, also found by the EM algorithm. For choosing the number of components and the model parameterization, we propose a modified version of BIC, where the likelihood is evaluated at the MAP instead of the MLE. We use a highly dispersed proper conjugate prior, containing a small fraction of one observation's worth of information. The resulting method avoids degeneracies and singularities, but when these are not present it gives similar results to the standard method using MLE, EM and BIC. [ABSTRACT FROM AUTHOR]

Abstract: We develop a method for assessing uncertainty about quantities of interest using urban simulation models. The method is called Bayesian melding, and extends a previous method developed for macrolevel deterministic simulation models to agent-based stochastic models. It encodes all the available information about model inputs and outputs in terms of prior probability distributions and likelihoods, and uses Bayes’s theorem to obtain the resulting posterior distribution of any quantity of interest that is a function of model inputs and/or outputs. It is Monte Carlo based, and quite easy to implement. We applied it to the projection of future household numbers by traffic activity zone in Eugene-Springfield, Oregon, using the UrbanSim model developed at the University of Washington. We compared it with a simpler method that uses repeated runs of the model with fixed estimated inputs. We found that the simple repeated runs method gave distributions of quantities of interest that were too narrow, while Bayesian melding gave well calibrated uncertainty statements. [Copyright &y& Elsevier]

Forecast ensembles typically show a spread–skill relationship, but they are also often underdispersive, and therefore uncalibrated. Bayesian model averaging (BMA) is a statistical postprocessing method for forecast ensembles that generates calibrated probabilistic forecast products for weather quantities at individual sites. This paper introduces the spatial BMA technique, which combines BMA and the geostatistical output perturbation (GOP) method, and extends BMA to generate calibrated probabilistic forecasts of whole weather fields simultaneously, rather than just weather events at individual locations. At any site individually, spatial BMA reduces to the original BMA technique. The spatial BMA method provides statistical ensembles of weather field forecasts that take the spatial structure of observed fields into account and honor the flow-dependent information contained in the dynamical ensemble. The members of the spatial BMA ensemble are obtained by dressing the weather field forecasts from the dynamical ensemble with simulated spatially correlated error fields, in proportions that correspond to the BMA weights for the member models in the dynamical ensemble. Statistical ensembles of any size can be generated at minimal computational cost. The spatial BMA technique was applied to 48-h forecasts of surface temperature over the Pacific Northwest in 2004, using the University of Washington mesoscale ensemble. The spatial BMA ensemble generally outperformed the BMA and GOP ensembles and showed much better verification results than the raw ensemble, both at individual sites, for weather field forecasts, and for forecasts of composite quantities, such as average temperature in National Weather Service forecast zones and minimum temperature along the Interstate 90 Mountains to Sound Greenway. [ABSTRACT FROM AUTHOR]

Scoring rules assess the quality of probabilistic forecasts, by assigning a numerical score based on the predictive distribution and on the event or value that materializes. A scoring rule is proper if the forecaster maximizes the expected score for an observation drawn from the distribution F if he or she issues the probabilistic forecast F, rather than G ≠ F. It is strictly proper if the maximum is unique. In prediction problems, proper scoring rules encourage the forecaster to make careful assessments and to be honest. In estimation problems, strictly proper scoring rules provide attractive loss and utility functions that can be tailored to the problem at hand. This article reviews and develops the theory of proper scoring rules on general probability spaces, and proposes and discusses examples thereof. Proper scoring rules derive from convex functions and relate to information measures, entropy functions, and Bregman divergences. In the case of categorical variables, we prove a rigorous version of the Savage representation. Examples of scoring rules for probabilistic forecasts in the form of predictive densities include the logarithmic, spherical, pseudospherical, and quadratic scores. The continuous ranked probability score applies to probabilistic forecasts that take the form of predictive cumulative distribution functions. It generalizes the absolute error and forms a special case of a new and very general type of score, the energy score. Like many other scoring rotes, the energy score admits a kernel representation in terms of negative definite functions, with links to inequalities of Hoeffding type, in both univariate and multivariate settings. Proper scoring ores for quantile and interval forecasts arc also discussed. We relate proper scoring rules to Bayes factors and to cross-validation. and propose a novel form of cross-validation known as random-fold cross-validation. A case study on probabilistic weather forecasts in the North American Pacific Northwest illustrates the importance of propriety. We note optimum score approaches to point and quantile estimation, and propose the intuitively appealing interval score as a utility function in interval estimation that addresses width as well as coverage. [ABSTRACT FROM AUTHOR]

This article proposes a method for approximating integrated likelihoods in finite mixture models. We formulate the model in terms of the unobserved group memberships, z, and make them the variables of integration. The integral is then evaluated using importance sampling over the z. We propose an adaptive importance sampling function which is itself a mixture, with two types of component distributions, one concentrated and one diffuse. The more concentrated type of component serves the usual purpose of an importance sampling function, sampling mostly group assignments of high posterior probability. The less concentrated type of component allows for the importance sampling function to explore the space in a controlled way to find other, unvisited assignments with high posterior probability. Components are added adaptively, one at a time, to cover areas of high posterior probability not well covered by the current importance sampling function. The method is called incremental mixture importance sampling (IMIS). IMIS is easy to implement and to monitor for convergence. It scales easily for higher dimensional mixture distributions when a conjugate prior is specified for the mixture parameters. The simulated values on which the estimate is based are independent, which allows for straightforward estimation of standard errors. The self-monitoring aspects of the method make it easier to adjust tuning parameters in the course of estimation than standard Markov chain Monte Carlo algorithms. With only small modifications to the code, one can use the method for a wide variety of mixture distributions of different dimensions. The method performed well in simulations and in mixture problems in astronomy and medical research. [ABSTRACT FROM AUTHOR]

We consider the problem of variable or feature selection for model-based clustering. The problem of comparing two nested subsets of variables is recast as a model comparison problem and addressed using approximate Bayes factors. A greedy search algorithm is proposed for finding a local optimum in model space. The resulting method selects variables (or features), the number of clusters, and the clustering model simultaneously. We applied the method to several simulated and real examples and found that removing irrelevant variables often improved performance. Compared with methods based on all of the variables, our variable selection method consistently yielded more accurate estimates of the number of groups and lower classification error rates, as well as more parsimonious clustering models and easier visualization of results. [ABSTRACT FROM AUTHOR]

We consider robust estimation of gene intensities from cDNA microarray data with replicates. Several statistical methods for estimating gene intensities from microarrays have been proposed, but little work has been done on robust estimation. This is particularly relevant for experiments with replicates, because even one outlying replicate can have a disastrous effect on the estimated intensity for the gene concerned. Because of the many steps involved in the experimental process from hybridization to image analysis, cDNA microarray data often contain outliers. For example, an outlying data value could occur because of scratches or dust on the surface, imperfections in the glass, or imperfections in the array production. We develop a Bayesian hierarchical model for robust estimation of cDNA microarray intensities. Outliers are modeled explicitly using a f-distribution, and our model also addresses such classical issues as design effects, normalization, transformation, and nonconstant variance. Parameter estimation is carried out using Markov chain Monte Carlo. By identifying potential outliers, the method provides automatic quality control of replicate, array, and gene measurements. The method is applied to three publicly available gene expression datasets and compared with three other methods: ANOVA-normalized log ratios, the median log ratio, and estimation after the removal of outliers based on Dixon's test. We find that the between-replicate variability of the intensity estimates is lower for our method than for any of the others. We also address the issue of whether the background should be subtracted when estimating intensities. It has been argued that this should not be done because it increases variability, whereas the arguments for doing so are that there is a physical basis for the image background, and that not doing so will bias downward the estimated log ratios of differentially expressed genes. We show that the arguments on both sides of this debate are correct for our data, but that by using our model one can have the best of both worlds: One can subtract the background without increasing variability by much. [ABSTRACT FROM AUTHOR]

We consider the problem of identifying differentially expressed genes under different conditions using gene expression microarrays. Because of the many steps involved in the experimental process, from hybridization to image analysis, cDNA microarray data often contain outliers. For example, an outlying data value could occur because of scratches or dust on the surface, imperfections in the glass, or imperfections in the array production. We develop a robust Bayesian hierarchical model for testing for differential expression. Errors are modeled explicitly using a t-distribution, which accounts for outliers. The model includes an exchangeable prior for the variances, which allows different variances for the genes but still shrinks extreme empirical variances. Our model can be used for testing for differentially expressed genes among multiple samples, and it can distinguish between the different possible patterns of differential expression when there are three or more samples. Parameter estimation is carried out using a novel version of Markov chain Monte Carlo that is appropriate when the model puts mass on subspaces of the full parameter space. The method is illustrated using two publicly available gene expression data sets. We compare our method to six other baseline and commonly used techniques, namely the t-test, the Bonferroni-adjusted t-test, significance analysis of microarrays (SAM), Efron's empirical Bayes, and EBarrays in both its lognormal–normal and gamma–gamma forms. In an experiment with HIV data, our method performed better than these alternatives, on the basis of between-replicate agreement and disagreement. [ABSTRACT FROM AUTHOR]

Abstract: We consider the problem of multiband image clustering and segmentation. We propose a new methodology for doing this, called model-based cluster trees. This is grounded in model-based clustering, which bases inference on finite mixture models estimated by maximum likelihood using the EM algorithm, and automatically chooses the number of clusters by Bayesian model selection, approximated using BIC, the Bayesian Information Criterion. For segmentation, model-based clustering is based on a Markov spatial dependence model. In the Markov model case, the Bayesian model selection criterion takes account of spatial neighborhood information, and is termed PLIC, the Pseudolikelihood Information Criterion. We build a cluster tree by first segmenting an image band, then using the second band to cluster each of the level 1 clusters, and continuing if required for further bands. The tree is pruned automatically as a part of the algorithm by using Bayesian model selection to choose the number of clusters at each stage. An efficient algorithm for implementing the methodology is proposed. An example is used to evaluate this new approach, and the advantages and disadvantages of alternative approaches to multiband segmentation and clustering are discussed. [Copyright &y& Elsevier]

Ensembles used for probabilistic weather forecasting often exhibit a spread-error correlation, but they tend to be underdispersive. This paper proposes a statistical method for postprocessing ensembles based on Bayesian model averaging (BMA), which is a standard method for combining predictive distributions from different sources. The BMA predictive probability density function (PDF) of any quantity of interest is a weighted average of PDFs centered on the individual bias-corrected forecasts, where the weights are equal to posterior probabilities of the models generating the forecasts and reflect the models' relative contributions to predictive skill over the training period. The BMA weights can be used to assess the usefulness of ensemble members, and this can be used as a basis for selecting ensemble members; this can be useful given the cost of running large ensembles. The BMA PDF can be represented as an unweighted ensemble of any desired size, by simulating from the BMA predictive distribution. The BMA predictive variance can be decomposed into two components, one corresponding to the between-forecast variability, and the second to the within-forecast variability. Predictive PDFs or intervals based solely on the ensemble spread incorporate the first component but not the second. Thus BMA provides a theoretical explanation of the tendency of ensembles to exhibit a spread-error correlation but yet be underdispersive. The method was applied to 48-h forecasts of surface temperature in the Pacific Northwest in January–June 2000 using the University of Washington fifth-generation Pennsylvania State University–NCAR Mesoscale Model (MM5) ensemble. The predictive PDFs were much better calibrated than the raw ensemble, and the BMA forecasts were sharp in that 90% BMA prediction intervals were 66% shorter on average than those produced by sample climatology. As a by-product, BMA yields a deterministic point forecast, and this had root-mean-square errors 7% lower than the best of the ensemble members and 8% lower than the ensemble mean. Similar results were obtained for forecasts of sea level pressure. Simulation experiments show that BMA performs reasonably well when the underlying ensemble is calibrated, or even overdispersed. [ABSTRACT FROM AUTHOR]

Ensemble prediction systems typically show positive spread-error correlation, but they are subject to forecast bias and dispersion errors, and are therefore uncalibrated. This work proposes the use of ensemble model output statistics (EMOS), an easy-to-implement postprocessing technique that addresses both forecast bias and underdispersion and takes into account the spread-skill relationship. The technique is based on multiple linear regression and is akin to the superensemble approach that has traditionally been used for deterministic-style forecasts. The EMOS technique yields probabilistic forecasts that take the form of Gaussian predictive probability density functions (PDFs) for continuous weather variables and can be applied to gridded model output. The EMOS predictive mean is a bias-corrected weighted average of the ensemble member forecasts, with coefficients that can be interpreted in terms of the relative contributions of the member models to the ensemble, and provides a highly competitive deterministic-style forecast. The EMOS predictive variance is a linear function of the ensemble variance. For fitting the EMOS coefficients, the method of minimum continuous ranked probability score (CRPS) estimation is introduced. This technique finds the coefficient values that optimize the CRPS for the training data. The EMOS technique was applied to 48-h forecasts of sea level pressure and surface temperature over the North American Pacific Northwest in spring 2000, using the University of Washington mesoscale ensemble. When compared to the bias-corrected ensemble, deterministic-style EMOS forecasts of sea level pressure had root-mean-square error 9% less and mean absolute error 7% less. The EMOS predictive PDFs were sharp, and much better calibrated than the raw ensemble or the bias-corrected ensemble. [ABSTRACT FROM AUTHOR]

Motivated by the problem of minefield detection, we investigate the problem of classifying mixtures of spatial point processes. In particular we are interested in testing the hypothesis that a given dataset was generated by a Poisson process versus a mixture of a Poisson process and a hard-core Strauss process. We propose testing this hypothesis by comparing the evidence for each model by using partial Bayes factors. We use the term partial Bayes factor to describe a Bayes factor, a ratio of integrated likelihoods, based on only part of the available information, namely that information contained in a small number of functionals of the data. We applied our method to both real and simulated data, and considering the difficulty of classifying these point patterns by eye, our approach overall produced good results. [ABSTRACT FROM AUTHOR]

Constructing maps of dry deposition pollution levels is vital for air quality management, and presents statistical problems typical of many environmental and spatial applications. Ideally, such maps would be based on a dense network of monitoring stations, but this does not exist. Instead, there are two main sources of information for dry deposition levels in the United States: one is pollution measurements at a sparse set of about 50 monitoring stations called CASTNet, and the other is the output of the regional scale air quality models, called Models-3. A related problem is the evaluation of these numerical models for air quality applications, which is crucial for control strategy selection. We develop formal methods for combining sources of information with different spatial resolutions and for the evaluation of numerical models. We specify a simple model for both the Models-3 output and the CASTNet observations in terms of the unobserved ground truth, and we estimate the model in a Bayesian way. This provides improved spatial prediction via the posterior distribution of the ground truth, allows us to validate Models-3 via the posterior predictive distribution of the CASTNet observations, and enables us to remove the bias in the Models-3 output. We apply our methods to data on SO2 concentrations, and we obtain high-resolution SO2 distributions by combining observed data with model output. We also conclude that the numerical models perform worse in areas closer to power plants, where the SO2 values are overestimated by the models. [ABSTRACT FROM AUTHOR]

Background: One of the primary tasks in analysing gene expression data is finding genes that are differentially expressed in different samples. Multiple testing issues due to the thousands of tests run make some of the more popular methods for doing this problematic. Results: We propose a simple method, Normal Uniform Differential Gene Expression (NUDGE) detection for finding differentially expressed genes in cDNA microarrays. The method uses a simple univariate normal-uniform mixture model, in combination with new normalization methods for spread as well as mean that extend the lowess normalization of Dudoit, Yang, Callow and Speed (2002) [1]. It takes account of multiple testing, and gives probabilities of differential expression as part of its output. It can be applied to either single-slide or replicated experiments, and it is very fast. Three datasets are analyzed using NUDGE, and the results are compared to those given by other popular methods: unadjusted and Bonferroni-adjusted t tests, Significance Analysis of Microarrays (SAM), and Empirical Bayes for microarrays (EBarrays) with both Gamma-Gamma and Lognormal-Normal models. Conclusion: The method gives a high probability of differential expression to genes known/suspected a priori to be differentially expressed and a low probability to the others. In terms of known false positives and false negatives, the method outperforms all multiple-replicate methods except for the Gamma-Gamma EBarrays method to which it offers comparable results with the added advantages of greater simplicity, speed, fewer assumptions and applicability to the single replicate case. An R package called nudge to implement the methods in this paper will be made available soon at http://www.bioconductor.org. [ABSTRACT FROM AUTHOR]

Probabilistic weather forecasting consists of finding a joint probability distribution for future weather quantities or events. It is typically done by using a numerical weather prediction model, perturbing the inputs to the model in various ways, and running the model for each perturbed set of Inputs. The result is then viewed as an ensemble of forecasts, taken to be a sample from the joint probability distribution of the future weather quantities of interest. This is typically not feasible for mesoscale weather prediction carried out locally by organizations without the vast data and computing resources of national weather centers. Instead, we propose a simpler method that breaks with much previous practice by perturbing the outputs, or deterministic forecasts, from the model. Forecast errors are modeled using a geostatistical model, and ensemble members are generated by simulating realizations of the geostatistical model. The method is applied to 48-hour mesoscale forecasts of temperature in the North American Pacific Northwest between 2000 and 2002. The resulting forecast intervals turn out to be empirically well calibrated for individual meteorological quantities, to be sharper than those obtained from approximate climatology, and to be consistent with aspects of the spatial correlation structure of the observations. [ABSTRACT FROM AUTHOR]