Spatial clustering of array CGH features in combination with hierarchical multiple testing

We propose a new approach for clustering DNA features using array CGH data from multiple tumor samples. We distinguish data-collapsing: joining contiguous DNA clones or probes with extremely similar data into regions, from clustering: joining contiguous, correlated regions based on a maximum likelihood principle. The model-based clustering algorithm accounts for the apparent spatial patterns in the data. We evaluate the randomness of the clustering result by a cluster stability score in combination with cross-validation. Moreover, we argue that the clustering really captures spatial genomic dependency by showing that coincidental clustering of independent regions is very unlikely. Using the region and cluster information, we combine testing of these for association with a clinical variable in an hierarchical multiple testing approach. This allows for interpreting the significance of both regions and clusters while controlling the Family-Wise Error Rate simultaneously. We prove that in the context of permutation tests and permutation-invariant clusters it is allowed to perform clustering and testing on the same data set. Our procedures are illustrated on two cancer data sets

Isgur-Wise Function from Bethe-Salpeter Amplitude

We develop the improved ladder approximation to QCD in order to apply it to the heavy quark mesons. The resulting Bethe-Salpeter equation is expanded in powers of the inverse heavy quark mass 1/M, and is shown to be consistent with the heavy quark spin symmetry. We calculate numerically the universal leading order BS amplitude for heavy pseudoscalar and vector mesons, and use this to evaluate the Isgur-Wise function and the decay constant F_B. The resulting Isgur-Wise function predicts a large charge radius, rho^2 = 1.8 - 2.0, which when fitted to the ARGUS data corresponds to the value Vcb = .044 - .050 for the Kobayashi-Maskawa matrix element.Comment: 26 pages, Plain TeX, 1 epsf and 6 PostScript files are included, KUNS 123

Preference for Randomization: Ambiguity Aversion and Inequality Aversion

In Anscombe and Aumann’s (1963) domain, there are two types of mixtures. One is an ex–ante mixture, or a lottery on acts. The other is an ex–post mixture, or a state–wise mixture of acts. These two mixtures have been assumed to be indifferent under the Reversal of Order axiom. However, we argue that the difference between these two mixtures is crucial in some important contexts. Under ambiguity aversion, an ex–ante mixture could provide only ex–ante hedging but not ex–post hedging. Under inequality aversion, an ex–ante mixture could provide only ex–ante equality but not ex–post equality. For each context, we develop a model that treats a preference for ex–ante mixtures separately from a preference for ex–post mixtures. One representation is an extension of Gilboa and Schmeidler’s (1989) Maxmin preferences. The other representation is an extension of Fehr and Schmidt’s (1999) Piecewise–linear preferences. In both representations, a single parameter characterizes a preference for ex–ante mixtures. For the both representations, instead of the Reversal of Order axiom, we propose a weaker axiom, the Indifference axiom, which is a criterion, suggested in Raiffa’s (1961) critique, for evaluating lotteries on acts. These models are consistent with much recent experimental evidence in each context.Ambiguity; randomization; Ellsberg paradox; other–regarding preferences; inequality; maxmin utility.