 STATISTICS SEMINAR
 Speaker: Dr Frank Tuyl, School of Mathematical and Physical Sciences, The University of Newcastle
 Title: From Bayes' theorem to Bayesian inference: some simple examples
 Location: Room W104, Behavioural Sciences Building (Callaghan Campus) The University of Newcastle
 Time and Date: 3:00 pm, Fri, 6^{th} Oct 2017
 Abstract:
Starting with Bayes' theorem that "we all agree on", I will argue that the step towards Bayesian inference seems rather small. I will give some simple examples of advantages of Bayesian over classical inference: 1. automatic inclusion of known constraints and 2. straightforward inference for functions of parameters.
Another point I will make is that posterior distributions (of unknown parameters) are often equivalent to sampling distributions (of estimators) required for classical inference. However, when the latter are difficult/impossible to obtain, and Normal approximations are applied, the former tend to be clearly preferable for inference.
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 STATISTICS SEMINAR
 Speaker: Dr Frank Tuyl, School of Mathematical and Physical Sciences, The University of Newcastle
 Title: On the multinomial, priors and zero counts
 Location: Room V103, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 3:00 pm, Fri, 16^{th} Sep 2016
 Abstract:
This talk is about estimation of multinomial parameters, from both Bayesian and nonBayesian points of view, and presents an interesting link between the two. Jeffreys (1939) derived the uniform prior as the default prior for the Bayesian approach, by considering a multivariate hypergeometric model first. More recently, different 'reference' and 'overall objective' priors have been proposed. I argue that, especially in the presence of zero counts, these priors are too informative, and that there is no need to deviate from the uniform prior. Things are different when relatively many zero counts are present, however, and I will describe a generalisation of an existing approach to the binomial case of successes or failures only, allowing for (practically) zero parameters. This method seems to handle very well an extreme example provided by Prof. Jim Berger, when discussing the above candidate priors.
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 STATISTICS SEMINAR
 Speaker: Dr Frank Tuyl, School of Mathematical and Physical Sciences, The University of Newcastle
 Title: Can we please agree on this interval for the binomial parameter?
 Location: Room V101, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 3:15 pm, Fri, 26^{th} Apr 2013
 Abstract:
For Bayesian estimation of the binomial parameter, when the aim is to
"let the data speak for themselves", the uniform or BayesLaplace
prior appears preferable to the reference/Jeffreys prior recommended by
objective Bayesians like Berger and Bernardo.
Here confidence intervals tend to be "exact" or "approximate",
aiming for either minimum or mean coverage to be close to nominal. The
latter criterion tends to be preferred, subject to "reasonable"
minimum coverage. I will first reiterate examples of how the highest
posterior density (HPD) credible interval based on the uniform prior
appears to outperform both common approximate intervals and Jeffreys
prior based intervals, which usually represent credible intervals in
review articles.
Second, an important aspect of the recommended interval is that it may
be seen to be invariant under transformation when taking into account
the likelihood function. I will also show, however, that this use of the
likelihood does not always lead to excellent, or even adequate,
frequentist coverage.
Third, this approach may be extended to nuisance parameter cases by
considering an "appropriate" likelihood of the parameter of
interest. For example, quantities arising from the 2x2 contingency table
(e.g. odds ratio and relative risk) are important practical
applications, apparently leading to intervals with better frequentist
performance than that found for HPD or central credible intervals.
Preliminary results suggest the same for "difficult" problems such
as the ratio of two Normal means ("FiellerCreasy") and the binomial
N problem.
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