Bayesian mixture modeling for spatial Poisson process intensities,with applications to extreme value analysis

We propose a method for the analysis of a spatial point pattern, which is assumed to arise as a set of observations from a spatial nonhomogeneous Poisson process. The spatial point pattern is observed in a bounded region, which, for most applications, is taken to be a rectangle in the space where the process is defined. The method is based on modeling a density function, defined on this bounded region, that is directly related with the intensity function of the Poisson process. We develop a flexible nonparametric mixture model for this density using a bivariate Beta distribution for the mixture kernel and a Dirichlet process prior for the mixing distribution. Using posterior simulation methods, we obtain full inference for the intensity function and any other functional of the process that might be of interest. We discuss applications to problems where inference for clustering in the spatial point pattern is of interest. Moreover, we consider applications of the methodology to extreme value analysis problems. We illustrate the modeling approach with three previously published data sets. Two of the data sets are from forestry and consist of locations of trees. The third data set consists of extremes from the Dow Jones index over a period of 1303 days.     

Bayesian adaptive dose‐escalation procedures for binary and continuous responses utilizing a gain function

One of the main aims of early phase clinical trials is to identify a safe dose with an indication of therapeutic benefit to administer to subjects in further studies. Ideally therefore, dose‐limiting events (DLEs) and responses indicative of efficacy should be considered in the dose‐escalation procedure. Several methods have been suggested for incorporating both DLEs and efficacy responses in early phase dose‐escalation trials. In this paper, we describe and evaluate a Bayesian adaptive approach based on one binary response (occurrence of a DLE) and one continuous response (a measure of potential efficacy) per subject. A logistic regression and a linear log‐log relationship are used respectively to model the binary DLEs and the continuous efficacy responses. A gain function concerning both the DLEs and efficacy responses is used to determine the dose to administer to the next cohort of subjects. Stopping rules are proposed to enable efficient decision making. Simulation results shows that our approach performs better than taking account of DLE responses alone. To assess the robustness of the approach, scenarios where the efficacy responses of subjects are generated from an E _max model, but modelled by the linear log–log model are also considered. This evaluation shows that the simpler log–log model leads to robust recommendations even under this model showing that it is a useful approximation to the difficulty in estimating E _max model. Additionally, we find comparable performance to alternative approaches using efficacy and safety for dose‐finding. Copyright © 2015 John Wiley & Sons, Ltd.     

Ordinal independence in nonlinear utility theory

Individual behavior under uncertainty is characterized using a new axiom, ordinal independence, which is a weakened form of the von Neumann-Morgenstern independence axiom It states that if two distributions share a tail in common, then this tail can be modified without altering the individual's preference between these distributions. Preference is determined by the tail on which the distributions differ. This axiom implies an appealing and simple functional form for a numerical representation of preferences. It generalizes the form of anticipated utility, and it explains some well-known forms of behavior, such as the Friedman-Savage paradox, that anticipated utility cannot.     

Compact labelings for efficient first-order model-checking

We consider graph properties that can be checked from labels, i.e., bit sequences, of logarithmic length attached to vertices. We prove that there exists such a labeling for checking a first-order formula with free set variables in the graphs of every class that is nicely locally clique-width-decomposable. This notion generalizes that of a nicely locally tree-decomposable class. The graphs of such classes can be covered by graphs of bounded clique-width with limited overlaps. We also consider such labelings for bounded first-order formulas on graph classes of bounded expansion. Some of these results are extended to counting queries.     

Auswirkungen von Macht auf das ��berleben in Extremsituationen: Ein Vergleich der Titanic und Lusitania Schiffskatastrophen

Comparing the Titanic and Lusitania disaster the impact of financial and physical power as well as the emergence of social norms on survival during life-and-death situations is analyzed. Despite the fact that some maritime disasters have become famous, a quantitative understanding of survival in life-and-death situations is still lacking. In a quasi-natural experiment multivariate probit estimations are conducted based on publicly available data. The paper suggests that in life-and-death situations differences in time restrictions are crucial. When time is scarce individual self-interested fight-or-flight behavior will predominate and result in a stronger competition for survival. In contrast, altruism and adherence to social norms emerge when there is sufficient time to reflect on the event and circumstances: Social norms require time to evolve, and they loose against physical strength in a shorter window of opportunity.     

A note on new confidence intervals for the difference between two proportions based on an Edgeworth expansion

Zhou and Qin [2004. New intervals for the difference between two independent binomial proportions. J. Statist. Plann. Inference 123, 97–115; 2005. A new confidence interval for the difference between two binomial proportions of paired data. J. Statist. Plann. Inference 128, 527–542] “new confidence intervals” for the difference between two treatment proportions exhibit a severe lack of invariance property that is a compelling reason not to use them.     

Tests of serial independence based on Kendall's process

The authors propose new rank statistics for testing the white noise hypothesis in a time series. These statistics are Cramér‐von Mises and Kolmogorov‐Smirnov functionals of an empirical distribution function whose mean is related to a serial version of Kendall's tau through a linear transform. The authors determine the asymptotic behaviour of the underlying serial process and the large‐sample distribution of the proposed statistics under the null hypothesis of white noise. They also present simulation results showing the power of their tests.