Guaranteed Accuracy of Semi-Modular Posteriors

Bayesian inference has widely acknowledged advantages in many problems, but it can also be unreliable when the model is misspecified. Bayesian modular inference is concerned with complex models which have been specified through a collection of coupled submodels, and is useful when there is misspecification in some of the submodels. The submodels are often called modules in the literature. Cutting feedback is a widely used Bayesian modular inference method which ensures that information from suspect model components is not used in making inferences about parameters in correctly specified modules. However, it may be hard to decide in what circumstances this ``cut posterior'' is preferred to the exact posterior. When misspecification is not severe, cutting feedback may increase the uncertainty in Bayesian posterior inference greatly without reducing estimation bias substantially. This motivates semi-modular inference methods, which avoid the binary cut of cutting feedback approaches. In this work, we precisely formalize the bias-variance trade-off involved in semi-modular inference for the first time in the literature, using a framework of local model misspecification. We then implement a mixture-based semi-modular inference approach, demonstrating theoretically that it delivers inferences that are more accurate, in terms of a user-defined loss function, than either the cut or full posterior on its own. The new method is demonstrated in a number of applications

Structural and functional analysis of a phospho-dependent molecular switch : Rv1827 from Mycobacterium tuberculosis

Forkhead-associated (FHA) domains have gained considerable prominence as ubiquitous phosphothreonine-dependent binding modules; however, their precise roles in Ser/Thr kinase pathways and mechanisms of regulation remain unclear. From experiments with Rv1827, an FHA domain–containing protein from Mycobacterium tuberculosis, a complete molecular description of an FHA-mediated Ser/Thr protein kinase signalling process is derived. First, binding of the FHA domain to each of three metabolic enzyme complexes regulates their catalytic activities but does not require priming phosphorylation. However, phosphorylation of a threonine residue within a conserved N-terminal motif of Rv1827 triggers its intramolecular association with the FHA domain of Rv1827, thus blocking its interactions with each of the three enzymes. The nuclear magnetic resonance structure of this inactivated form and further mutagenic studies show how a novel intramolecular phospho-switch blocks the access of the target enzymes to a common FHA interaction surface and how this shared surface accommodates three functionally related, but structurally diverse, binding partners. Thus a remarkable and unsuspected versatility in the FHA domain that allows for the transformation of multiple kinase inputs into various downstream regulatory signals has been revealed.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Improving the Accuracy of Marginal Approximations in Likelihood-Free Inference via Localisation

Likelihood-free methods are an essential tool for performing inference for implicit models which can be simulated from, but for which the corresponding likelihood is intractable. However, common likelihood-free methods do not scale well to a large number of model parameters. A promising approach to high-dimensional likelihood-free inference involves estimating low-dimensional marginal posteriors by conditioning only on summary statistics believed to be informative for the low-dimensional component, and then combining the low-dimensional approximations in some way. In this paper, we demonstrate that such low-dimensional approximations can be surprisingly poor in practice for seemingly intuitive summary statistic choices. We describe an idealized low-dimensional summary statistic that is, in principle, suitable for marginal estimation. However, a direct approximation of the idealized choice is difficult in practice. We thus suggest an alternative approach to marginal estimation which is easier to implement and automate. Given an initial choice of low-dimensional summary statistic that might only be informative about a marginal posterior location, the new method improves performance by first crudely localising the posterior approximation using all the summary statistics to ensure global identifiability, followed by a second step that hones in on an accurate low-dimensional approximation using the low-dimensional summary statistic. We show that the posterior this approach targets can be represented as a logarithmic pool of posterior distributions based on the low-dimensional and full summary statistics, respectively. The good performance of our method is illustrated in several examples.Comment: 30 pages, 9 figure

Variable Selection and Model Averaging in Semiparametric Overdispersed Generalized Linear Models

We express the mean and variance terms in a double exponential regression model as additive functions of the predictors and use Bayesian variable selection to determine which predictors enter the model, and whether they enter linearly or flexibly. When the variance term is null we obtain a generalized additive model, which becomes a generalized linear model if the predictors enter the mean linearly. The model is estimated using Markov chain Monte Carlo simulation and the methodology is illustrated using real and simulated data sets.Comment: 8 graphs 35 page

Theory of Suspension Segregation in Partially Filled Horizontal Rotating Cylinders

It is shown that a suspension of particles in a partially-filled, horizontal, rotating cylinder is linearly unstable towards axial segregation and an undulation of the free surface at large enough particle concentrations. Relying on the shear-induced diffusion of particles, concentration-dependent viscosity, and the existence of a free surface, our theory provides an explanation of the experiments of Tirumkudulu et al., Phys. Fluids 11, 507-509 (1999); ibid. 12, 1615 (2000).Comment: Accepted for publication in Phys Fluids (Lett) 10 pages, two eps figure

Variational approximation for mixtures of linear mixed models

Mixtures of linear mixed models (MLMMs) are useful for clustering grouped data and can be estimated by likelihood maximization through the EM algorithm. The conventional approach to determining a suitable number of components is to compare different mixture models using penalized log-likelihood criteria such as BIC.We propose fitting MLMMs with variational methods which can perform parameter estimation and model selection simultaneously. A variational approximation is described where the variational lower bound and parameter updates are in closed form, allowing fast evaluation. A new variational greedy algorithm is developed for model selection and learning of the mixture components. This approach allows an automatic initialization of the algorithm and returns a plausible number of mixture components automatically. In cases of weak identifiability of certain model parameters, we use hierarchical centering to reparametrize the model and show empirically that there is a gain in efficiency by variational algorithms similar to that in MCMC algorithms. Related to this, we prove that the approximate rate of convergence of variational algorithms by Gaussian approximation is equal to that of the corresponding Gibbs sampler which suggests that reparametrizations can lead to improved convergence in variational algorithms as well.Comment: 36 pages, 5 figures, 2 tables, submitted to JCG

Long-term mortality trends in functionally-dependent adults following severe traumatic-brain injury

Abstract Primary objective: To investigate mortality trends in functionally dependent adults following traumatic brain injury (TBI). Methods: Data for 966 consecutive admissions to a specialist TBI rehabilitation service were reviewed. Details for 69 subjects who were functionally dependent at rehabilitation discharge were cross-referenced against the State Government Death Register. The observed mortality rate was compared to an equivalent population sample derived from Australian Life Tables. Results: Twenty-five subjects (36%) were deceased at an average 10.5 years post-injury (SD 5 years; range 1.7-18.8 years). The observed numbers of deaths far exceeded the expected population figure (1.9) for the same period (1989)(1990)(1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007) yielding a standardized mortality rate of 13.2. Mortality trends suggested a bimodal distribution, with more deaths in the first 5 years post-injury followed by no further deaths until 9 years post-injury. Conclusions: Mortality in this functionally-dependent group was significantly associated with age, male sex and degree of disability at discharge. The bimodal distribution of mortality data suggests different contributory mechanisms to early vs. late mortality in this group

Gastrointestinal perforation in metastatic colorectal cancer patients with peritoneal metastases receiving bevacizumab

Published online: May 7, 2015Aim: To investigate the safety and efficacy of adding bevacizumab to first-line chemotherapy in metastatic colorectal cancer patients with peritoneal disease. Methods: We compared rates of gastrointestinal perforation in patients with metastatic colorectal cancer and peritoneal disease receiving first-line chemotherapy with and without bevacizumab in three distinct cohorts: (1) the AGITG MAX trial (Phase III randomised clinical trial comparing capecitabine vs capecitabine and bevacizumab vs capecitabine, bevacizumab and mitomycinC); (2) the prospective Treatment of Recurrent and Advanced Colorectal Cancer (TRACC) registry (any first-line regimen ± bevacizumab); and (3) two cancer centres in New South Wales, Australia [Macarthur Cancer Therapy Centre and Liverpool Cancer Therapy Centre (NSWCC) from January 2005 to Decenber 2012, (any first-line regimen ± bevacizumab). For the AGITG MAX trial capecitabine was compared to the other two arms (capecitabine/bevacizumab and capecitabine/bevacizumab/mitomycinC). In the AGITG MAX trial and the TRACC registry rates of gastrointestinal perforation were also collected in patients who did not have peritoneal metastases. Secondary endpoints included progression-free survival, chemotherapy duration, and overall survival. Time-to-event outcomes were estimated using the Kaplan-Meier method and compared using the log-rank test. Results: Eighty-four MAX, 179 TRACC and 69 NSWCC patients had peritoneal disease. There were no gastrointestinal perforations recorded in either the MAX subgroup or the NSWCC cohorts. Of the patients without peritoneal disease in the MAX trial, 4/300 (1.3%) in the bevacizumab arms had gastrointestinal perforations compared to 1/123 (0.8%) in the capecitabine alone arm. In the TRACC registry 3/126 (2.4%) patients who had received bevacizumab had a gastrointestinal perforation compared to 1/53 (1.9%) in the chemotherapy alone arm. In a further analysis of patients without peritoneal metastases in the TRACC registry, the rate of gastrointestinal perforations was 9/369 (2.4%) in the chemotherapy/bevacizumab group and 5/177 (2.8%) in the chemotherapy alone group. The addition of bevacizumab to chemotherapy was associated with improved progression-free survival in all three cohorts: MAX 6.9 m vs 4.9 m, HR = 0.64 (95%CI: 0.42-1.02); P = 0.063; TRACC 9.1 m vs 5.5 m, HR = 0.61 (95%CI: 0.37-0.86); P = 0.009; NSWCC 8.7 m vs 6.8 m, HR = 0.75 (95%CI: 0.43-1.32); P = 0.32. Chemotherapy duration was similar across the groups. Conclusion: Patients with peritoneal disease do not appear to have an increased risk of gastrointestinal perforations when receiving first-line therapy with bevacizumab compared to systemic therapy alone.Aflah Roohullah, Hui-Li Wong, Katrin M Sjoquist, Peter Gibbs, Kathryn Field, Ben Tran, Jeremy Shapiro, Joe Mckendrick, Desmond Yip, Louise Nott, Val Gebski, Weng Ng, Wei Chua, Timothy Price, Niall Tebbutt, Lorraine Chantril