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Copyright and Moral Rights for the articles on this site are retained by the individual authors and/or other copyright owners. For more information on Open Research Online's data policy on reuse of materials please consult the policies page. Exponential families are the workhorses of parametric modelling theory. One reason for their popularity is their… (More)
In this study, we discuss a decision theoretic or fully Bayesian approach to the sample size question in clinical trials with binary responses. Data are assumed to come from two binomial distributions. A Dirichlet distribution is assumed to describe prior knowledge of the two success probabilities p1 and p2. The parameter of interest is p = p1 - p2. The… (More)
In this article, we discuss an optimization approach to the sample size question, founded on maximizing the value of information in comparison studies with binary responses. The expected value of perfect information (EVPI) is calculated and the optimal sample size is obtained by maximizing the expected net gain of sampling (ENGS), the difference between the… (More)
A brief synopsis of progress in differential geometry in statistics is followed by a note of some points of tension in the developing relationship between these disciplines. The preferred point nature of much of statistics is described and suggests the adoption of a corresponding geometry which reduces these tensions. Applications of preferred point… (More)
Di¤erential geometry has found fruitful application in statistical inference. In particular, Amari's (1990) expected geometry is used in higher order asymptotic analysis, and in the study of su¢ciency and ancillarity. However, we can see three drawbacks to the use of a di¤erential geometric approach in econometrics and statistics more generally. Firstly,… (More)
This paper lays the foundations for a new framework for numerically and computationally applying information geometric methods to statistical modelling.
This paper lays the foundations for a unified framework for numerically and computationally applying methods drawn from a range of currently distinct geometrical approaches to statistical modelling. In so doing, it extends information geometry from a manifold based approach to one where the simplex is the fundamental geometrical object, thereby allowing… (More)
This paper applies the tools of computation information geometry  – in particular, high dimensional extended multinomial families as proxies for the 'space of all distributions' – in the inferentially demanding area of statistical mixture modelling. A range of resultant benefits are noted.