Table of contents, International Statistical Review, vol. 71, no. 2 (2003)

Environmental Statistics---A Personal View authors: Peter Guttorp

\bf Hierarchical Models in Environmental Science authors: Christopher K. Wikle

Statistical Assessment of Numerical Models authors: Montserrat Fuentes , Peter Guttorp , Peter Challenor

Sequential Data Assimilation Techniques in Oceanography authors: Laurent Bertino, , Geir Evensen , Hans Wackernagel

Health Effects of Air Pollution:\\ A Statistical Review authors: Francesca Dominici , Lianne Sheppard , Merlise Clyde

Reflections on Fourteen Cryptic Issues Concerning the Nature of Statistical Inference authors: O.J.W.F. Kardaun , D. Salomé , W. Schaafsma , A.G.M. Steerneman , J.C. Willems , D.R. Cox

Statistical Regularity and Free Will:\\ L.A.J. Quetelet and P.A. Nekrasov authors: Eugene Seneta

Bridging the Gap between Different Statistical Approaches: An Integrated Framework for Modelling authors: Petra M. Kuhnert , Kerrie Mengersen , Peter Tesar

A Bayesian Formulation of Exploratory Data Analysis and Goodness-of-fit Testing authors: Andrew Gelman

Some Aspects Of Neutral To Right Priors authors: Jyotirmoy Dey , R.V. Erickson , R.V. Ramamoorthi

Statistical Surveillance. Optimality and Methods authors: Marianne Frisén

Bootstrap Methods for Time Series authors: Wolfgang Härdle , Joel Horowitz , Jens-Peter Kreiss

The Future Direction of Statistical Training for the Promotion of Cooperation between Government and Academy authors: Yunkee Ahn , Buhn Nam , Chul Eung Kim

The field of environmental statistics is one of rapid growth at the moment. Environmental decision-making is prevalent in much of the world, and politicians and other decision makers are requesting new tools for understanding the state of the environment. In this paper, three case studies involving water pollution, air pollution, and climate change assessment are presented, together with brief descriptions of some other areas of environmental statistics. A discussion of future directions of the field concludes the paper.

Environmental systems are complicated. They include very intricate spatio-temporal processes, interacting on a wide variety of scales. There is increasingly vast amounts of data for such processes from geographical information systems, remote sensing platforms, monitoring networks, and computer models. In addition, often there is a great variety of scientific knowledge available for such systems, from partial differential equations based on first principles to panel surveys. It is argued that it is not generally adequate to consider such processes from a joint perspective. Instead, the processes often must be considered as a coherently linked system of conditional models. This paper provides a brief overview of hierarchical approaches applied to environmental processes. The key elements of such models can be considered in three general stages, the data stage, process stage, and parameter stage. In each stage, complicated dependence structure is mitigated by conditioning. For example, the data stage can incorporate measurement errors as well as multiple datasets with varying supports. The process and parameter stages can allow spatial and spatio-temporal processes as well as the direct inclusion of scientific knowledge. The paper concludes with a discussion of some outstanding problems in hierarchical modelling of environmental systems, including the need for new collaboration approaches.

Evaluation of physically based computer models for air quality applications is crucial to assist in control strategy selection. The high risk of getting the wrong control strategy has costly economic and social consequences. The objective comparison of modeled concentrations with observed field data is one approach to assessment of model performance. For dry deposition fluxes and concentrations of air pollutants there is a very limited supply of evaluation data sets. We develop a formal method for evaluation of the performance of numerical models, which can be implemented even when the field measurements are very sparse. This approach is applied to a current U.S. Environmental Protection Agency air quality model. In other cases, exemplified by an ozone study from the California Central Valley, the observed field is relatively data rich, and more or less standard geostatistical tools can be used to compare model to data. Yet another situation is when the cost of model runs is prohibitive, and a statistical approach to approximating the model output is needed. We describe two ways of obtaining such approximations.

footnote: This research was sponsored by a National Science Foundation grant DMS 0002790 and by a US EPA award R-8287801.

A common technical issue in the assessment of environmental numerical models is the need for tools to estimate nonstationary spatial covariance structures. We describe in detail two such approaches.

We review recent developments of sequential data assimilation techniques used in oceanography to integrate spatio-temporal observations into numerical models describing physical and ecological dynamics. Theoretical aspects from the simple case of linear dynamics to the general case of nonlinear dynamics are described from a geostatistical point-of-view. Current methods derived from the Kalman filter are presented from the least complex to the most general and perspectives for nonlinear estimation by sequential importance resampling filters are discussed. Furthermore an extension of the ensemble Kalman filter to transformed Gaussian variables is presented and illustrated using a simplified ecological model. The described methods are designed for predicting over geographical regions using a high spatial resolution under the practical constraint of keeping computing time sufficiently low to obtain the prediction before the fact. Therefore the paper focuses on widely used and computationally efficient methods.

We critically review and compare epidemiological designs and statistical approaches to estimate associations between air pollution and health. More specifically, we aim to address the following questions: \begin{enumerate} \item[1.]{\bf<i>Which epidemiological designs and statistical methods are available to estimate associations between air pollution and health?</i>} \item[2.]{\bf<i>What are the recent methodological advances in the estimation of the health effects of air pollution in time series studies?</i>} \item[3.]{\bf<i>What are the the main methodological challenges and future research opportunities relevant to regulatory policy?</i>} \end{enumerate} In question 1, we identify strengths and limitations of time series, cohort, case-crossover and panel sampling designs. In question 2, we focus on time series studies and we review statistical methods for: 1) combining information across multiple locations to estimate overall air pollution effects; 2) estimating the health effects of air pollution taking into account of model uncertainties; 3) investigating the consequences of exposure measurement error in the estimation of the health effects of air pollution; and 4) estimating air pollution-health exposure-response curves. Here, we also discuss the extent to which these statistical contributions have addressed key substantive questions. In question 3, within a set of policy-relevant-questions, we identify research opportunities and point out current data limitations.

The present paper provides the original formulation and a joint response of a group of statistically trained scientists statisticians to fourteen cryptic issues for discussion, which were handed out to the public by Professor Dr. D.R. Cox after his Bernoulli Lecture 1997 at Groningen University.

footnote: Part of this work was funded by a collaboration between IPP and Euratom. The contents of this work is the sole responsibility of the authors. In particular, the views expressed therein are not to be construed as being official and do not necessarily reflect those of the European Commission or the Max-Planck-Gesellschaft.

In the 19th century, causes of empirically observed stability of averages in settings relating to human behaviour were a topic of intense discussion in western Europe. This followed an extensive study of empirical stability by the founder of modern statistics (and of the International Statistical Institute) L.A.J. Quetelet, published in 1835, in what he called "Social Physics''. The eminent mathematician of strong probabilistic and philosophical inclination and Russian Orthodox religious belief, P.A. Nekrasov, took up and modified Quetelet's Social Physics in 1902, with (social) independence seen as prime cause of statistical regularity. Our paper focuses on the role free will plays in the statistical writings of Quetelet and of Nekrasov. The work of the latter has remained little known in general, mainly for politico-ideological reasons.

This paper proposes a template for modelling complex datasets that integrates traditional statistical modelling approaches with more recent advances in statistics and modelling through an exploratory framework. Our approach builds on the well-known and long standing traditional idea of `good practice in statistics' by establishing a comprehensive framework for modelling that focuses on exploration, prediction, interpretation and reliability assessment, a relatively new idea that allows individual assessment of predictions.

The integrated framework we present comprises two stages. The first involves the use of exploratory methods to help visually understand the data and identify a parsimonious set of explanatory variables. The second encompasses a two step modelling process, where the use of non-parametric methods such as decision trees and generalized additive models are promoted to identify important variables and their modelling relationship with the response before a final predictive model is considered. We focus on fitting the predictive model using parametric, non-parametric and Bayesian approaches.

This paper is motivated by a medical problem where interest focuses on developing a risk stratification system for morbidity of 1,710 cardiac patients given a suite of demographic, clinical and preoperative variables. Although the methods we use are applied specifically to this case study, these methods can be applied across any field, irrespective of the type of response.

Exploratory data analysis (EDA) and Bayesian inference (or, more generally, complex statistical modeling)---which are generally considered as unrelated statistical paradigms---can be particularly effective in combination. In this paper, we present a Bayesian framework for EDA based on posterior predictive checks. We explain how posterior predictive simulations can be used to create reference distributions for EDA graphs, and how this approach resolves some theoretical problems in Bayesian data analysis. We show how the generalization of Bayesian inference to include replicated data $y^{\rm rep}$ and replicated parameters $\theta^{\rm rep}$ follows a long tradition of generalizations in Bayesian theory.

On the theoretical level, we present a predictive Bayesian formulation of goodness-of-fit testing, distinguishing between $p$-values (posterior probabilities that specified antisymmetric discrepancy measures will exceed 0) and $u$-values (data summaries with uniform sampling distributions). We explain that $p$-values, unlike $u$-values, are Bayesian probability statements in that they condition on observed data.

Having reviewed the general theoretical framework, we discuss the implications for statistical graphics and exploratory data analysis, with the goal being to unify exploratory data analysis with more formal statistical methods based on probability models. We interpret various graphical displays as posterior predictive checks and discuss how Bayesian inference can be used to determine reference distributions.

The goal of this work is not to downgrade descriptive statistics, or to suggest they be replaced by Bayesian modeling, but rather to suggest how exploratory data analysis fits into the probability-modeling paradigm.

We conclude with a discussion of the implications for practical Bayesian inference. In particular, we anticipate that Bayesian software can be generalized to draw simulations of replicated data and parameters from their posterior predictive distribution, and these can in turn be used to calibrate EDA graphs.

footnote: Based on a paper presented at the Seventh Valencia Meeting on Bayesian Statistics.

Neutral to right priors are generalizations of Dirichlet process priors that fit in well with right-censored data. These priors are naturally induced by increasing processes with independent increments which, in turn, may be viewed as priors for the cumulative hazard function. This connection together with the L\'{e}vy representation of independent increment processes provides a convenient means of studying properties of \nr\ priors.

This article is a review of the theoretical aspects of \nr\ priors and provides a number of new results on their structural properties. Notable among the new results are characterizations of \nr\ priors in terms of the posterior and the cumulative hazard function. We also show that \nr\ priors are of the following nature: Consistency of Bayes' estimates implies consistency of the posterior, and posterior-consistency for complete observations automatically yields posterior-consistency for right-censored data.

Different criteria of optimality are used in different subcultures of statistical surveillance. One aim with this review is to bridge the gap between the different areas. The shortcomings of some criteria of optimality are demonstrated by their implications. Some commonly used methods are examined in detail, with respect to optimality. The examination is made for a standard situation in order to focus on the inferential principles. A uniform presentation of methods, by expressions of likelihood ratios, facilitates the comparisons between methods. The correspondences between criteria of optimality and methods are examined. The situations and parameter values for which some commonly used methods have optimality properties are thus determined. A linear approximation of the full likelihood ratio method, which satisfies several criteria of optimality, is presented. This linear approximation is used to examine when linear methods are approximately optimal. Methods for complicated situations are reviewed with respect to optimality and robustness.

The bootstrap is a method for estimating the distribution of an estimator or test statistic by resampling one's data or a model estimated from the data. The methods that are available for implementing the bootstrap and the accuracy of bootstrap estimates depend on whether the data are an independent random sample or a time series. This paper is concerned with the application of the bootstrap to time-series data when one does not have a finite-dimensional parametric model that reduces the data generation process to independent random sampling. We review the methods that have been proposed for implementing the bootstrap in this situation and discuss the accuracy of these methods relative to that of first-order asymptotic approximations. We argue that methods for implementing the bootstrap with time-series data are not as well understood as methods for data that are independent random samples. Although promising bootstrap methods for time series are available, there is a considerable need for further research in the application of the bootstrap to time series. We describe some of the important unsolved problems.

A survey was carried out showing that the knowledge of academic statisticians about the governmental data needs to be improved. We also state the current cooperative activities between government and academy, university education program, and statistical training program by the Korean National Statistical Office. We present some suggestions to promote cooperation between academia and government.