CARISMA-LMS Workshop on Statistics for Risk Analysis

Transcription

1 Department of Mathematics CARISMA-LMS Workshop on Statistics for Risk Analysis Thursday 28 th May 2015 Location: Department of Mathematics, John Crank Building, Room JNCK128 (Campus map can be found at ) Programme Welcome and Registration 10:30 Prof David Banks, Duke University Adversarial Risk Analysis Overview 11:20 Tea break 11:30 Prof David Banks, Duke University ARA for Auctions 12:10 Dr Hauke Riesch, Brunel University London Levels of Uncertainty 12:50 Lunch 13:40 Prof James Taylor, Oxford University Probabilistic Forecasting of Wind Power Ramps using Autoregressive Logit Models 14:20 Dr Ujjwal Bharadwaj, TWI in Cambridge Industry applications of risk assessment techniques in the integrity 15:00 Tea break 15:10 Dr Alex Lewin, Brunel University London Bayesian hierarchical models for large-scale data integration and variable selection

2 15:50 Prof John Quigley, University of Strathclyde Empirical Bayes Approach to Ranking Suppliers with Heterogeneous Operational Experience 16:30 end Registration Details The registration is free. However, for catering numbers please Dr Keming Yu by Thursday 21 st May to confirm your attendance.

3 Abstracts Adversarial Risk Analysis Overview Author: David Banks Adversarial Risk Analysis (ARA) is a Bayesian approach to strategic decision-making. One builds a model of one's opponents, expressing subjective uncertainty about the solution concept each opponent uses, as well as their utilities, probabilities, and capabilities. Within that framework, the decision-maker makes the choice that maximizes expected utility. ARA allows the opponent to seek a Nash equilibrium solution, or a mirroring equilibrium, or to use level-k thinking, or prospect theory, and so forth, and it allows the decision-maker to relax the common-knowledge assumption that arises in classical game theory. The methodology applies to corporate competition and counterterrorism. The main ideas are illustrated in the context of the Borel game La Relance, the Defend-Attack game, and a convoy-routing problem. Levels of Uncertainty Author: Hauke Riesch There exist a variety of different understandings, definitions, and classifications of risk, which can make the resulting landscape of academic literature on the topic seem somewhat disjointed and often confusing. I will introduce a map on how to think about risks, and in particular uncertainty, which is arranged along the different questions of what the different academic disciplines find interesting about risk. This aims to give a more integrated idea of where the different literatures intersect and thus provide some order in our understanding of what risk is and what is interesting about it. One particular dimension will be presented in more detail, answering the question of what exactly we are uncertain about and distinguishing between five different levels of uncertainty. I will argue, through some concrete examples, that concentrating on the objects of uncertainty can give us an appreciation on how different perspectives on a given risk scenario are formed and will use the more general map to show how this perspective intersects with other classifications and analyses of risk. Probabilistic Forecasting of Wind Power Ramps using Autoregressive Logit Models Author: James W. Taylor A challenge for the efficient operation of power systems and wind farms is the occurrence of wind power ramps, which are sudden large changes in the power output from a wind farm. This paper considers the probabilistic forecasting of a ramp, defined as exceedance beyond

4 a specified threshold. We directly model the exceedance probability using autoregressive logit models fitted to the change in wind power. These models can be estimated by maximizing a Bernoulli likelihood. To try to capture the extent to which an observation does or does not exceed the threshold, we also consider a likelihood-based on the asymmetric Laplace density, which has previously been employed for quantile estimation. We introduce a model that simultaneously estimates the ramp probabilities for different thresholds using a multinomial logit structure and categorical distribution. To model jointly the probability of ramps at more than one wind farm, we develop a multinomial logit formulation, with parameters estimated using a bivariate Bernoulli distribution. We use a similar approach in a model for jointly predicting one and two steps-ahead. We provide empirical results based on hourly wind power data. Industry applications of risk assessment techniques in the integrity management of assets Author: Ujjwal Bharadwaj There is increasing acceptance of risk based approaches in the integrity management of assets. Faced with budgetary constraints, integrity managers are often under pressure to prioritise their inspection and maintenance resources such that the reliability and availability of their assets remain within acceptable or target levels. The presentation will start with an overview of the risk based approaches as applied to integrity management and then present case studies from industry showing the application of some of the techniques for risk assessment. The case studies will include probabilistic models to assess damage due to fracture, corrosion and creep mechanisms. In addition, the importance of taking a systems engineering approach in the context of risk assessments and how it can be applied will be presented. Bayesian hierarchical models for large-scale data integration and variable selection Author: Alex Lewin Genetic association studies are used to find regions of the genome associated with phenotypes of interest. Most association studies to date have been carried out for a single phenotype, or for small combination of phenotypes, with a single regression being performed for each marker. Rather than carrying out thousands of separate univariate analyses, we model all the data simultaneously. We use the Bayesian model HESS (Hierarchical Evolutionary Stochastic Search) developed by Bottolo et al. 2011, for detecting genetic regulation of gene

5 expression, in particular for finding genetic markers which are associated with multiple expression or metabolite phenotypes. The hierarchical formulation incorporates a regression model for each phenotype against all the genetic markers, with a sparsity prior to induce variable selection amongst the markers. The Bayesian hierarchical model treats the multiple phenotypes in parallel, enabling information sharing across phenotypes, whilst allowing for different markers to be associated with different phenotypes. We discuss several output measures and decision theoretic tools for declaring gene-metabolite associations and hotspots', genetic markers associated with multiple phenotypes. Bottolo L., Petretto E., Blankenberg S., Cambien F., Cook S., Tiret L. and Richardson S. 2011, Bayesian Detection of Expression Quantitative Trait Loci Hot Spots, Genetics, Vol. 189, Empirical Bayes Approach to Ranking Suppliers with Heterogeneous Operational Experience Author: John Quigley Ranking can be used to help managers prioritise which suppliers are under or over performing and so allocate limited resources more appropriately. Sensible ranking can be challenging when confronted with variability of experience across a pool of suppliers and it has been reported in the literature that naive ranks based on simple performance measures can be inappropriate. For this presentation we are concerned with ranking based on count data, such as the number of late deliveries or the number of non-conformances, which we model using Homogeneous Poisson Processes (HPP) where the underlying rate varies across suppliers. Empirical Bayes methods provide a useful inference framework for supporting estimates of such rates through first pooling data across the pool to obtain an overall average rate and subsequently adjusting this for each supplier subject to their performance. We explore how ranking can be based on alternative summary statistics and the associated computational challenges of identifying significant differences in ranks between suppliers. We propose a process for supporting inference which we evaluate through simulation and in a case study.