A simple approach for modeling multivariate extremes is to consider the vector of component-wise maxima and their max-stable distributions. The extremal dependence can be inferred by estimating the angular measure or, alternatively, the Pickands dependence function. We propose a nonparametric Bayesian model that allows, in the bivariate case, the simultaneous estimation of both functional representations through the use of polynomials in the Bernstein form. The constraints required to provide a valid extremal dependence are addressed in a straightforward manner, by placing a prior on the coefficients of the Bernstein polynomials which gives probability one to the set of valid functions. The prior is extended to the polynomial degree, making our approach fully nonparametric. Although the analytical expression of the posterior is unknown, inference is possible via a trans-dimensional MCMC scheme. We show the efficiency of the proposed methodology by means of a simulation study. The extremal behaviour of log-returns of daily exchange rates between the Pound Sterling vs the U.S. Dollar and the Pound Sterling vs the Japanese Yen is analysed for illustrative purposes.MSC 2010 subject classifications: 62G05, 62G07, 62G32.

Stationary processes are a natural choice as statistical models for time series data, owing to their good estimating properties. In practice, however, alternative models are often proposed that sacrifice stationarity in favour of the greater modelling flexibility required by many real-life applications. We present a family of time-homogeneous Markov processes with nonparametric stationary densities, which retain the desirable statistical properties for inference, while achieving substantial modelling flexibility, matching those achievable with certain non-stationary models. A latent extension of the model enables exact inference through a trans-dimensional Markov chain Monte Carlo method. Numerical illustrations are presented.

In probabilistic risk assessment, attention is often focused on the expected value of a risk metric. The sensitivity of this expectation to changes in the parameters of the distribution characterizing uncertainty in the inputs becomes of interest. Approaches based on differentiation encounter limitations when (i) distributional parameters are expressed in different units or (ii) the analyst wishes to transfer sensitivity insights from individual parameters to parameter groups, when alternating between different levels of a probabilistic safety assessment model. Moreover, the analyst may also wish to examine the effect of assuming independence among inputs. This work proposes an approach based on the differential importance measure, which solves these issues. Estimation aspects are discussed in detail, in particular the problem of obtaining all sensitivity measures from a single Monte Carlo sample, thus avoiding potentially costly model runs. The approach is illustrated through an analytical example, highlighting how it can be used to assess the impact of removing the independence assumption. An application to the probabilistic risk assessment model of the Advanced Test Reactor large loss of coolant accident sequence concludes the work.

A Bayesian nonparametric regression model with normalized weights ; a study of hippocampal atrophy in Alzheimer's disease. Journal of the American Statistical Association, 109 . pp. 477-490. Permanent WRAP URL:http://wrap.warwick.ac.uk/71932 Copyright and reuse:The Warwick Research Archive Portal (WRAP) makes this work by researchers of the University of Warwick available open access under the following conditions. Copyright © and all moral rights to the version of the paper presented here belong to the individual author(s) and/or other copyright owners. To the extent reasonable and practicable the material made available in WRAP has been checked for eligibility before being made available.Copies of full items can be used for personal research or study, educational, or not-for profit purposes without prior permission or charge. Provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way. A note on versions:The version presented here may differ from the published version or, version of record, if you wish to cite this item you are advised to consult the publisher's version. Please see the 'permanent WRAP url' above for details on accessing the published version and note that access may require a subscription. AbstractHippocampal volume is one of the best established biomarkers for Alzheimer's disease. However, for appropriate use in clinical trials research, the evolution of hippocampal volume needs to be well understood. Recent theoretical models propose a sigmoidal pattern for its evolution. To support this theory, the use of Bayesian nonparametric regression mixture models seems particularly suitable due to the flexibility that models * Bocconi University, Milan, Italy. PhD research funded by CONACyT † University of Cambridge, Cambridge, UK. ‡ University of Texas at Austin, USA. § Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database (adni.loni.ucla.edu). As such, the investigators within the ADNI provided data but did not participate in analysis or writing of this report. A complete listing of ADNI investigators can be found at: http://adni.loni.ucla.edu/wp-content/uploads/how_to_apply/ADNI_ Acknowledgement_List.pdf. 1 of this type can achieve and the unsatisfactory predictive properties of semiparametric methods. In this paper, our aim is to develop an interpretable Bayesian nonparametric regression model which allows inference with combinations of both continuous and discrete covariates, as required for a full analysis of the data set. Simple arguments regarding the interpretation of Bayesian nonparametric regression mixtures lead naturally to regression weights based on normalized sums. Difficulty in working with the intractable normalizing constant is overcome thanks to recent advances in MCMC methods and the development of a novel auxiliary variable scheme. We apply the new model and MCMC method to study the dyna...

Although animal locations gained via GPS, etc. are typically observed on a discrete time scale, movement models formulated in continuous time are preferable in order to avoid the struggles experienced in discrete time when faced with irregular observations or the prospect of comparing analyses on different time scales. A class of models able to emulate a range of movement ideas are defined by representing movement as a combination of stochastic processes describing both speed and bearing.A method for Bayesian inference for such models is described through the use of a Markov chain Monte Carlo approach. Such inference relies on an augmentation of the animal's locations in discrete time that have been observed with error, with a more detailed movement path gained via simulation techniques. Analysis of real data on an individual reindeer Rangifer tarandus illustrates the presented methods.