this paper I discuss a Bayesian approach to solving this problem that has long been available in principle but is only now becoming routinely feasible, by virtue of recent computational advances, and examine its implementation in examples that involve forecasting the price of oil and estimating the chance of catastrophic failure of the U.S. Space Shuttle.

Exploratory data analysis (EDA) is as much a matter of strategy as of selecting specific statistical operations. We have developed a knowledge-based planning system, called Aide, to help users with EDA. Aide strikes a balance between conventional statistical packages, which need guidance for every step in the exploration, and autonomous systems, which leave the user entirely out of the decision-making process. Aide's processing is based on artificial intelligence planning techniques, which give us a useful means of representing some types of statistical strategy. In this article we describe the design of Aide and its behavior in exploring a small, complex dataset. Keywords: exploratory data analysis, artificial intelligence 1 1 Strategic aspects of exploration Exploring data is as much a matter of strategy as of selecting specific statistical operations. In his introduction to exploratory data analysis, for example, Tukey begins by laying out some general guidelines for desc...

Operational risk has become an important risk component in the banking and insurance world. The availability of (few) reasonable data sets has given some authors the opportunity to analyze operational risk data and to propose different models for quantification. As proposed in Dutta and Perry [12], the parametric g-and-h distribution has recently emerged as an interesting candidate. In our paper, we discuss some fundamental properties of the g-and-h distribu-tion and their link to extreme value theory (EVT). We show that for the g-and-h distribution, convergence of the excess distribution to the generalized Pareto dis-tribution (GPD) is extremely slow and therefore quantile estimation using EVT may lead to inaccurate results if data are well modeled by a g-and-h distribution. We further discuss the subadditivity property of Value-at-Risk (VaR) for g-and-h random variables and show that for reasonable g and h parameter values, super-additivity may appear when estimating high quantiles. Finally, we look at the g-and-h distribution in the one-claim-causes-ruin paradigm.

Prepared with partial support from the United Nations Environment Programme (UNEP) Division of Early Warning and Assessment (DEWA), MOU Number FP/1020-00-01-2218. The contents have not been subjected to Programme review and therefore do not necessarily reflect the views of the Programme

The boxplot is a very popular graphical tool to visualize the distribution of con-tinuous unimodal data. It shows information about the location, spread, skewness as well as the tails of the data. However, since the fences are derived from the normal distribution, usually too many points are classified as outliers when the data are skewed. We present an adjustment of the boxplot that includes a robust measure of skewness in the determination of the whiskers. We show with several examples and simulation results that this adjusted boxplot gives a more accurate representation of the data and of possible outliers.

Statistical operations are often facilitated by other operations. We can facilitate modeling operations by testing their input for irregularities and removing problems wherever possible. A planning representation is well-suited to this task. We describe the representation used in Igor, a system for exploratory data analysis, and its integration with two modeling systems, Pearl's IC and Cohen's FBD. We show that introducing outliers into the inputs of the algorithms can influence their performance. We demonstrate that a planning representation offers a flexible way of integrating outlier detection and removal into the modeling process, taking account of specific characteristics of the modeling operations involved.

. The two-way analysis of variance with interactions is a well established and integral part of statistics. In spite of its long standing it is hown that the standard definition of interactions is counter intuitive and obfuscates rather than clarifies. A different definition of interaction is given which amongst other advantages allows the detection of interactions even in the case of one observation per cell. A characterization of unconditionally identifiable interaction patterns is given and it is proved that such patterns can be identified by the L 1 -functional. The unconditionally identifiable interaction patterns describe the optimal breakdown behaviour of any equivariant location functional from which it follows that the L 1 -functional has optimal breakdown behaviour. Possible lack of uniqueness of the L 1 -functional can be overcome using an M-functional with an external scale derived independently from the observations. The resulting procedures are applied to some data ...

People nowadays are relying more and more on OLAP data to find business solutions. A typical OLAP data cube usually contains four to eight dimensions, with two to six hierarchical levels and tens to hundreds of categories for each dimension. It is often too large and has too many levels for users to browse it effectively. In this thesis we propose a system prototype which will guide users to efficiently explore exceptions in data cubes. It automatically computes the degree of exceptions for cube cells at different aggregation levels. When user browses the cube, exceptional cells as well as interesting drilling-down paths that will lead to lower level exceptions are highlighted according to their interestingness. Different statistical methods such as log-linear model, adapted linear model and Z-tests are used to compute the degree of exceptions. We present algorithms and address the issue of improving the performance on large data sets. Our study on exceptions leads to mining quantitati...

The classical chi-square test of goodness-of-fit compares the hypothesis that data arise from some parametric family of distributions, against the nonparametric alternative that they arise from some other distribution. However, the chi-square test requires continuous data to be grouped into arbitrary categories. Furthermore, as the test is based upon an approximation, it can only be used if there is su#cient data. In practice, these requirements are often wasteful of information and overly restrictive. The authors explore the use of the fractional Bayes factor to obtain a Bayesian alternative to the chi-square test when no specific prior information is available. They consider the extent to which their methodology can handle small data sets and continuous data without arbitrary grouping. R ESUM E Le test classique d'ajustement du khi-deux confronte l'hypothese que les observations proviennent d'une famille parametrique de lois a l'hypothese non parametrique qu'elles sont issues d'un...

Lockheed-Martin Company (LMCO) must design lander vehicles to survive their landings on the rock-strewn surface of the planet Mars. Given the basic structure of the lander and the characteristics of rocks that are likely to cover the planet's surface, what is the probability that the lander will survive its mission? Students enrolled in mathematics course MATH 4779/5779 during the Spring 2000 semester developed an algorithm to simulate this probability. We characterize the distribution of rock features from previous Viking Lander missions and describe the components of a algorithm to simulate a rocky surface as well as the algorithm to determine whether the Lander survives the landing on Mars. We present some simulation results which indicate that rock density (average number of rocks per square meter) has a signicant eect on the probability of a successful landing. Finally, we discuss other enhancements for future work, including a possible Monte Carlo Swindles to increase simulatio...