Reflections on statistical modelling:A conversation with Murray Aitkin

A virtual interview with Murray Aitkin by Brian Francis and John Hinde, two of the original members of the Centre for Applied Statistics that Murray created at Lancaster University. The talk ranges over Murray's reflections of a career in statistical modelling and the many different collaborations across the world that have been such a significant part of it

Bayesian evidence as a tool for comparing datasets

We introduce a new conservative test for quantifying the consistency of two or more datasets. The test is based on the Bayesian answer to the question, ``How much more probable is it that all my data were generated from the same model system than if each dataset were generated from an independent set of model parameters?''. We make explicit the connection between evidence ratios and the differences in peak chi-squared values, the latter of which are more widely used and more cheaply calculated. Calculating evidence ratios for three cosmological datasets (recent CMB data (WMAP, ACBAR, CBI, VSA), SDSS and the most recent SNe Type 1A data) we find that concordance is favoured and the tightening of constraints on cosmological parameters is indeed justified.Comment: 4 pages, accepted by Phys. Rev.

Symbolic Formulae for Linear Mixed Models

A statistical model is a mathematical representation of an often simplified or idealised data-generating process. In this paper, we focus on a particular type of statistical model, called linear mixed models (LMMs), that is widely used in many disciplines e.g.~agriculture, ecology, econometrics, psychology. Mixed models, also commonly known as multi-level, nested, hierarchical or panel data models, incorporate a combination of fixed and random effects, with LMMs being a special case. The inclusion of random effects in particular gives LMMs considerable flexibility in accounting for many types of complex correlated structures often found in data. This flexibility, however, has given rise to a number of ways by which an end-user can specify the precise form of the LMM that they wish to fit in statistical software. In this paper, we review the software design for specification of the LMM (and its special case, the linear model), focusing in particular on the use of high-level symbolic model formulae and two popular but contrasting R-packages in lme4 and asreml

Co‐foundress confinement elicits kinship effects in a naturally sub‐social parasitoid

Kinship among interacting individuals is often associated with sociality and also with sex ratio effects. Parasitoids in the bethylid genus Goniozus are sub-social, with single foundress females exhibiting post-ovipositional maternal care via short-term aggressive host and brood defence against conspecific females. Due to local mate competition (LMC) and broods normally being produced by a single foundress, sex ratios are female biased. Contests between adult females are, however, not normally fatal and aggression is reduced when competing females are kin, raising the possibility of multi-foundress reproduction on some hosts. Here we screen for further life-history effects of kinship by varying the numbers and relatedness of foundresses confined together with a host resource and also by varying the size of host. We confined groups of 1 to 8 Goniozus nephantidis females together with a host for 5+ days. Multi-foundress groups were either all siblings or all non-siblings. Our chief expectations included that that competition for resources would be more intense among larger foundress groups but diminished by both larger host size and closer foundress relatedness, affecting both foundress mortality and reproductive output. From classical LMC theory, we expected that offspring group sex ratios would be less female biased when there were more foundresses and from extended LMC theory we expected that sex ratios would be more female biased when foundresses were close kin. We found that confinement led to the death of some females (11% overall) but only when host resources were most limiting. Mortality of foundresses was less common when foundresses were siblings. Developmental mortality among offspring was considerably higher in multi-foundress clutches but was unaffected by foundress relatedness. Groups of sibling foundresses collectively produced similar numbers of offspring to non-sibling groups. There was little advantage for individual females to reproduce in multi-foundress groups: single foundresses suppressed even the largest hosts presented and had the highest per capita production of adult offspring. Despite single-foundress reproduction being the norm, G. nephantidis females in multi-foundress groups appear to attune sex allocation according to both foundress number and foundress relatedness: broods produced by sibling foundresses had sex ratios similar to broods produced by single foundresses (ca. 11% males) whereas the sex ratios of broods produced by non-sibling females were approximately 20% higher and broadly increased with foundress number. We conclude that relatedness and host size may combine to reduce selection against communal reproduction on hosts and that, unlike other studied parasitoids, G. nephantidis sex ratios conform to predictions of both classical and extended LMC theor

Using the posterior distribution of deviance to measure evidence of association for rare susceptibility variants

Aitkin recently proposed an integrated Bayesian/likelihood approach that he claims is general and simple. We have applied this method, which does not rely on informative prior probabilities or large-sample results, to investigate the evidence of association between disease and the 16 variants in the KDR gene provided by Genetic Analysis Workshop 17. Based on the likelihood of logistic regression models and considering noninformative uniform prior probabilities on the coefficients of the explanatory variables, we used a random walk Metropolis algorithm to simulate the distributions of deviance and deviance difference. The distribution of probability values and the distribution of the proportions of positive deviance differences showed different locations, but the direction of the shift depended on the genetic factor. For the variant with the highest minor allele frequency and for any rare variant, standard logistic regression showed a higher power than the novel approach. For the two variants with the strongest effects on Q1 under a type I error rate of 1%, the integrated approach showed a higher power than standard logistic regression. The advantages and limitations of the integrated Bayesian/likelihood approach should be investigated using additional regions and considering alternative regression models and collapsing methods

From bioavailability science to regulation of organic chemicals

The bioavailability of organic chemicals in soil and sediment is an important area of scientific investigation for environmental scientists, although this area of study remains only partially recognized by regulators and industries working in the environmental sector. Regulators have recently started to consider bioavailability within retrospective risk assessment frameworks for organic chemicals; by doing so, realistic decision-making with regard to polluted environments can be achieved, rather than relying on the traditional approach of using total-extractable concentrations. However, implementation remains difficult because scientific developments on bioavailability are not always translated into ready-to-use approaches for regulators. Similarly, bioavailability remains largely unexplored within prospective regulatory frameworks that address the approval and regulation of organic chemicals. This article discusses bioavailability concepts and methods, as well as possible pathways for the implementation of bioavailability into risk assessment and regulation; in addition, this article offers a simple, pragmatic and justifiable approach for use within retrospective and prospective risk assessmen

Sailing into the wind : new disciplines in Australian higher education

Much is made of the potential of lifelong learning for individuals and organisations. In this article we tend to make much less of it, certainly with respect to its use in universities to discipline academics. Nevertheless, we argue that academics now need to re-learn the positions they occupy and the stances they take in response to the marketisation of Australian universities. In particular, we suggest that the position of (pure) critique no longer commands attention in Australian contexts of higher education, although the paper does not suggest a disregard for a critical stance purely for the sake of participation. It is in understanding the interconnections between position and stance , and how they might be strategically performed during the everyday practices of academics, that a more promising way of engaging with the venalities of the market is envisaged; a strategy that could be described as \u27sailing into the wind\u27. In discussing these matters, the paper draws on semi-structured interviews with academics located in university faculties/departments/schools of education along Australia\u27s eastern seaboard