Seminars

We are interested in the behavior of MCMC algorithms in high dimensions. Results in the literature have shown that the 'vanilla' Random Walk Metropolis scales as 1/n, with n being the dimension of the state space. The so-called Metropolis-adjusted Langevin algorithm scales as 1/n^{1/3}, as it uses information about the gradient of the target density. We consider an MCMC algorithm popular amongst physicists (but not statisticians): the Hybrid Monte-Carlo (HMC) algorithm. HMC scales as 1/n^{1/4}. In connection with related results for other MCMC algorithms, for a simple class of target distributions we identify a single asymptotically optimal acceptance probability for HMC (which is 0.651, to three decimal places) irrespectively of the the particular selection of target distribution.

The aim of this work is to detect spatial clusters based on the number of connected components of a graph. We link Erd\"os graph and Poisson point process. We give the probability distribution function (pdf) of the number of connected component for an Erd\"os graph and obtain the pdf of the number of clusters for a Poisson process. We also obtain the pdf of the number of clusters bigger than a given threshold for Poisson process. We extend this results to marked point process by using multi-class Erd\"os graph. Using this result, we obtain a test for complete spatial randomness and also identify the clusters that violates the CSR hypothesis. Border effects are computed. We illustrate our results on a tropical forest example.

Abstract: Quantile regression may be used to analyze higher or lower quantilesof the response distribution when they exhibit a different structuralrelationship to the covariates than the average responses. We developBayesian semiparametric models based on Dirichlet process (DP) mixturepriors for the error distribution, and dependent DP prior for errordensities that change with covariates. We also study a fully nonparametric model using Gaussian process priors for the quantile regression function and a DP mixture prior for the error distribution. The stochastic prior sepecifications enable uncovering of non-linearity in the quantile regression function and non-standard features in the response distribution. Inference is based on a combination of posterior simulation methods for Dirichlet process mixtures. The proposed models are illustrated using simulated and real data sets.

Abstract: Modelling of past mortality trends and projecting future mortality rates is an important area of actuarial research. In this presentation two statistical methods – generalised additive and generalised linear mixed models – are considered for modelling Irish mortality data. Generalised additive models are used to project future mortality rates and are compared with two methods recently reviewed by the UK Actuarial Profession. The models are applied to Irish population data (from the Central Statistics Office) and mortality rates projected to approximately 2050. The generalised linear mixed model is used to model the impact of pension amount on Irish pensioner mortality. Mortality rates amongst pensioners are known to vary by pension amount and the generalised linear mixed model is compared with traditional actuarial approaches for analysing the impact of pension amount on mortality.

Motivation: The US National Cancer Institute maintains a database of 60 cancer cell-lines (NCI-60) representing nine different tissues of origin. Enormous stores of information about each cell-line may be compared to find like behaviour across subsets of this panel. Here we focus on finding associations between gene expression and resistance to anti-cancer drugs. Previous studies have found some expected and some surprising associations in subpopulations, e.g., associations over estrogen-regulated cell-lines and association over less differentiated cell-lines. The proposed methods would greatly reduce the amount of effort required to detect such associations.

Methods: We use a sequence of Kendall's tau statistics, constructed according to an optimal/admissible ordering, to form a path, whose crossing over pre-specified boundaries provides a statistical test for association in an unspecified subpopulation. For each cell-line, we also provide a posterior probability that it is included in the association. Finally, we apply to the test to convex combinations of two predictors (e.g., pairs of gene expressions) and produce diagnostics that suggest asymmetric roles in the type of association each predictor provides.

Results: Compared with Kendall's classical test for association over the whole population, the tau-path test has substantially greater power in situations where there is a strong association over a subset. This comes at a small cost of having slightly less power when there is a weak association over the whole population. The tau-path method confirms a strong, negative correlation between ASNS expression level and L-asparaginase potency over the leukemia and ovarian subsets of the NCI-60; antisense technology has previously shown a causal link in the ovarian cell-lines, but only in estrogen sensitive cell-lines. The tau-path method also found significant negative compound-gene associations between all five quassinoid drugs under test and IGFBP6 gene, with a common subset of 36 cells for all compounds. We hope to verify this association through laboratory experiments.

Extensions: The method is also currently being used to detect which of the 210 designated market areas of the US demonstrate the most sensitivity to incentives to repurchase products.