A general framework for updating belief distributions.

We propose a framework for general Bayesian inference. We argue that a valid update of a prior belief distribution to a posterior can be made for parameters which are connected to observations through a loss function rather than the traditional likelihood function, which is recovered as a special case. Modern application areas make it increasingly challenging for Bayesians to attempt to model the true data-generating mechanism. For instance, when the object of interest is low dimensional, such as a mean or median, it is cumbersome to have to achieve this via a complete model for the whole data distribution. More importantly, there are settings where the parameter of interest does not directly index a family of density functions and thus the Bayesian approach to learning about such parameters is currently regarded as problematic. Our framework uses loss functions to connect information in the data to functionals of interest. The updating of beliefs then follows from a decision theoretic approach involving cumulative loss functions. Importantly, the procedure coincides with Bayesian updating when a true likelihood is known yet provides coherent subjective inference in much more general settings. Connections to other inference frameworks are highlighted.

Quantification of subclonal distributions of recurrent genomic aberrations in paired pre-treatment and relapse samples from patients with B-cell chronic lymphocytic leukemia.

Genome-wide array approaches and sequencing analyses are powerful tools for identifying genetic aberrations in cancers, including leukemias and lymphomas. However, the clinical and biological significance of such aberrations and their subclonal distribution are poorly understood. Here, we present the first genome-wide array based study of pre-treatment and relapse samples from patients with B-cell chronic lymphocytic leukemia (B-CLL) that uses the computational statistical tool OncoSNP. We show that quantification of the proportion of copy number alterations (CNAs) and copy neutral loss of heterozygosity regions (cnLOHs) in each sample is feasible. Furthermore, we (i) reveal complex changes in the subclonal architecture of paired samples at relapse compared with pre-treatment, (ii) provide evidence supporting an association between increased genomic complexity and poor clinical outcome (iii) report previously undefined, recurrent CNA/cnLOH regions that expand or newly occur at relapse and therefore might harbor candidate driver genes of relapse and/or chemotherapy resistance. Our findings are likely to impact on future therapeutic strategies aimed towards selecting effective and individually tailored targeted therapies.

CNV discovery using SNP genotyping arrays.

Genome-wide single nucleotide polymorphism (SNP) genotyping platforms have made an important contribution to population genetics and genetic epidemiology. Recently there has been a realisation that these SNP platforms can also be used for typing copy number variants (CNVs). This allows for 'generalised' genotyping of both SNPs and CNVs simultaneously on a common sample set, with advantages in terms of cost and unified analysis. In this article we review various statistical approaches to calling CNVs from SNP data. We highlight three tiers of algorithms depending on the level of information used.

Generalized monotonic regression using random change points.

We introduce a procedure for generalized monotonic curve fitting that is based on a Bayesian analysis of the isotonic regression model. Conventional isotonic regression fits monotonically increasing step functions to data. In our approach we treat the number and location of the steps as random. For each step level we adopt the conjugate prior to the sampling distribution of the data as if the curve was unconstrained. We then propose to use Markov chain Monte Carlo simulation to draw samples from the unconstrained model space and retain only those samples for which the monotonic constraint holds. The proportion of the samples collected for which the constraint holds can be used to provide a value for the weight of evidence in terms of Bayes factors for monotonicity given the data. Using the samples, probability statements can be made about other quantities of interest such as the number of change points in the data and posterior distributions on the location of the change points can be provided. The method is illustrated throughout by a reanalysis of the leukaemia data studied by Schell and Singh.

Bayesian partitioning for estimating disease risk.

This paper presents a Bayesian nonlinear approach for the analysis of spatial count data. It extends the Bayesian partition methodology of Holmes, Denison, and Mallick (1999, Bayesian partitioning for classification and regression, Technical Report, Imperial College, London) to handle data that involve counts. A demonstration involving incidence rates of leukemia in New York state is used to highlight the methodology. The model allows us to make probability statements on the incidence rates around point sources without making any parametric assumptions about the nature of the influence between the sources and the surrounding location.

Bayesian wavelet networks for nonparametric regression.

Radial wavelet networks have recently been proposed as a method for nonparametric regression. In this paper we analyze their performance within a Bayesian framework. We derive probability distributions over both the dimension of the networks and the network coefficients by placing a prior on the degrees of freedom of the model. This process bypasses the need to test or select a finite number of networks during the modeling process. Predictions are formed by mixing over many models of varying dimension and parameterization.We show that the complexity of the models adapts to the complexity of the data and produces good results on a number of benchmark test series.

Dietary chitosan inhibits hypercholesterolaemia and atherogenesis in the apolipoprotein E-deficient mouse model of atherosclerosis.

Chitosan, the deacetylated form of chitin, is extracted from the shells of crustaceans. The strong positive charge carried by the chitosan molecule causes it to bind negatively charged substrates such as lipids. Orally administered chitosan binds fat in the intestine, blocking absorption, and has been shown to lower blood cholesterol in animals and humans. As a result it has been proposed that dietary supplementation with chitosan may inhibit the formation of atherosclerotic plaque. We have tested this hypothesis using the apolipoprotein E-deficient mouse model of atherosclerosis. This hypercholesterolaemic animal develops atherosclerosis without the need for dietary or surgical intervention. The apolipoprotein E-deficient mouse therefore provides an ideal model in which to study the effects of dietary chitosan on both blood cholesterol and atherosclerosis. Animals were fed for 20 weeks on a diet containing 5% chitosan or on a control diet. Blood cholesterol levels were significantly lower in the chitosan fed animals throughout the study, and at 20 weeks were 64% of control levels. When the area of aortic plaque in the two groups was compared a highly significant inhibition of atherogenesis, in both the whole aorta and the aortic arch, was observed in the chitosan fed animals--42 and 50%, respectively. Body growth was significantly greater in the chitosan fed animals. This study is the first to show a direct correlation between lowering of serum cholesterol with chitosan and inhibition of atherogenesis, and suggests that the agent could be used to inhibit the development of atherosclerosis in individuals with hypercholesterolaemia.