Global sensitivity analysis of computer models with functional inputs

Global sensitivity analysis is used to quantify the influence of uncertain input parameters on the response variability of a numerical model. The common quantitative methods are applicable to computer codes with scalar input variables. This paper aims to illustrate different variance-based sensitivity analysis techniques, based on the so-called Sobol indices, when some input variables are functional, such as stochastic processes or random spatial fields. In this work, we focus on large cpu time computer codes which need a preliminary meta-modeling step before performing the sensitivity analysis. We propose the use of the joint modeling approach, i.e., modeling simultaneously the mean and the dispersion of the code outputs using two interlinked Generalized Linear Models (GLM) or Generalized Additive Models (GAM). The ``mean'' model allows to estimate the sensitivity indices of each scalar input variables, while the ``dispersion'' model allows to derive the total sensitivity index of the functional input variables. The proposed approach is compared to some classical SA methodologies on an analytical function. Lastly, the proposed methodology is applied to a concrete industrial computer code that simulates the nuclear fuel irradiation

A comparison of statistical models for short categorical or ordinal time series with applications in ecology

We study two statistical models for short-length categorical (or ordinal) time series. The first one is a regression model based on generalized linear model. The second one is a parametrized Markovian model, particularizing the discrete autoregressive model to the case of categorical data. These models are used to analyze two data-sets: annual larch cone production and weekly planktonic abundance.Comment: 18 page

Effective Genetic Risk Prediction Using Mixed Models

To date, efforts to produce high-quality polygenic risk scores from genome-wide studies of common disease have focused on estimating and aggregating the effects of multiple SNPs. Here we propose a novel statistical approach for genetic risk prediction, based on random and mixed effects models. Our approach (termed GeRSI) circumvents the need to estimate the effect sizes of numerous SNPs by treating these effects as random, producing predictions which are consistently superior to current state of the art, as we demonstrate in extensive simulation. When applying GeRSI to seven phenotypes from the WTCCC study, we confirm that the use of random effects is most beneficial for diseases that are known to be highly polygenic: hypertension (HT) and bipolar disorder (BD). For HT, there are no significant associations in the WTCCC data. The best existing model yields an AUC of 54%, while GeRSI improves it to 59%. For BD, using GeRSI improves the AUC from 55% to 62%. For individuals ranked at the top 10% of BD risk predictions, using GeRSI substantially increases the BD relative risk from 1.4 to 2.5.Comment: main text: 14 pages, 3 figures. Supplementary text: 16 pages, 21 figure

Impacts of land cover data selection and trait parameterisation on dynamic modelling of species' range expansion

Peer reviewedPublisher PD

Mixture models for distance sampling detection functions

Funding: EPSRC DTGWe present a new class of models for the detection function in distance sampling surveys of wildlife populations, based on finite mixtures of simple parametric key functions such as the half-normal. The models share many of the features of the widely-used “key function plus series adjustment” (K+A) formulation: they are flexible, produce plausible shapes with a small number of parameters, allow incorporation of covariates in addition to distance and can be fitted using maximum likelihood. One important advantage over the K+A approach is that the mixtures are automatically monotonic non-increasing and non-negative, so constrained optimization is not required to ensure distance sampling assumptions are honoured. We compare the mixture formulation to the K+A approach using simulations to evaluate its applicability in a wide set of challenging situations. We also re-analyze four previously problematic real-world case studies. We find mixtures outperform K+A methods in many cases, particularly spiked line transect data (i.e., where detectability drops rapidly at small distances) and larger sample sizes. We recommend that current standard model selection methods for distance sampling detection functions are extended to include mixture models in the candidate set.Publisher PDFPeer reviewe