Exploration of a novel bootstrap technique for estimating the distribution of outstanding claims reserves in general insurance

This is a report on an exploration of the effectiveness of a novel non-parametric bootstrap method for estimating claims reserves, which we call the local chain ladder bootstrap technique. The method is simple and can readily be implemented in a spreadsheet. In addition analytic estimates of the first few moments of reserves are shown to the readily evaluated, obviating the need for simulation if desired. The behaviour of the method on three datasets is presented and compared to published predictions of some other stochastic methods. In addition, a small study of the method using simulated claims triangles is presented and compared with other stochastic models

Identification and separation of DNA mixtures using peak area information

We introduce a new methodology, based upon probabilistic expert systems, for analysing forensic identification problems involving DNA mixture traces using quantitative peak area information. Peak area is modelled with conditional Gaussian distributions. The expert system can be used for ascertaining whether individuals, whose profiles have been measured, have contributed to the mixture. It can also be used to predict DNA profiles of unknown contributors by separating the mixture into its individual components. The potential of our probabilistic methodology is illustrated on case data examples and compared with alternative approaches. The advantages are that identification and separation issues can be handled in a unified way within a single probabilistic model and the uncertainty associated with the analysis is quantified. Further work, required to bring the methodology to a point where it could be applied to the routine analysis of casework, is discussed.

Probabilistic expert systems for handling artifacts in complex DNA mixtures

This paper presents a coherent probabilistic framework for taking account of allelic dropout, stutter bands and silent alleles when interpreting STR DNA profiles from a mixture sample using peak size information arising from a PCR analysis. This information can be exploited for evaluating the evidential strength for a hypothesis that DNA from a particular person is present in the mixture. It extends an earlier Bayesian network approach that ignored such artifacts. We illustrate the use of the extended network on a published casework example

A simple greedy algorithm for reconstructing pedigrees

This paper introduces a simple greedy algorithm for searching for high likelihood pedigrees using micro-satellite (STR) genotype information on a complete sample of related individuals. The core idea behind the algorithm is not new, but it is believed that putting it into a greedy search setting, and specifically the application to pedigree learning, is novel. The algorithm does not require age or sex information, but this information can be incorporated if desired. The algorithm is applied to human and non-human genetic data and in a simulation study

Identification and separation of DNA mixtures using peak area information (Updated version of Statistical Research Paper No. 25)

We introduce a new methodology, based upon probabilistic expert systems, for analysing forensic identification problems involving DNA mixture traces using quantitative peak area information. Peak area is modelled with conditional Gaussian distributions. The expert system can be used for ascertaining whether individuals, whose profiles have been measured, have contributed to the mixture, but also to predict DNA profiles of unknown contributors by separating the mixture into its individual components. The potential of our probabilistic methodology is illustrated on case data examples and compared with alternative approaches. The advantages are that identification and separation issues can be handled in a unified way within a single probabilistic model and the uncertainty associated with the analysis is quantified. Further work, required to bring the methodology to a point where it could be applied to the routine analysis of casework, is discussed

The quest for a donor: probability based methods offer help

When a patient in need of a stem cell transplant has no compatible donor within his or her closest family, and no matched unrelated donor can be found, a remaining option is to search within the patient’s extended family. This situation often arises when the patient is of an ethnic minority, originating from a country that lacks a well-developed stem cell donor program, and has HLA haplotypes that are rare in his or her country of residence. Searching within the extended family may be time-consuming and expensive, and tools to calculate the probability of a match within groups of untested relatives would facilitate the search. We present a general approach to calculating the probability of a match in a given relative, or group of relatives, based on the pedigree, and on knowledge of the genotypes of some of the individuals. The method extends previous approaches by allowing the pedigrees to be consanguineous and arbitrarily complex, with deviations from Hardy-Weinberg equilibrium. We show how this extension has a considerable effect on results, in particular for rare haplotypes. The methods are exemplified using freeware programs to solve a case of practical importance

Causal discovery through MAP selection of stratified chain event graphs

We introduce a subclass of chain event graphs that we call stratified chain event graphs, and present a dynamic programming algorithm for the optimal selection of such chain event graphs that maximizes a decomposable score derived from a complete independent sample. We apply the algorithm to such a dataset, with a view to deducing the causal structure of the variables under the hypothesis that there are no unobserved confounders. We show that the algorithm is suitable for small problems. Similarities with and differences to a dynamic programming algorithm for MAP learning of Bayesian networks are highlighted, as are the relations to causal discovery using Bayesian networks

Estimation of Parameters in DNA Mixture Analysis

In Cowell et al. (2007), a Bayesian network for analysis of mixed traces of DNA was presented using gamma distributions for modelling peak sizes in the electropherogram. It was demonstrated that the analysis was sensitive to the choice of a variance factor and hence this should be adapted to any new trace analysed. In the present paper we discuss how the variance parameter can be estimated by maximum likelihood to achieve this. The unknown proportions of DNA from each contributor can similarly be estimated by maximum likelihood jointly with the variance parameter. Furthermore we discuss how to incorporate prior knowledge about the parameters in a Bayesian analysis. The proposed estimation methods are illustrated through a few examples of applications for calculating evidential value in casework and for mixture deconvolution