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[This corrects the article DOI: 10.1021/acsomega.3c01613.].

Biological volatilome analysis is inherently complex due to the considerable number of compounds (i.e., dimensions) and differences in peak areas by orders of magnitude, between and within compounds found within datasets. Traditional volatilome analysis relies on dimensionality reduction techniques which aid in the selection of compounds that are considered relevant to respective research questions prior to further analysis. Currently, compounds of interest are identified using either supervised or unsupervised statistical methods which assume the data residuals are normally distributed and exhibit linearity. However, biological data often violate the statistical assumptions of these models related to normality and the presence of multiple explanatory variables which are innate to biological samples. In an attempt to address deviations from normality, volatilome data can be log transformed. However, whether the effects of each assessed variable are additive or multiplicative should be considered prior to transformation, as this will impact the effect of each variable on the data. If assumptions of normality and variable effects are not investigated prior to dimensionality reduction, ineffective or erroneous compound dimensionality reduction can impact downstream analyses. It is the aim of this manuscript to assess the impact of single and multivariable statistical models with and without the log transformation to volatilome dimensionality reduction prior to any supervised or unsupervised classification analysis. As a proof of concept, Shingleback lizard (Tiliqua rugosa) volatilomes were collected across their species distribution and from captivity and were assessed. Shingleback volatilomes are suspected to be influenced by multiple explanatory variables related to habitat (Bioregion), sex, parasite presence, total body volume, and captive status. This work determined that the exclusion of relevant multiple explanatory variables from analysis overestimates the effec

In both criminal cases and civil cases there is an increasing demand for the analysis of DNA mixtures involving relationships. The goal might be, for example, to identify the contributors to a DNA mixture where the unknown donors may be related, or to infer the relationship between individuals based on a DNA mixture. This paper applies a new approach to modelling and computation for DNA mixtures involving contributors with arbitrarily complex relationships to two real cases from the Spanish Forensic Police.

© 2019 Biometrika Trust. This article concerns a class of generalized linear mixed models for two-level grouped data, where the random effects are uniquely indexed by groups and are independent. We derive necessary and sufficient conditions for the marginal likelihood to be expressed in explicit form. These models are unified under the conjugate generalized linear mixed models framework, where conjugate refers to the fact that the marginal likelihood can be expressed in closed form, rather than implying inference via the Bayesian paradigm. The proposed framework allows simultaneous conjugacy for Gaussian, Poisson and gamma responses, and thus can accommodate both unit-and group-level covariates. Only group-level covariates can be incorporated for the binomial distribution. In a simulation of Poisson data, our framework outperformed its competitors in terms of computational time, and was competitive in terms of robustness against misspecification of the random effects distributions.

© 2017 Biometrika Trust. We present a new kind of structural Markov property for probabilistic laws on decomposable graphs, which allows the explicit control of interactions between cliques and so is capable of encoding some interesting structure. We prove the equivalence of this property to an exponential family assumption, and discuss identifiability, modelling, inferential and computational implications.

© 2017 Elsevier B.V. We present methods for inference about relationships between contributors to a DNA mixture and other individuals of known genotype: a basic example would be testing whether a contributor to a mixture is the father of a child of known genotype. The evidence for such a relationship is evaluated as the likelihood ratio for the specified relationship versus the alternative that there is no relationship. We analyse real casework examples from a criminal case and a disputed paternity case; in both examples part of the evidence was from a DNA mixture. DNA samples are of varying quality and therefore present challenging problems in interpretation. Our methods are based on a recent statistical model for DNA mixtures, in which a Bayesian network (BN) is used as a computational device; the present work builds on that approach, but makes more explicit use of the BN in the modelling. The R code for the analyses presented is freely available as supplementary material. We show how additional information of specific genotypes relevant to the relationship under analysis greatly strengthens the resulting inference. We find that taking full account of the uncertainty inherent in a DNA mixture can yield likelihood ratios very close to what one would obtain if we had a single source DNA profile. Furthermore, the methods can be readily extended to analyse different scenarios as our methods are not limited to the particular genotyping kits used in the examples, to the allele frequency databases used, to the numbers of contributors assumed, to the number of traces analysed simultaneously, nor to the specific hypotheses tested.

© 2015 John Wiley & Sons, Ltd. All rights reserved. Professor Kanti Mardia has made numerous original contributions to an area of unlabelled shape analysis inspired by matching and alignment problems arising in protein bioinformatics. In this chapter, a Bayesian model proposed by Mardia and Green in 2006, and others related to it, are revisited to investigate the potential for using modern optimisation algorithms to expedite calculations of properties of the posterior distribution, in place of the Monte Carlo computational methods originally proposed.

© 2015, The Author(s). Recent decades have seen enormous improvements in computational inference for statistical models; there have been competitive continual enhancements in a wide range of computational tools. In Bayesian inference, first and foremost, MCMC techniques have continued to evolve, moving from random walk proposals to Langevin drift, to Hamiltonian Monte Carlo, and so on, with both theoretical and algorithmic innovations opening new opportunities to practitioners. However, this impressive evolution in capacity is confronted by an even steeper increase in the complexity of the datasets to be addressed. The difficulties of modelling and then handling ever more complex datasets most likely call for a new type of tool for computational inference that dramatically reduces the dimension and size of the raw data while capturing its essential aspects. Approximate models and algorithms may thus be at the core of the next computational revolution.

© Institute of Mathematical Statistics, 2014. We study the asymptotic behaviour of the posterior distribution in a broad class of statistical models where the "true" solution occurs on the boundary of the parameter space. We show that in this case Bayesian inference is consistent, and that the posterior distribution has not only Gaussian components as in the case of regular models (the Bernstein-von Mises theorem) but also has Gamma distribution components whose form depends on the behaviour of the prior distribution near the boundary and have a faster rate of convergence. We also demonstrate a remarkable property of Bayesian inference, that for some models, there appears to be no bound on efficiency of estimating the unknown parameter if it is on the boundary of the parameter space. We illustrate the results on a problem from emission tomography.

Full Bayesian computational inference for model determination in undirected graphical models is currently restricted to decomposable graphs or other special cases, except for small-scale problems, say up to 15 variables. In this paper we develop new, more efficient methodology for such inference, by making two contributions to the computational geometry of decomposable graphs. The first of these provides sufficient conditions under which it is possible to completely connect two disconnected complete subsets of vertices, or perform the reverse procedure, yet maintain decomposability of the graph. The second is a new Markov chainMonte Carlo sampler for arbitrary positive distributions on decomposable graphs, taking a junction tree representing the graph as its state variable. The resulting methodology is illustrated with numerical experiments on three models. © 2013 Biometrika Trust.

Methodology for regression beyond the mean has been a goal of researchers for many years. This discussion provides some additional context for the important ideas in the present paper, by recounting some of the historical background to the GAMLSS approach and pointing to the power and appeal of fully probabilistic regression analysis in the setting of Bayesian nonparametrics. © 2013 SAGE Publications.

We review the across-model simulation approach to computation for Bayesian model determination, based on the reversible jump Markov chain Monte Carlo method. Advantages, difficulties and variations of the methods are discussed. We also discuss some limitations of the ideal Bayesian view of the model determination problem, for which no computational methods can provide a cure. © 2012 The Authors. Statistica Neerlandica © 2012 VVS.

© 2009 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America. We describe a method for aligning multiple unlabeled configurations simultaneously. Specifically, we extend the two-configuration matching approach of Green and Mardia (2006) to the multiple configuration setting. Our approach is based on the introduction of a set of hidden locations underlying the observed configuration points. A Poisson process prior is assigned to these locations, resulting in a simplified formulation of the model. We make use of a structure containing the relevant information on the matches, of which there are different types to take into account. Bayesian inference can be made simultaneously on the matching and the relative transformations between the configurations. We focus on the particular case of rigid-body transformations and Gaussian observation errors. We apply our method to a problem in chemoinformatics: the alignment of steroid molecules. Supplementary materials are available online.

Deep sequencing technologies such as Illumina, SOLiD, and 454 platforms have become very powerful tools in discovering and quantifying small RNAs in diverse organisms. Sequencing small RNA fractions always identifies RNAs derived from abundant RNA species such as rRNAs, tRNAs, snRNA, and snoRNA, and they are widely considered to be random degradation products. We carried out bioinformatic analysis of deep sequenced HeLa RNA and after quality filtering, identified highly abundant small RNA fragments, derived from mature tRNAs that are likely produced by specific processing rather than from random degradation. Moreover, we showed that the processing of small RNAs derived from tRNA Gln is dependent on Dicer in vivo and that Dicer cleaves the tRNA in vitro. Published by Cold Spring Harbor Laboratory Press. Copyright © 2009 RNA Society.

We derive methods for enumerating the distinct junction tree representations for any given decomposable graph. We discuss the relevance of the method to estimating conditional independence graphs of graphical models and give an algorithm that, given a junction tree, will generate uniformly at random a tree from the set of those that represent the same graph. Programs implementing these methods are included as supplemental material. © 2009 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.

Given a decomposable graph, we characterize and enumerate the set of pairs of vertices whose connection or disconnection results in a new graph that is also decomposable. We discuss the relevance of these results to Markov chain Monte Carlo methods that sample or optimize over the space of decomposable graphical models according to probabilities determined by a posterior distribution given observed multivariate data. © 2008 Elsevier B.V. All rights reserved.

Many forensic genetics problems can be handled using structured systems of discrete variables, for which Bayesian networks offer an appealing practical modeling framework, and allow inferences to be computed by probability propagation methods. However, when standard assumptions are violated-for example, when allele frequencies are unknown, there is identity by descent or the population is heterogeneous-dependence is generated among founding genes, that makes exact calculation of conditional probabilities by propagation methods less straightforward. Here we illustrate different methodologies for assessing sensitivity to assumptions about founders in forensic genetics problems. These include constrained steepest descent, linear fractional programming and representing dependence by structure. We illustrate these methods on several forensic genetics examples involving criminal identification, simple and complex disputed paternity and DNA mixtures. © Institute of Mathematical Statistics, 2009.

Summary. The Sloan digital sky survey is an extremely large astronomical survey that is conducted with the intention of mapping more than a quarter of the sky. Among the data that it is generating are spectroscopic and photometric measurements, both containing information about the red shift of galaxies. The former are precise and easy to interpret but expensive to gather; the latter are far cheaper but correspondingly more difficult to interpret. Recently, Csabai and co-workers have described various calibration techniques aiming to predict red shift from photometric measurements. We investigate what a structured Bayesian approach to the problem can add. In particular, we are interested in providing uncertainty bounds that are associated with the underlying red shifts and the classifications of the galaxies. We find that quite a generic statistical modelling approach, using for the most part standard model ingredients, can compete with much more specific custom-made and highly tuned techniques that are already available in the astronomical literature. © 2008 Royal Statistical Society.

Background: Matching functional sites is a key problem for the understanding of protein function and evolution. The commonly used graph theoretic approach, and other related approaches, require adjustment of a matching distance threshold a priori according to the noise in atomic positions. This is difficult to pre-determine when matching sites related by varying evolutionary distances and crystallographic precision. Furthermore, sometimes the graph method is unable to identify alternative but important solutions in the neighbourhood of the distance based solution because of strict distance constraints. We consider the Bayesian approach to improve graph based solutions. In principle this approach applies to other methods with strict distance matching constraints. The Bayesian method can flexibly incorporate all types of prior information on specific binding sites (e.g. amino acid types) in contrast to combinatorial formulations. Results: We present a new meta-algorithm for matching protein functional sites (active sites and ligand binding sites) based on an initial graph matching followed by refinement using a Markov chain Monte Carlo (MCMC) procedure. This procedure is an innovative extension to our recent work. The method accounts for the 3-dimensional structure of the site as well as the physico-chemical properties of the constituent amino acids. The MCMC procedure can lead to a significant increase in the number of significant matches compared to the graph method as measured independently by rigorously derived p-values. Conclusion: MCMC refinement step is able to significantly improve graph based matches. We apply the method to matching NAD(P)(H) binding sites within single Rossmann fold families, between different families in the same superfamily, and in different folds. Within families sites are often well conserved, but there are examples where significant shape based matches do not retain similar amino acid chemistry, indicating that even within families the

This article establishes a general formulation for Bayesian model-based clustering, in which subset labels are exchangeable, and items are also exchangeable, possibly up to covariate effects. The notational framework is rich enough to encompass a variety of existing procedures, including some recently discussed methods involving stochastic search or hierarchical clustering, but more importantly allows the formulation of clustering procedures that are optimal with respect to a specified loss function. Our focus is on loss functions based on pairwise coincidences, that is, whether pairs of items are clustered into the same subset or not. Optimization of the posterior expected loss function can be formulated as a binary integer programming problem, which can be readily solved by standard software when clustering a modest number of items, but quickly becomes impractical as problem scale increases. To combat this, a new heuristic item-swapping algorithm is introduced. This performs well in our numerical experiments, on both simulated and real data examples. The article includes a comparison of the statistical performance of the (approximate) optimal clustering with earlier methods that are model-based but ad hoc in their detailed definition. © 2007 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.

An important problem in shape analysis is to match configurations of points in space after filtering out some geometrical transformation. In this paper we introduce hierarchical models for such tasks, in which the points in the configurations are either unlabelled or have at most a partial labelling constraining the matching, and in which some points may only appear in one of the configurations. We derive procedures for simultaneous inference about the matching and the transformation, using a Bayesian approach. Our hierarchical model is based on a Poisson process for hidden true point locations; this leads to considerable mathematical simplification and efficiency of implementation of EM and Markov chain Monte Carlo algorithms. We find a novel use for classical distributions from directional statistics in a conditionally conjugate specification for the case where the geometrical transformation includes an unknown rotation. Throughout, we focus on the case of affine or rigid motion transformations. Under a broad parametric family of loss functions, an optimal Bayesian point estimate of the matching matrix can be constructed that depends only on a single parameter of the family. Our methods are illustrated by two applications from bioinformatics. The first problem is of matching protein gels in two dimensions, and the second consists of aligning active sites of proteins in three dimensions. In the latter case, we also use information related to the grouping of the amino acids, as an example of a more general capability of our methodology to include partial labelling information. We discuss some open problems and suggest directions for future work. © 2006 Biometrika Trust.

We present Bayesian hierarchical models for the analysis of Affymetrix GeneChip data. The approach we take differs from other available approaches in two fundamental aspects. Firstly, we aim to integrate all processing steps of the raw data in a common statistically coherent framework, allowing all components and thus associated errors to be considered simultaneously. Secondly, inference is based on the full posterior distribution of gene expression indices and derived quantities, such as fold changes or ranks, rather than on single point estimates. Measures of uncertainty on these quantities are thus available. The models presented represent the first building block for integrated Bayesian Analysis of Affymetrix GeneChip data: the models take into account additive as well as multiplicative error, gene expression levels are estimated using perfect match and a fraction of mismatch probes and are modeled on the log scale. Background correction is incorporated by modeling true signal and cross-hybridization explicitly, and a need for further normalization is considerably reduced by allowing for array-specific distributions of nonspecific hybridization. When replicate arrays are available for a condition, posterior distributions of condition-specific gene expression indices are estimated directly, by a simultaneous consideration of replicate probe sets, avoiding averaging over estimates obtained from individual replicate arrays. The performance of the Bayesian model is compared to that of standard available point estimate methods on subsets of the well known GeneLogic and Affymetrix spike-in data. The Bayesian model is found to perform well and the integrated procedure presented appears to hold considerable promise for further development.

We extend the model of Karlof and Wagner for modelling side channel attacks via Input Driven Hidden Markov Models (IDHMM) to the case where not every state corresponds to a single observable symbol. This allows us to examine algorithms where errors in measurements can occur between sub-operations, e.g. there may be an error probability of distinguishing an add (A) versus a double (D) for an elliptic curve system. The prior work of Karlof and Wagner would assume the error was between distinguishing an add-double (AD) versus a double (D). Our model also allows the modelling of unknown values, where one is unable to determine whether a given observable is add or double, and is the first model to allow one to analyse incomplete traces. Hence, our extension allows a more realistic modelling of real side channel attacks. In addition we look at additional heuristic approaches to combine multiple traces together so as to deduce further information. © International Association for Cryptologic Research 2005.

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For a left-continuous random walk, absorbing at 0, the joint distribution of the maximum and time to absorption is derived. A description of the tails of the distributions and a conditional limit theorem are obtained for the cases where absorption is certain.