Abstract: The paper brings together methods from two disciplines: machine learning theory and robust statistics. Robustness properties of machine learning methods based on convex risk minimization are investigated for the problem of pattern recognition. Assumptions are given for the existence of the influence function of the classifiers and for bounds of the influence function. Kernel logistic regression, support vector machines, least squares and the AdaBoost loss function are treated as special cases. A sensitivity analysis of the support vector machine is given.

Abstract: For the common binary response model we propose a direct method for the nonparametric estimation of the effective dose level ED? (0

Abstract: The analysis of temporal data is an important issue of current research, because most real-world data either explicitly or implicitly contains some information about time. The key to successfully solving temporal learning tasks is to analyze the assumptions that can be made and prior knowledge one has about the temporal process of the learning problem and find a representation of the data and a learning algorithm that makes effective use of this knowledge. This paper will present a concise overview of the application Support Vector Machines to different temporal learning tasks and the corresponding temporal representations.

Abstract: We analyze IF/hyper-classical games by bringing together two viewpoints from Jaakko Hintikka's work: game semantics, and epistemic logic. In the process, we link up between logic and game theory. 1 Logic meets games Game theory and logic met in the 1950s – and Jaakko Hintikka has been a pioneer ever since in introducing game-theoretic viewpoints into logic, from his early basic evaluation games for predicate logic to his more recent ‘information-friendly’ logic based on extended games that go far beyond classical systems. The grand philosophical program behind these technical efforts is found in his books “Logic, Language Games and Information” (1973), “The Game of Language” (1985), the Handbook of Logic & Language chapter with Gabriel Sandu on ‘Game-Theoretical Semantics’ (1997), and many recent papers and manifestoes (cf. Hintikka 2002). Connections between logic and games are attracting attention these days, ranging from special-purpose ‘logic games’ to 'game logics' analyzing general game structure (cf. the general program in van Benthem 1999–2002). IF logic is intriguing in this respect, as it sits at the interface of ordinary logic games, whose players have perfect information about their position during play, and general game theory, where players may typically have imperfect information of various sorts. My aim in this paper is to explore the game content of Hintikka’s systems using tools from epistemic logic, and more generally, clarify their thrust at the interface of logic and game theory. Exegetically, however, this is a somewhat tricky business. There is much less game content to Hintikka’s systems than one might expect. His true interest is closer to the classical logical agenda of meaning and expressive power, mainly for quantifier expressions, viz. the notion of (in-)dependence. Despite occasional declarations of love for games as such as the basis of rational enquiry, they remain mostly a didactic device for studying dependence in quantification – and a way of drawing battle-lines

Abstract: We give a simple example of a variety V of modal algebras that is canonical but cannot be axiomatised by canonical equations or first-order sentences. We then show that the variety RRA of representable relation algebras, although canonical, has no canonical axiomatisation. Indeed, we show that every axiomatisation of these varieties involves infinitely many non- canonical sentences. Using probabilistic methods of Erd˝os, we construct an infinite sequence G0,G1,... of finite graphs with arbitrarily large chromatic number, such that each Gn is a bounded morphic image of Gn+1 and has no odd cycles of length at most n. The inverse limit of the sequence is a graph with no odd cycles, and hence is 2-colourable. It follows that a modal algebra (respectively, a relation algebra) obtained from the Gn satisfies arbitrarily many axioms from a certain axiomatisation of V (RRA), while its canonical extension satisfies only a bounded number of them. First-order compactness will now establish that V (RRA) has no canonical axiomatisation. A variant of this argument shows that all axiomatisations of these classes have infinitely many non-canonical sentences.

Abstract: In this note we examine the relevance of Sheppard's correction for variances and (both the original and a valid weak form of) the so-called 'quantization noise model' to understanding the effects of integer-rounding on continuous random variables. We further consider whether there is any real relationship between the two. We observe that the strong form of the model is not really relevant to describing rounding effects, demonstrate using simple cases the substantial limitations of the Sheppard correction, and use simple versions of a weak form of the model to establish that there is no real connection between the correction and the model.

Abstract: Some initial motivations for the Guarded Fragment still seem of interest in carrying its program further. First, we stress the equivalence between two perspectives: (a) satisfiability on standard models for guarded first-order formulas, and (b) satisfiability on general assignment models for arbitrary first-order formulas. In particular, we give a new straightforward reduction from the former notion to the latter. We also show how a perspective shift to general assignment models provides a new look at the fixed-point extension LFP(FO) of first-order logic, making it decidable. Next, we relate guarded syntax to earlier quantifier restriction strategies for achieving effective axiomatizability in second-order logic – pointing at analogies with ‘persistent’ formulas, which are essentially in the Bounded Fragment of many-sorted first-order logic. Finally, we look at some further unexplored directions, including the systematic use of ‘quasi-models’ as a semantics by itself.

Abstract: The four essays published here provide a useful overview for anyone interested in understanding the issues and policy environment surrounding financial system stability.

Abstract: I am not a Bolzano scholar, but among practising logicians, my encounters with his work seem above average. The first of these was in my student days, when reading some history of logic on my own in the great works by Boche›ski, and the Kneales. I was intrigued by finding how my standard textbooks had crafted an eschatological history of the field, with latter-day saints like Tarski, relegating earlier pioneers that do not fit the story line to oblivion. Later, I read my first real sample of Bolzano as a mathematician, viz. Paradoxes of Infinity, out of an interest in pre-Cantorian science in the making. Admittedly, not an easy read – as is true for all his texts I have seen. Bolzano as a philosopher entered my life around 1980, when looking for topics for a joint course with my more continentally trained philosophical colleague Detlev Pätzold. We settled eventually on the accounts of propositions in Leibniz, Hegel, Bolzano, and Frege – and a nice course it was! And then, at last, I was ready for the heavy bulk of the Wissenschaftslehre. This was partly through an interest in interfaces between logic and methodology of science, and partly as an aspiring radical in logic, intrigued by a book which is about logic, but with a quite different agenda from the modern one. My documented reaction to this reading is in van Benthem 1984, 1985. Our final encounter took place a few years ago in Prague, after wandering through a large cemetery with my colleague Eva Hajicova – trying to locate Bolzano’s grave among overgrown paths, while talking about logical inference and intelligent search to a Dutch TV crew following us. We did reach the target.

Abstract: The problem of constructing standardized maximin D-optimal designs for weighted polynomial regression models is addressed. In particular it is shown that, by following the broad approach to the construction of maximin designs introduced recently by Dette, Haines and Imhof (2003), such designs can be obtained as weak limits of the corresponding Bayesian Φq-optimal designs. The approach is illustrated for two specific weighted polynomial models and also for a particular growth model.

Abstract: We consider 1927 borrowers from 54 countries who had a credit rating by both Moody's and S&P as of the end of 1998, and their subsequent default history up to the end of 2002. Viewing bond ratings as predicted probabilities of default, we show that it is unlikely that both agencies are well calibrated, and that the ranking of the agencies depends crucially on the way in which probability predictions are compared.

Abstract: Microarrays enable to measure the expression levels of tens of thousands of genes simultaneously. One important statistical question in such experiments is which of the several thousand genes are differentially expressed. Answering this question requires methods that can deal with multiple testing problems. One such approach is the control of the False Discovery Rate (FDR). Two recently developed methods for the identification of differentially expressed genes and the estimation of the FDR are the SAM (Significance Analysis of Microarrays) procedure and an empirical Bayes approach. In the two group case, both methods are based on a modified version of the standard t-statistic. However, it is also possible to use the Wilcoxon rank sum statistic. While there already exists a version of the empirical Bayes approach based on this rank statistic, we introduce in this paper a new version of SAM based on Wilcoxon rank sums. We furthermore compare these four procedures by applying them to simulated and real gene expression data.

Abstract: The major focus of this paper is to determine whether the accuracy of German macroeconomic forecasts has improved over time. We examine 1-year-ahead forecasts of real GDP and inflation for 1967 to 2001 made by three major German forecasting groups and the OECD. We examine the accuracy of the forecasts over the entire period and in three sub-periods. We conclude that, with some exceptions, the errors of the German forecasters were similar to those of their US and UK counterparts. While the absolute size of the forecast errors has declined, this is not the case for relative accuracy. A benchmark comparison of these predictions with the ex post forecasts of a macroeconometric model indicates that the quality of the growth forecasts can be improved but that the expected increase in accuracy may not be substantial.

Abstract: Methods of optimal experimental design potentially are very useful tool in research practice. There exists, unfortunately, some distance between mathematicians who investigating models of biological processes and practical researchers who do experiments. The beautiful, efficient and potentially very useful mathematical results are often not available for the wide range of experimental researchers which each time face the same problems. The purpose of this paper is to review applications of optimal experimental design in microbiology and to introduce those methods in such a way as to be accessible for scientists who making experimental research with no deep mathematical background. Examples in this paper are taken from microbiology but it should be also interesting for the wide group of researchers in biomedical sciences, such as biophysicists, pharmacologists, plant physiologists or for anyone facing the problem of identifying parameters of non-linear biological models. The mathematical methods of optimal experimental design for non-linear models have been developed very intensively since 1960 when the basic theorems by Kiefer and Wolfowitz were published

Abstract: Motivated in part by applications in model selection in statistical genetics and sequential monitoring of financial data, we study an empirical process framework for a class of stopping rules which rely on kernel-weighted averages of past data. We are interested in the asymptotic distribution for time series data and an analysis of the joint influence of the smoothing policy and the alternative defining the deviation from the null model (in-control state). We employ a certain type of local alternative which provides meaningful insights. Our results hold true for short memory processes which satisfy a weak mixing condition. By relying on an empirical process framework we obtain both asymptotic laws for the classical fixed sample design and the sequential monitoring design. As a by-product we establish the asymptotic distribution of the Nadaraya-Watson kernel smoother when the regressors do not get dense as the sample size increases.

Abstract: We consider the problem of finding D-optimal designs for estimating the coefficients in a weighted polynominal regression model with a certain efficiency function depending on two unknown parameters, which models he heteroscedastic error structure. This problem is tackled by adopting a Bayesian and a maximin approach, and optimal designs supported on a minimal number of support points are determined explicitly.

Abstract: Categorial grammars are driven by resource logics in a proof format Benthem, 1991; Mootrgat, 1997). Thus, they revolve around derivation and computation, with theCurry-Howard. 1997 Gestalt switch taking proofs to type-theoretic denotions for the expression analyzed. But over thye past decades, categorial logics have also been analyzed model-theoretically in modal logics with standard possible worlds-style models (cf. Kurtonina, 1995). Then, e.g., a categorial product A•B ‘true ‚ of some objects, t, u satisfying A,B, respectively. This is a standard binary modality, which needs a ternary accessibility relation R for its abstract truth condition: M,8⊨ A•B iff ∃t, υ: Rs, tu & M,t ⊨ A & M,u ⊨ B Modal logic is a world of research rather different from the usual concerns in categorial grammar. What happens when we put the two agendas side by side?

Abstract: We provide a method for distinguishing long-range dependence from deterministic trends such as structural breaks. The method is based on the comparison of standard log-periodogram regression estimation of the memory parameter with its tapered counterpart. The difference of these estimators provides the desired test. Its asymptotic distribution depends on the true memory parameter under the null, and is therefore estimated by bootstrapping. The test is applied to inflation rates of three industrialized countries.

Abstract: Stochastic models approximate data and are not true representations of the same. Statistical procedure make use of approximate stochastic models to facilitate the analysis of data.

Abstract: We discuss formats for formal theories, from sets of models to more complex constructs with an epistemic slant, clarifying the issue of what it means to update a theory. Using properties of verisimilitude as a lead, we also provide some connections between formal calculus of theories in the philosophy of science and modal-epistemic logics. Throughout, we use this case study as a platform for discussing more general connections between logic and general methodology.

Abstract: With the demise of monetary targeting over the past 20 years in many major countries, the question has arisen as to whether central banks should look at money at all when formulating and conducting monetary policy. The author argues that the mainstream paradigm, which gives no useful role to money, is unlikely to capture the full richness of the transmission mechanism. Moreover, on the face of it, the empirical evidence in Canada is inconsistent with the mainstream paradigm. For these reasons, the Bank of Canada devotes significant attention in its research, analysis, and communication to the behaviour of monetary aggregates and their possible role in the transmission mechanism. This report describes the use of the aggregates as of the end of 2001.

Abstract: In this paper we investigate locally E- and c-optimal designs for exponential regression models of the form _k i=1 ai exp(??ix). We establish a numerical method for the construction of efficient and locally optimal designs, which is based on two results. First we consider the limit ?i ? ? and show that the optimal designs converge weakly to the optimal designs in a heteroscedastic polynomial regression model. It is then demonstrated that in this model the optimal designs can be easily determined by standard numerical software. Secondly, it is proved that the support points and weights of the locally optimal designs in the exponential regression model are analytic functions of the nonlinear parameters ?1, . . . , ?k. This result is used for the numerical calculation of the locally E-optimal designs by means of a Taylor expansion for any vector (?1, . . . , ?k). It is also demonstrated that in the models under consideration E-optimal designs are usually more efficient for estimating individual parameters than D-optimal designs.

Abstract: We present logic games as a research topic in its own right, providing attractive models for dynamic interaction between agents. First, we survey the most basic logic games. Then we show how their common properties raise interesting general issues of possible structures for games and corresponding 'game logics'. Next, we review logic games in the light of this general game logic. Finally, we discuss what happens when we import more 'realistic' themes from game theory into logic games, including players' preferences, and imperfect information.

Abstract: Classical regression analysis is usually performed in two steps. In a first step an appropriate model is identified to describe the data generating process and in a second step statistical inference is performed in the identified model. An intuitively appealing approach to the design of experiment for these different purposes are sequential strategies, which use parts of the sample for model identification and adapt the design according to the outcome of the identification steps. In this paper we investigate the finite sample properties of two sequential design strategies, which were recently proposed in the literature. A detailed comparison of sequential designs for model discrimination in several regression models is given by means of a simulation study. Some non-sequential designs are also included in the study.

Abstract: We discuss infinite zero-sum perfect-information games with more than two players. They are not determined in the traditional sense, but as soon as you fix a preference function for the players and assume common knowledge of rationality and this preference function among the players, you get determinacy for open and closed payoff sets. 2000 AMS Mathematics Subject Classification. 91A06 91A10 03B99 03E99.