Massey Documents by Type

Permanent URI for this communityhttps://mro.massey.ac.nz/handle/10179/294

Browse

Subject: search.filters.subject.Bayesian statistical decision theory

Search Results

Now showing 1 - 3 of 3
  • Thumbnail Image
    Item
    The Bayesian approach to statistics : a review of methodology with selected applications : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Statistics at Massey University
    (Massey University, 1984) Wood, Shane Byram
    In this thesis we present a review of the Bayesian approach to Statistical Inference. In Chapter One we develop the theory and methodology behind the approach. Starting from its basis in subjective probability we outline the Bayesian philosophy towards such problems as Point and Interval estimation, Hypothesis testing and Decision Theory. For each of these areas, we indicate the corresponding Classical approach and comment on the differences between this and the Bayesian one. We then develop the idea of conjugate families of prior distributions which is central to the practice of Bayesian statistics, and follow this with a section on the assessment of subjective probability distributions, their functional specification and the problem of mathematically representing a state of 'ignorance'. The Decision Theoretic approach to statistical analysis is then integrated into the Bayesian framework, and reference is made to the assessment of 'loss' functions, and their subjective nature. Finally we consider the concepts of Empirical Bayes, Exchangeability, and Likelihood, and their relevence to the Bayesian scheme. Chapter Two consists of a review of areas such as econometrics, medicine, industry, and education, where Bayesian methods have been applied, accompanied by a number of particularly interesting applications which illustrate the principles outlined in chapter one.
  • Thumbnail Image
    Item
    Bayesian methods to address multiple comparisons and misclassification bias in studies of occupational and environmental risks of cancer : a thesis by publications presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Public Health, Massey University, Wellington, New Zealand
    (Massey University, 2013) Corbin, Marine
    In this thesis I explore the application of several Bayesian approaches, implemented with standard statistical software, in environmental and occupational epidemiology. These methods are applied to case-control studies of occupational risks for lung and upper aerodigestive tract cancers conducted in New Zealand and Europe. The findings are of interest in themselves, but the focus of the thesis is on the application of Bayesian methods to produce these findings. It is not intended to represent a comprehensive overview of all Bayesian methods, but rather to explore Bayesian methods which are most appropriate for the studies which are presented here. In the first section, I review the underlying theory involved in such analyses. In the second section, I use Bayesian methods to address the problem of multiple comparisons. In occupational case-control studies, we may collect information on hundreds of occupations/exposures for which there is little or no prior evidence. For those occupations/exposures, we get a false positive finding by chance about 5% of the time. This means that if we repeat the study in a new population, these chance associations are likely to exhibit ‘regression to the mean’ and will not show such extreme risks again. Bayesian methods can be used to ‘shrink’ effect estimates based on how strong the regression to the mean is likely to be. In the third section, I use Bayesian methods for assessing and correcting systematic error. Although the methods I use can be applied to several situations (selection bias, misclassification, residual confounding), I apply them to the specific situation of misclassification of the main exposure. In particular, I apply four different methods for such sensitivity analyses: multiple imputation for measurement error (MIME); imputation based on specifying the sensitivity and specificity (SS), Direct Imputation (DI) of the ‘true’ exposure using a regression model for the predictive values and imputation based on a fully Bayesian analysis. I conclude by summarising the strengths, limitations, and areas of future development for the use of these methods. It is anticipated that, in 5-10 years time, such analyses may become standard supplements to ‘traditional’ forms of analysis, i.e. that Bayesian methods may be routinely used, and may form part of the ‘epidemiological toolkit’ for assessing and correcting for both random and systematic error.
  • Thumbnail Image
    Item
    Computationally tractable fitting of graphical models : the cost and benefits of decomposable Bayesian and penalized likelihood approaches : a thesis presented in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Statistics at Massey University, Albany, New Zealand
    (Massey University, 2012) Fitch, Anne Marie
    Gaussian graphical models are a useful tool for eliciting information about relationships in data with a multivariate normal distribution. In the rst part of this thesis we demonstrate that partial correlation graphs facilitate di erent and better insight into high-dimensional data than sample correlations. This raises the question of which method one should use to model and estimate the parameters. In the second, and major part, we take a more theoretical focus examining the costs and bene ts of two popular approaches to model selection and parameter estimation (penalized likelihood and decomposable Bayesian) when the true graph is non-decomposable. We rst consider the e ect a restriction to decomposable models has on the estimation of both the inverse covariance matrix and the covariance matrix. Using the variance as a measure of variability we compare non-decomposable and decomposable models. Here we nd that, if the true model is non-decomposable, the variance of estimates is demonstrably larger when a decomposable model is used. Although the cost in terms of accuracy is fairly small when estimating the inverse covariance matrix, this is not the case when estimation of the covariance matrix is the goal. In this case using a decomposable model caused up to 200-fold increases in the variance of estimates. Finally we compare the latest decomposable Bayesian method (the feature-inclusion stochastic search) with penalized likelihood methods (graphical lasso and adaptive graphical lasso) on measures of model selection and prediction performance. Here we nd that graphical lasso is clearly outclassed on all measures by both adaptive graphical lasso and feature-inclusion stochastic search. The sample size and the ultimate goal of the estimation will determine whether adaptive graphical lasso or feature-inclusion stochastic search is better.