Developments of the total entropy utility function for the dual purpose of model discrimination and parameter estimation in Bayesian design

The total entropy utility function is considered for the dual purpose of Bayesian design for model discrimination and parameter estimation. A sequential design setting is proposed where it is shown how to efficiently estimate the total entropy utility for a wide variety of data types. Utility estimation relies on forming particle approximations to a number of intractable integrals which is afforded by the use of the sequential Monte Carlo algorithm for Bayesian inference. A number of motivating examples are considered for demonstrating the performance of total entropy in comparison to utilities for model discrimination and parameter estimation. The results suggest that the total entropy utility selects designs which are efficient under both experimental goals with little compromise in achieving either goal. As such, the total entropy utility is advocated as a general utility for Bayesian design in the presence of model uncertainty.

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

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

Topological SLAM Using Fast Vision Techniques

In this paper we propose a method for vision only topological simultaneous localisation and mapping (SLAM). Our approach does not use motion or odometric information but a sequence of colour histograms from visited places. In particular, we address the perceptual aliasing problem which occurs using external observations only in topological navigation. We propose a Bayesian inference method to incrementally build a topological map by inferring spatial relations from the sequence of observations while simultaneously estimating the robot's location. The algorithm aims to build a small map which is consistent with local adjacency information extracted from the sequence measurements. Local adjacency information is incorporated to disambiguate places which otherwise would appear to be the same. Experiments in an indoor environment show that the proposed technique is capable of dealing with perceptual aliasing using visual observations only and successfully performs topological SLAM.

Best basis-based intelligent machine fault diagnosis

The wavelet packet transform decomposes a signal into a set of bases for time–frequency analysis. This decomposition creates an opportunity for implementing distributed data mining where features are extracted from different wavelet packet bases and served as feature vectors for applications. This paper presents a novel approach for integrated machine fault diagnosis based on localised wavelet packet bases of vibration signals. The best basis is firstly determined according to its classification capability. Data mining is then applied to extract features and local decisions are drawn using Bayesian inference. A final conclusion is reached using a weighted average method in data fusion. A case study on rolling element bearing diagnosis shows that this approach can greatly improve the accuracy ofdiagno sis.

Hierarchical models for 2D presence/absence data having ambiguous zeroes: With a biogeographical case study on dingo behaviour

This dissertation is primarily an applied statistical modelling investigation, motivated by a case study comprising real data and real questions. Theoretical questions on modelling and computation of normalization constants arose from pursuit of these data analytic questions. The essence of the thesis can be described as follows. Consider binary data observed on a two-dimensional lattice. A common problem with such data is the ambiguity of zeroes recorded. These may represent zero response given some threshold (presence) or that the threshold has not been triggered (absence). Suppose that the researcher wishes to estimate the effects of covariates on the binary responses, whilst taking into account underlying spatial variation, which is itself of some interest. This situation arises in many contexts and the dingo, cypress and toad case studies described in the motivation chapter are examples of this. Two main approaches to modelling and inference are investigated in this thesis. The first is frequentist and based on generalized linear models, with spatial variation modelled by using a block structure or by smoothing the residuals spatially. The EM algorithm can be used to obtain point estimates, coupled with bootstrapping or asymptotic MLE estimates for standard errors. The second approach is Bayesian and based on a three- or four-tier hierarchical model, comprising a logistic regression with covariates for the data layer, a binary Markov Random field (MRF) for the underlying spatial process, and suitable priors for parameters in these main models. The three-parameter autologistic model is a particular MRF of interest. Markov chain Monte Carlo (MCMC) methods comprising hybrid Metropolis/Gibbs samplers is suitable for computation in this situation. Model performance can be gauged by MCMC diagnostics. Model choice can be assessed by incorporating another tier in the modelling hierarchy. This requires evaluation of a normalization constant, a notoriously difficult problem. Difficulty with estimating the normalization constant for the MRF can be overcome by using a path integral approach, although this is a highly computationally intensive method. Different methods of estimating ratios of normalization constants (N Cs) are investigated, including importance sampling Monte Carlo (ISMC), dependent Monte Carlo based on MCMC simulations (MCMC), and reverse logistic regression (RLR). I develop an idea present though not fully developed in the literature, and propose the Integrated mean canonical statistic (IMCS) method for estimating log NC ratios for binary MRFs. The IMCS method falls within the framework of the newly identified path sampling methods of Gelman & Meng (1998) and outperforms ISMC, MCMC and RLR. It also does not rely on simplifying assumptions, such as ignoring spatio-temporal dependence in the process. A thorough investigation is made of the application of IMCS to the three-parameter Autologistic model. This work introduces background computations required for the full implementation of the four-tier model in Chapter 7. Two different extensions of the three-tier model to a four-tier version are investigated. The first extension incorporates temporal dependence in the underlying spatio-temporal process. The second extensions allows the successes and failures in the data layer to depend on time. The MCMC computational method is extended to incorporate the extra layer. A major contribution of the thesis is the development of a fully Bayesian approach to inference for these hierarchical models for the first time. Note: The author of this thesis has agreed to make it open access but invites people downloading the thesis to send her an email via the 'Contact Author' function.

Statistical and Econometric Methods for Transportation Data Analysis, 2nd edition

Now in its second edition, this book describes tools that are commonly used in transportation data analysis. The first part of the text provides statistical fundamentals while the second part presents continuous dependent variable models. With a focus on count and discrete dependent variable models, the third part features new chapters on mixed logit models, logistic regression, and ordered probability models. The last section provides additional coverage of Bayesian statistical modeling, including Bayesian inference and Markov chain Monte Carlo methods. Data sets are available online to use with the modeling techniques discussed.

Systematics of the Ustilago-Sporisorium-Macalpinomyces complex of smut fungi

Smut fungi are important pathogens of grasses, including the cultivated crops maize, sorghum and sugarcane. Typically, smut fungi infect the inflorescence of their host plants. Three genera of smut fungi (Ustilago, Sporisorium and Macalpinomyces) form a complex with overlapping morphological characters, making species placement problematic. For example, the newly described Macalpinomyces mackinlayi possesses a combination of morphological characters such that it cannot be unambiguously accommodated in any of the three genera. Previous attempts to define Ustilago, Sporisorium and Macalpinomyces using morphology and molecular phylogenetics have highlighted the polyphyletic nature of the genera, but have failed to produce a satisfactory taxonomic resolution. A detailed systematic study of 137 smut species in the Ustilago-Sporisorium- Macalpinomyces complex was completed in the current work. Morphological and DNA sequence data from five loci were assessed with maximum likelihood and Bayesian inference to reconstruct a phylogeny of the complex. The phylogenetic hypotheses generated were used to identify morphological synapomorphies, some of which had previously been dismissed as a useful way to delimit the complex. These synapomorphic characters are the basis for a revised taxonomic classification of the Ustilago-Sporisorium-Macalpinomyces complex, which takes into account their morphological diversity and coevolution with their grass hosts. The new classification is based on a redescription of the type genus Sporisorium, and the establishment of four genera, described from newly recognised monophyletic groups, to accommodate species expelled from Sporisorium. Over 150 taxonomic combinations have been proposed as an outcome of this investigation, which makes a rigorous and objective contribution to the fungal systematics of these important plant pathogens.

Accuracy of rate estimation using relaxed-clock models with a critical focus on the early metazoan radiation

In recent years, a number of phylogenetic methods have been developed for estimating molecular rates and divergence dates under models that relax the molecular clock constraint by allowing rate change throughout the tree. These methods are being used with increasing frequency, but there have been few studies into their accuracy. We tested the accuracy of several relaxed-clock methods (penalized likelihood and Bayesian inference using various models of rate change) using nucleotide sequences simulated on a nine-taxon tree. When the sequences evolved with a constant rate, the methods were able to infer rates accurately, but estimates were more precise when a molecular clock was assumed. When the sequences evolved under a model of autocorrelated rate change, rates were accurately estimated using penalized likelihood and by Bayesian inference using lognormal and exponential models of rate change, while other models did not perform as well. When the sequences evolved under a model of uncorrelated rate change, only Bayesian inference using an exponential rate model performed well. Collectively, the results provide a strong recommendation for using the exponential model of rate change if a conservative approach to divergence time estimation is required. A case study is presented in which we use a simulation-based approach to examine the hypothesis of elevated rates in the Cambrian period, and it is found that these high rate estimates might be an artifact of the rate estimation method. If this bias is present, then the ages of metazoan divergences would be systematically underestimated. The results of this study have implications for studies of molecular rates and divergence dates.

Segmentation of cone-beam CT using a hidden Markov random field with informative priors

Cone-beam computed tomography (CBCT) has enormous potential to improve the accuracy of treatment delivery in image-guided radiotherapy (IGRT). To assist radiotherapists in interpreting these images, we use a Bayesian statistical model to label each voxel according to its tissue type. The rich sources of prior information in IGRT are incorporated into a hidden Markov random field model of the 3D image lattice. Tissue densities in the reference CT scan are estimated using inverse regression and then rescaled to approximate the corresponding CBCT intensity values. The treatment planning contours are combined with published studies of physiological variability to produce a spatial prior distribution for changes in the size, shape and position of the tumour volume and organs at risk. The voxel labels are estimated using iterated conditional modes. The accuracy of the method has been evaluated using 27 CBCT scans of an electron density phantom. The mean voxel-wise misclassification rate was 6.2\%, with Dice similarity coefficient of 0.73 for liver, muscle, breast and adipose tissue. By incorporating prior information, we are able to successfully segment CBCT images. This could be a viable approach for automated, online image analysis in radiotherapy.

The effect of prior visual information on recognition of speech and sounds

To identify and categorize complex stimuli such as familiar objects or speech, the human brain integrates information that is abstracted at multiple levels from its sensory inputs. Using cross-modal priming for spoken words and sounds, this functional magnetic resonance imaging study identified 3 distinct classes of visuoauditory incongruency effects: visuoauditory incongruency effects were selective for 1) spoken words in the left superior temporal sulcus (STS), 2) environmental sounds in the left angular gyrus (AG), and 3) both words and sounds in the lateral and medial prefrontal cortices (IFS/mPFC). From a cognitive perspective, these incongruency effects suggest that prior visual information influences the neural processes underlying speech and sound recognition at multiple levels, with the STS being involved in phonological, AG in semantic, and mPFC/IFS in higher conceptual processing. In terms of neural mechanisms, effective connectivity analyses (dynamic causal modeling) suggest that these incongruency effects may emerge via greater bottom-up effects from early auditory regions to intermediate multisensory integration areas (i.e., STS and AG). This is consistent with a predictive coding perspective on hierarchical Bayesian inference in the cortex where the domain of the prediction error (phonological vs. semantic) determines its regional expression (middle temporal gyrus/STS vs. AG/intraparietal sulcus).

Leaf and inflorescence structure and phylogenetics of Tripogon and affiliated genera (Poaceae: Chloridoideae)

This thesis provides new knowledge on an understudied group of grasses, some of which are resurrection grasses (i.e. able to withstand extreme drought). The sole Australian species (Tripogon loliiformis) is morphologically diverse and could be more than one species. This study sought to determine how many species of Tripogon occur in Australia, their relationships to other species in the genus and to two other genera of resurrection grasses (Eragrostiella and Oropetium). Results of the research indicate there is not enough evidence, from DNA sequence data, to warrant splitting up T. loliiformis into multiple species. The extensive morphological diversity seems to be influenced by environmental conditions. The three genera are so closely related that they could be grouped into a single genus. This new knowledge opens up pathways for future investigations, including studying genes responsible for desiccation tolerance and the conservation of native grasses that occur in rocky habitats.

A mitochondrial genome phylogeny of owlet moths (Lepidoptera: Noctuoidea), and examination of the utility of mitochondrial genomes for lepidopteran phylogenetics

A phylogenetic hypothesis for the lepidopteran superfamily Noctuoidea was inferred based on the complete mitochondrial (mt) genomes of 12 species (six newly sequenced). The monophyly of each noctuoid family in the latest classification was well supported. Novel and robust relationships were recovered at the family level, in contrast to previous analyses using nuclear genes. Erebidae was recovered as sister to (Nolidae+(Euteliidae+Noctuidae)), while Notodontidae was sister to all these taxa (the putatively basalmost lineage Oenosandridae was not included). In order to improve phylogenetic resolution using mt genomes, various analytical approaches were tested: Bayesian inference (BI) vs. maximum likelihood (ML), excluding vs. including RNA genes (rRNA or tRNA), and Gblocks treatment. The evolutionary signal within mt genomes had low sensitivity to analytical changes. Inference methods had the most significant influence. Inclusion of tRNAs positively increased the congruence of topologies, while inclusion of rRNAs resulted in a range of phylogenetic relationships varying depending on other analytical factors. The two Gblocks parameter settings had opposite effects on nodal support between the two inference methods. The relaxed parameter (GBRA) resulted in higher support values in BI analyses, while the strict parameter (GBDH) resulted in higher support values in ML analyses.

A Model to Estimate the Population Contributing to the Wastewater Using Samples Collected on Census Day

An important uncertainty when estimating per capita consumption of, for example, illicit drugs by means of wastewater analysis (sometimes referred to as “sewage epidemiology”) relates to the size and variability of the de facto population in the catchment of interest. In the absence of a day-specific direct population count any indirect surrogate model to estimate population size lacks a standard to assess associated uncertainties. Therefore, the objective of this study was to collect wastewater samples at a unique opportunity, that is, on a census day, as a basis for a model to estimate the number of people contributing to a given wastewater sample. Mass loads for a wide range of pharmaceuticals and personal care products were quantified in influents of ten sewage treatment plants (STP) serving populations ranging from approximately 3500 to 500 000 people. Separate linear models for population size were estimated with the mass loads of the different chemical as the explanatory variable: 14 chemicals showed good, linear relationships, with highest correlations for acesulfame and gabapentin. De facto population was then estimated through Bayesian inference, by updating the population size provided by STP staff (prior knowledge) with measured chemical mass loads. Cross validation showed that large populations can be estimated fairly accurately with a few chemical mass loads quantified from 24-h composite samples. In contrast, the prior knowledge for small population sizes cannot be improved substantially despite the information of multiple chemical mass loads. In the future, observations other than chemical mass loads may improve this deficit, since Bayesian inference allows including any kind of information relating to population size.