Bayesian parametric bootstrap for models with intractable likelihoods

In this paper it is demonstrated how the Bayesian parametric bootstrap can be adapted to models with intractable likelihoods. The approach is most appealing when the semi-automatic approximate Bayesian computation (ABC) summary statistics are selected. After a pilot run of ABC, the likelihood-free parametric bootstrap approach requires very few model simulations to produce an approximate posterior, which can be a useful approximation in its own right. An alternative is to use this approximation as a proposal distribution in ABC algorithms to make them more efficient. In this paper, the parametric bootstrap approximation is used to form the initial importance distribution for the sequential Monte Carlo and the ABC importance and rejection sampling algorithms. The new approach is illustrated through a simulation study of the univariate g-and- k quantile distribution, and is used to infer parameter values of a stochastic model describing expanding melanoma cell colonies.

Scalable Bayesian Computation for intractable likelihoods in image analysis

The inverse temperature hyperparameter of the hidden Potts model governs the strength of spatial cohesion and therefore has a substantial influence over the resulting model fit. The difficulty arises from the dependence of an intractable normalising constant on the value of the inverse temperature, thus there is no closed form solution for sampling from the distribution directly. We review three computational approaches for addressing this issue, namely pseudolikelihood, path sampling, and the approximate exchange algorithm. We compare the accuracy and scalability of these methods using a simulation study.

Bayesian refinement of association signals for 14 loci in 3 common diseases

To further investigate susceptibility loci identified by genome-wide association studies, we genotyped 5,500 SNPs across 14 associated regions in 8,000 samples from a control group and 3 diseases: type 2 diabetes (T2D), coronary artery disease (CAD) and Graves' disease. We defined, using Bayes theorem, credible sets of SNPs that were 95% likely, based on posterior probability, to contain the causal disease-associated SNPs. In 3 of the 14 regions, TCF7L2 (T2D), CTLA4 (Graves' disease) and CDKN2A-CDKN2B (T2D), much of the posterior probability rested on a single SNP, and, in 4 other regions (CDKN2A-CDKN2B (CAD) and CDKAL1, FTO and HHEX (T2D)), the 95% sets were small, thereby excluding most SNPs as potentially causal. Very few SNPs in our credible sets had annotated functions, illustrating the limitations in understanding the mechanisms underlying susceptibility to common diseases. Our results also show the value of more detailed mapping to target sequences for functional studies. © 2012 Nature America, Inc. All rights reserved.

Comparing multilevel and Bayesian spatial random effects survival models to assess geographical inequalities in colorectal cancer survival: a case study

Background Multilevel and spatial models are being increasingly used to obtain substantive information on area-level inequalities in cancer survival. Multilevel models assume independent geographical areas, whereas spatial models explicitly incorporate geographical correlation, often via a conditional autoregressive prior. However the relative merits of these methods for large population-based studies have not been explored. Using a case-study approach, we report on the implications of using multilevel and spatial survival models to study geographical inequalities in all-cause survival. Methods Multilevel discrete-time and Bayesian spatial survival models were used to study geographical inequalities in all-cause survival for a population-based colorectal cancer cohort of 22,727 cases aged 20–84 years diagnosed during 1997–2007 from Queensland, Australia. Results Both approaches were viable on this large dataset, and produced similar estimates of the fixed effects. After adding area-level covariates, the between-area variability in survival using multilevel discrete-time models was no longer significant. Spatial inequalities in survival were also markedly reduced after adjusting for aggregated area-level covariates. Only the multilevel approach however, provided an estimation of the contribution of geographical variation to the total variation in survival between individual patients. Conclusions With little difference observed between the two approaches in the estimation of fixed effects, multilevel models should be favored if there is a clear hierarchical data structure and measuring the independent impact of individual- and area-level effects on survival differences is of primary interest. Bayesian spatial analyses may be preferred if spatial correlation between areas is important and if the priority is to assess small-area variations in survival and map spatial patterns. Both approaches can be readily fitted to geographically enabled survival data from international settings

Bayesian predictive modeling and comparison of oil samples

Statistical comparison of oil samples is an integral part of oil spill identification, which deals with the process of linking an oil spill with its source of origin. In current practice, a frequentist hypothesis test is often used to evaluate evidence in support of a match between a spill and a source sample. As frequentist tests are only able to evaluate evidence against a hypothesis but not in support of it, we argue that this leads to unsound statistical reasoning. Moreover, currently only verbal conclusions on a very coarse scale can be made about the match between two samples, whereas a finer quantitative assessment would often be preferred. To address these issues, we propose a Bayesian predictive approach for evaluating the similarity between the chemical compositions of two oil samples. We derive the underlying statistical model from some basic assumptions on modeling assays in analytical chemistry, and to further facilitate and improve numerical evaluations, we develop analytical expressions for the key elements of Bayesian inference for this model. The approach is illustrated with both simulated and real data and is shown to have appealing properties in comparison with both standard frequentist and Bayesian approaches

Methods for constructing uncertainty intervals for queries of Bayesian nets

In this paper the issue of finding uncertainty intervals for queries in a Bayesian Network is reconsidered. The investigation focuses on Bayesian Nets with discrete nodes and finite populations. An earlier asymptotic approach is compared with a simulation-based approach, together with further alternatives, one based on a single sample of the Bayesian Net of a particular finite population size, and another which uses expected population sizes together with exact probabilities. We conclude that a query of a Bayesian Net should be expressed as a probability embedded in an uncertainty interval. Based on an investigation of two Bayesian Net structures, the preferred method is the simulation method. However, both the single sample method and the expected sample size methods may be useful and are simpler to compute. Any method at all is more useful than none, when assessing a Bayesian Net under development, or when drawing conclusions from an ‘expert’ system.

Potential uses of Bayesian networks as tools for synthesis of systematic reviews of complex interventions

Bayesian networks (BNs) are tools for representing expert knowledge or evidence. They are especially useful for synthesising evidence or belief concerning a complex intervention, assessing the sensitivity of outcomes to different situations or contextual frameworks and framing decision problems that involve alternative types of intervention. Bayesian networks are useful extensions to logic maps when initiating a review or to facilitate synthesis and bridge the gap between evidence acquisition and decision-making. Formal elicitation techniques allow development of BNs on the basis of expert opinion. Such applications are useful alternatives to ‘empty’ reviews, which identify knowledge gaps but fail to support decision-making. Where review evidence exists, it can inform the development of a BN. We illustrate the construction of a BN using a motivating example that demonstrates how BNs can ensure coherence, transparently structure the problem addressed by a complex intervention and assess sensitivity to context, all of which are critical components of robust reviews of complex interventions. We suggest that BNs should be utilised to routinely synthesise reviews of complex interventions or empty reviews where decisions must be made despite poor evidence.

Analysis of differential gene expression based on Bayesian estimation of variance

Gene expression is arguably the most important indicator of biological function. Thus identifying differentially expressed genes is one of the main aims of high throughout studies that use microarray and RNAseq platforms to study deregulated cellular pathways. There are many tools for analysing differentia gene expression from transciptomic datasets. The major challenge of this topic is to estimate gene expression variance due to the high amount of ‘background noise’ that is generated from biological equipment and the lack of biological replicates. Bayesian inference has been widely used in the bioinformatics field. In this work, we reveal that the prior knowledge employed in the Bayesian framework also helps to improve the accuracy of differential gene expression analysis when using a small number of replicates. We have developed a differential analysis tool that uses Bayesian estimation of the variance of gene expression for use with small numbers of biological replicates. Our method is more consistent when compared to the widely used cyber-t tool that successfully introduced the Bayesian framework to differential analysis. We also provide a user-friendly web based Graphic User Interface for biologists to use with microarray and RNAseq data. Bayesian inference can compensate for the instability of variance caused when using a small number of biological replicates by using pseudo replicates as prior knowledge. We also show that our new strategy to select pseudo replicates will improve the performance of the analysis. - See more at: http://www.eurekaselect.com/node/138761/article#sthash.VeK9xl5k.dpuf

Spatio-temporal modelling of cancer data in Queensland using Bayesian methods

Cancer is the leading contributor to the disease burden in Australia. This thesis develops and applies Bayesian hierarchical models to facilitate an investigation of the spatial and temporal associations for cancer diagnosis and survival among Queenslanders. The key objectives are to document and quantify the importance of spatial inequalities, explore factors influencing these inequalities, and investigate how spatial inequalities change over time. Existing Bayesian hierarchical models are refined, new models and methods developed, and tangible benefits obtained for cancer patients in Queensland. The versatility of using Bayesian models in cancer control are clearly demonstrated through these detailed and comprehensive analyses.

Rationality, governmentality, natio(norm)ality: Shaping social science, scientific objects, and the invisible

The discipline of education in Anglophone-dominant contexts has always grappled with a kind of status anxiety relative to other disciplines. This is in part due to the ways in which evidence has been thought about in the theoretico-experimental sciences relative to the ethico-redemptive ones. By examining that which was considered to fall to the side of science, even of social science, this paper complexifies contemporary debates over educational science and research, including debates over evidence-based education or assumed divisions between the quantitative/qualitative and empirical/conceptual. It reapproaches historical vagaries in discourses of vision that underscore the arbitrariness of approaches to social scientific research and its objects. A less-considered set of spatializations and regionalisms in social scientific conceptions of rationality especially are exposed through a close reading of the Harvard University philosopher William James' more marginalized texts.

Ship Seakeeping Operability, Motion Control, and Autonomy - A Bayesian Perspective

Ship seakeeping operability refers to the quantification of motion performance in waves relative to mission requirements. This is used to make decisions about preferred vessel designs, but it can also be used as comprehensive assessment of the benefits of ship-motion-control systems. Traditionally, operability computation aggregates statistics of motion computed over over the envelope of likely environmental conditions in order to determine a coefficient in the range from 0 to 1 called operability. When used for assessment of motion-control systems, the increase of operability is taken as the key performance indicator. The operability coefficient is often given the interpretation of the percentage of time operable. This paper considers an alternative probabilistic approach to this traditional computation of operability. It characterises operability not as a number to which a frequency interpretation is attached, but as a hypothesis that a vessel will attain the desired performance in one mission considering the envelope of likely operational conditions. This enables the use of Bayesian theory to compute the probability of that this hypothesis is true conditional on data from simulations. Thus, the metric considered is the probability of operability. This formulation not only adheres to recent developments in reliability and risk analysis, but also allows incorporating into the analysis more accurate descriptions of ship-motion-control systems since the analysis is not limited to linear ship responses in the frequency domain. The paper also discusses an extension of the approach to the case of assessment of increased levels of autonomy for unmanned marine craft.

A Bayesian Framework for the Assessment of Vision-based Weed and Fruit Detection and Classification Algorithms

This paper proposes new metrics and a performance-assessment framework for vision-based weed and fruit detection and classification algorithms. In order to compare algorithms, and make a decision on which one to use fora particular application, it is necessary to take into account that the performance obtained in a series of tests is subject to uncertainty. Such characterisation of uncertainty seems not to be captured by the performance metrics currently reported in the literature. Therefore, we pose the problem as a general problem of scientific inference, which arises out of incomplete information, and propose as a metric of performance the(posterior) predictive probabilities that the algorithms will provide a correct outcome for target and background detection. We detail the framework through which these predicted probabilities can be obtained, which is Bayesian in nature. As an illustration example, we apply the framework to the assessment of performance of four algorithms that could potentially be used in the detection of capsicums (peppers).

A simple Bayesian decision-theoretic design for dose-finding trials

A flexible and simple Bayesian decision-theoretic design for dose-finding trials is proposed in this paper. In order to reduce the computational burden, we adopt a working model with conjugate priors, which is flexible to fit all monotonic dose-toxicity curves and produces analytic posterior distributions. We also discuss how to use a proper utility function to reflect the interest of the trial. Patients are allocated based on not only the utility function but also the chosen dose selection rule. The most popular dose selection rule is the one-step-look-ahead (OSLA), which selects the best-so-far dose. A more complicated rule, such as the two-step-look-ahead, is theoretically more efficient than the OSLA only when the required distributional assumptions are met, which is, however, often not the case in practice. We carried out extensive simulation studies to evaluate these two dose selection rules and found that OSLA was often more efficient than two-step-look-ahead under the proposed Bayesian structure. Moreover, our simulation results show that the proposed Bayesian method's performance is superior to several popular Bayesian methods and that the negative impact of prior misspecification can be managed in the design stage.

Bayesian designs with frequentist and Bayesian error rate considerations

So far, most Phase II trials have been designed and analysed under a frequentist framework. Under this framework, a trial is designed so that the overall Type I and Type II errors of the trial are controlled at some desired levels. Recently, a number of articles have advocated the use of Bavesian designs in practice. Under a Bayesian framework, a trial is designed so that the trial stops when the posterior probability of treatment is within certain prespecified thresholds. In this article, we argue that trials under a Bayesian framework can also be designed to control frequentist error rates. We introduce a Bayesian version of Simon's well-known two-stage design to achieve this goal. We also consider two other errors, which are called Bayesian errors in this article because of their similarities to posterior probabilities. We show that our method can also control these Bayesian-type errors. We compare our method with other recent Bayesian designs in a numerical study and discuss implications of different designs on error rates. An example of a clinical trial for patients with nasopharyngeal carcinoma is used to illustrate differences of the different designs.

A Bayesian decision approach for sample size determination in phase II trials

Stallard (1998, Biometrics 54, 279-294) recently used Bayesian decision theory for sample-size determination in phase II trials. His design maximizes the expected financial gains in the development of a new treatment. However, it results in a very high probability (0.65) of recommending an ineffective treatment for phase III testing. On the other hand, the expected gain using his design is more than 10 times that of a design that tightly controls the false positive error (Thall and Simon, 1994, Biometrics 50, 337-349). Stallard's design maximizes the expected gain per phase II trial, but it does not maximize the rate of gain or total gain for a fixed length of time because the rate of gain depends on the proportion: of treatments forwarding to the phase III study. We suggest maximizing the rate of gain, and the resulting optimal one-stage design becomes twice as efficient as Stallard's one-stage design. Furthermore, the new design has a probability of only 0.12 of passing an ineffective treatment to phase III study.