Recent work by Ding and Kay has demonstrated that the Bayesian information criterion (BIC) is an inconsistent estimator of model order in nested model selection as the noise variance τ*→ 0. Unfortunately, Ding and Kay have erroneously concluded that the minimum description length (MDL) principle also leads to inconsistent estimates of model order in this setting by equating BIC with MDL. This correspondence shows that only the earlier MDL criterion based on asymptotic assumptions has this problem, and proves that the new MDL linear regression criteria based on normalized maximum likelihood and Bayesian mixture codes satisfy the notion of consistency as τ*→ 0. The main result may be used as a basis to easily establish similar consistency results for other closely related information theoretic regression criteria.

Most published GWAS do not examine SNP interactions due to the high computational complexity of computing p-values for the interaction terms. Our aim is to utilize supercomputing resources to apply complex statistical techniques to the world's accumulating GWAS, epidemiology, survival and pathology data to uncover more information about genetic and environmental risk, biology and aetiology. We performed the Bayesian Posterior Probability test on a pseudo data set with 500,000 single nucleotide polymorphism and 100 samples as proof of principle. We carried out strong scaling simulations on 2 to 4,096 processing cores with factor 2 increments in partition size. On two processing cores, the run time is 317h, i.e. almost two weeks, compared to less than 10 minutes on 4,096 processing cores. The speedup factor is 2,020 that is very close to the theoretical value of 2,048. This work demonstrates the feasibility of performing exhaustive higher order analysis of GWAS studies using independence testing for contingency tables. We are now in a position to employ supercomputers with hundreds of thousands of threads for higher order analysis of GWAS data using complex statistics.

Background CDKN2A mutations confer a substantial risk of cutaneous melanoma; however, the magnitude of risk is uncertain. Methods The study estimated the hazard ratio (HR) and the average age specific cumulative risk (ie, penetrance) of reported melanoma for CDKN2A mutation carriers in case families using a modified segregation analysis of the first and higher degree relatives of 35 population-based cases. The study sample included 223 relatives of 13 melanoma cases diagnosed when aged 18–39 years from Melbourne, Sydney and Brisbane, Australia, and 322 relatives of 22 melanoma cases diagnosed at any age from Yorkshire, UK. Results The estimated HR for melanoma for mutation carriers relative to the general population decreased with regions of increasing ambient ultraviolet (UV) irradiance, being higher for the UK than Australia (87, 95% CI 50 to 153 vs 31, 95% CI 20 to 50, p=0.008), and across Australia, 49 (95% CI 24 to 98) for Melbourne, 44 (95% CI 22 to 88) for Sydney, and 9 (95% CI 2 to 33) for Brisbane (p=0.02). Penetrance did not differ by geographic region. It is estimated that 16% (95% CI 10% to 27%) of UK and 20% (95% CI 13% to 30%) of Australian CDKN2A mutation carriers would be diagnosed with melanoma by age 50 years, and 45% (95% CI 29% to 65%) and 52% (95% CI 37% to 69%), respectively, by age 80 years. Conclusions Contrary to the strong association between UV radiation exposure and melanoma risk for the general population, CDKN2A mutation carriers appear to have the same cumulative risk of melanoma irrespective of the ambient UV irradiance of the region in which they live.

This paper examines the estimation of the order of an autoregressive model using the minimum description length principle. A closed form for an approximation of the parametric complexity of the autoregressive model class is derived by exploiting a relationship between coefficients and partial autocorrelations. The parametric complexity over the complete parameter space is found to diverge. A model selection criterion is subsequently derived by bounding the parameter space, and simulations suggest that it compares well against standard autoregressive order selection techniques in terms of correct order identification and prediction error.

1 IBM Research Collaboratory for Life Sciences-Melbourne, Carlton, Australia, {reumann; John.Wagner; mattdton; stevemoore@au1.ibm.com} 2 Dept. Microbiology and Immunology, University of Melbourne, Carlton, Australia, {kholt; tstinear, sjturner}@unimelb.edu.au 3 Walter and Eliza Hall Institute in Melbourne, Australia, inouye@wehi.edu.au 4 Dept. Computer Science and Software Engineering, University of Melbourne, Carlton, Australia, {bwgoudey; gabraham}@csse.unimelb.edu.au; {qwan; adrianrp; jz}@unimelb.edu.au 5 National ICT Australia, Victoria Research Laboratories, Carlton, Australia, {Fan.Shi; adam.kowalczyk@nicta.com.au} 6 Victorian Life Sciences Computation Initiative, Carlton, Australia, {aisaac; bjpope@unimelb.edu.au} 7 Dept. of Medicine, University of Melbourne, Carlton, Australia {butz; slavep; obrientj@unimelb.edu.au 8 Deakin University, Science and Technology pcc@deakin.edu.au Howard Florey Institute, Carlton, Australia, Judith.field@florey.edu.au 10 Dept. of Pathology, University of Melbourne, msouthey@unimelb.edu.au 11 Peter MacCullum Cancer Center, Melbourne, David.Bowtell@petermac.org 12 Melbourne School of Population Health, University of Melbourne, Carlton, Australia