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Modern soil mapping is characterised by the need to interpolate samples of geostatistical response observations and the availability of relatively large numbers of environmental characteristics for consideration as covariates to aid this interpolation. We demonstrate the efficiency of the Least Angle Regression algorithm for Least Absolute Shrinkage and Selection Operator (LASSO) penalized multiple linear regression at selecting covariates to aid the spatial interpolation of geostatistical soil carbon observations under an ultrahigh dimensional scenario. Where an exhaustive search of the models that could be constructed from 800 potential covariate terms and 60 observations would be prohibitively demanding, LASSO variable selection is accomplished with trivial computational investment., Comment: 69 pages, 4 Figures

When making inferences concerning the environment, ground truthed data will frequently be available as point referenced (geostatistical) observations that are clustered into multiple sites rather than uniformly spaced across the area of interest. In such situations, the similarity of the dominant processes influencing the observed data across sites and the accuracy with which models fitted to data from one site can predict data from another site provide valuable information for scientists seeking to make inferences from these data. Such information may motivate a more informed second round of modelling of the data and also provides insight into the generality of the models developed and an indication of how these models may perform at predicting observations from other sites. We have investigated the geographic transferability of site specific models and compared the results of using different implementations of site specific effects in models for data combined from two sites. Since we have access to data on a broad collection of environmental characteristics that each held potential to aid the interpolation of our geostatistical response observations we have investigated these issues within the framework of a computationally efficient method for variable selection when the number of explanatory variables exceeds the number of observations. We have applied Least Absolute Shrinkage Selection Operator (LASSO) regularized Multiple Linear Regression (MLR) as fitted by the computationally efficient Least Angle Regression algorithm. The response variable in our case study, soil carbon, is of interest as a potential location for the sequestration of atmospheric carbon dioxide and for its positive contribution to soil health and fertility., Comment: 40 pages, 10 Figures, 4 Supplementary Figures, 2 Appendices

It can be important in Bayesian analyses of complex models to construct informative prior distributions which reflect knowledge external to the data at hand. Nevertheless, how much prior information an analyst can elicit from an expert will be limited due to constraints of time, cost and other factors. This paper develops effective numerical methods for exploring reasonable choices of a prior distribution from a parametric class, when prior information is specified in the form of some limited constraints on prior predictive distributions, and where these prior predictive distributions are analytically intractable. The methods developed may be thought of as a novel application of the ideas of history matching, a technique developed in the literature on assessment of computer models. We illustrate the approach in the context of logistic regression and sparse signal shrinkage prior distributions for high-dimensional linear models.

This paper presents new theory and methodology for the Bayesian estimation of overfitted hidden Markov models, with finite state space. The goal is then to achieve posterior emptying of extra states. A prior configuration is constructed which favours configurations where the hidden Markov chain remains ergodic although it empties out some of the states. Asymptotic posterior convergence rates are proven theoretically, and demonstrated with a large sample simulation. The problem of overfitted HMMs is then considered in the context of smaller sample sizes, and due to computational and mixing issues two alternative prior structures are studied, one commonly used in practice, and a mixture of the two priors. The Prior Parallel Tempering approach of van Havre (2015) is also extended to HMMs to allow MCMC estimation of the complex posterior space. A replicate simulation study and an in-depth exploration is performed to compare the three priors with hyperparameters chosen according to the asymptotic constraints alongside less informative alternatives., Comment: Submitted to Bayesian Analysis on 04-August-2015

The modelling of action potentials from extracellular recordings, or spike sorting, is a rich area of neuroscience research in which latent variable models are often used. Two such models, Overfitted Finite Mixture models (OFMs) and Dirichlet Process Mixture models (DPMs) are considered to provide insights for unsupervised clustering of complex, multivariate medical data when the number of clusters is unknown. OFM and DPM are structured in a similar hierarchical fashion but they are based on different philosophies with different underlying assumptions. This study investigates how these differences impact on a real study of spike sorting, for the estimation of multivariate Gaussian location-scale mixture models in the presence of common difficulties arising from complex medical data. The results provide insights allowing the future analyst to choose an approach suited to the situation and goal of the research problem at hand., Comment: Submitted to Australian & New Zealand Journal of Statistics on 31-Aug-2015

The inverse temperature parameter of the Potts model governs the strength of spatial cohesion and therefore has a major influence over the resulting model fit. A difficulty arises from the dependence of an intractable normalising constant on the value of this parameter and thus there is no closed-form solution for sampling from the posterior distribution directly. There are a variety of computational approaches for sampling from the posterior without evaluating the normalising constant, including the exchange algorithm and approximate Bayesian computation (ABC). A serious drawback of these algorithms is that they do not scale well for models with a large state space, such as images with a million or more pixels. We introduce a parametric surrogate model, which approximates the score function using an integral curve. Our surrogate model incorporates known properties of the likelihood, such as heteroskedasticity and critical temperature. We demonstrate this method using synthetic data as well as remotely-sensed imagery from the Landsat-8 satellite. We achieve up to a hundredfold improvement in the elapsed runtime, compared to the exchange algorithm or ABC. An open source implementation of our algorithm is available in the R package "bayesImageS."

This paper proposes solutions to three issues pertaining to the estimation of finite mixture models with an unknown number of components: the non-identifiability induced by overfitting the number of components, the mixing limitations of standard Markov Chain Monte Carlo (MCMC) sampling techniques, and the related label switching problem. An overfitting approach is used to estimate the number of components in a finite mixture model via a Zmix algorithm. Zmix provides a bridge between multidimensional samplers and test based estimation methods, whereby priors are chosen to encourage extra groups to have weights approaching zero. MCMC sampling is made possible by the implementation of prior parallel tempering, an extension of parallel tempering. Zmix can accurately estimate the number of components, posterior parameter estimates and allocation probabilities given a sufficiently large sample size. The results will reflect uncertainty in the final model and will report the range of possible candidate models and their respective estimated probabilities from a single run. Label switching is resolved with a computationally light-weight method, Zswitch, developed for overfitted mixtures by exploiting the intuitiveness of allocation-based relabelling algorithms and the precision of label-invariant loss functions. Four simulation studies are included to illustrate Zmix and Zswitch, as well as three case studies from the literature. All methods are available as part of the R package Zmix, which can currently be applied to univariate Gaussian mixture models

We consider a novel paradigm for Bayesian testing of hypotheses and Bayesian model comparison. Our alternative to the traditional construction of posterior probabilities that a given hypothesis is true or that the data originates from a specific model is to consider the models under comparison as components of a mixture model. We therefore replace the original testing problem with an estimation one that focus on the probability weight of a given model within a mixture model. We analyze the sensitivity on the resulting posterior distribution on the weights of various prior modeling on the weights. We stress that a major appeal in using this novel perspective is that generic improper priors are acceptable, while not putting convergence in jeopardy. Among other features, this allows for a resolution of the Lindley-Jeffreys paradox. When using a reference Beta B(a,a) prior on the mixture weights, we note that the sensitivity of the posterior estimations of the weights to the choice of a vanishes with the sample size increasing and avocate the default choice a=0.5, derived from Rousseau and Mengersen (2011). Another feature of this easily implemented alternative to the classical Bayesian solution is that the speeds of convergence of the posterior mean of the weight and of the corresponding posterior probability are quite similar., Comment: 25 pages, 6 figures, 2 tables

The issue of using informative priors for estimation of mixtures at multiple time points is examined. Several different informative priors and an independent prior are compared using samples of actual and simulated aerosol particle size distribution (PSD) data. Measurements of aerosol PSDs refer to the concentration of aerosol particles in terms of their size, which is typically multimodal in nature and collected at frequent time intervals. The use of informative priors is found to better identify component parameters at each time point and more clearly establish patterns in the parameters over time. Some caveats to this finding are discussed., Comment: Published in at http://dx.doi.org/10.1214/13-AOAS678 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

In images with low contrast-to-noise ratio (CNR), the information gain from the observed pixel values can be insufficient to distinguish foreground objects. A Bayesian approach to this problem is to incorporate prior information about the objects into a statistical model. This paper introduces a method for representing spatial prior information as an external field in a hidden Potts model of the image lattice. The prior distribution of the latent pixel labels is a mixture of Gaussian fields, centred on the positions of the objects at a previous point in time. This model is particularly applicable in longitudinal imaging studies, where the manual segmentation of one image can be used as a prior for automatic segmentation of subsequent images. The model is demonstrated by application to cone-beam computed tomography (CT), an imaging modality that exhibits distortions in pixel values due to X-ray scatter. The external field prior results in a substantial improvement in segmentation accuracy, reducing the mean pixel misclassification rate on our test images from 87% to 6%.

Most of the existing algorithms for approximate Bayesian computation (ABC) assume that it is feasible to simulate pseudo-data from the model at each iteration. However, the computational cost of these simulations can be prohibitive for high dimensional data. An important example is the Potts model, which is commonly used in image analysis. Images encountered in real world applications can have millions of pixels, therefore scalability is a major concern. We apply ABC with a synthetic likelihood to the hidden Potts model with additive Gaussian noise. Using a pre-processing step, we fit a binding function to model the relationship between the model parameters and the synthetic likelihood parameters. Our numerical experiments demonstrate that the precomputed binding function dramatically improves the scalability of ABC, reducing the average runtime required for model fitting from 71 hours to only 7 minutes. We also illustrate the method by estimating the smoothing parameter for remotely sensed satellite imagery. Without precomputation, Bayesian inference is impractical for datasets of that scale., Comment: 5th IMS-ISBA joint meeting (MCMSki IV)

Many interacting factors contribute to a student's choice of a university. This study takes a systems perspective of the choice and develops a Bayesian Network to represent and quantify these factors and their interactions. The systems model is illustrated through a small study of traditional school leavers in Australia, and highlights similarities and differences between universities' perceptions of student choices, students' perceptions of factors that they should consider and how students really make choices. The study shows the range of information that can be gained from this approach, including identification of important factors and scenario assessment.

We introduce a dependent Bayesian nonparametric model for the probabilistic modeling of membership of subgroups in a community based on partially replicated data. The focus here is on species-by-site data, i.e. community data where observations at different sites are classified in distinct species. Our aim is to study the impact of additional covariates, for instance environmental variables, on the data structure, and in particular on the community diversity. To that purpose, we introduce dependence a priori across the covariates, and show that it improves posterior inference. We use a dependent version of the Griffiths-Engen-McCloskey distribution defined via the stick-breaking construction. This distribution is obtained by transforming a Gaussian process whose covariance function controls the desired dependence. The resulting posterior distribution is sampled by Markov chain Monte Carlo. We illustrate the application of our model to a soil microbial dataset acquired across a hydrocarbon contamination gradient at the site of a fuel spill in Antarctica. This method allows for inference on a number of quantities of interest in ecotoxicology, such as diversity or effective concentrations, and is broadly applicable to the general problem of communities response to environmental variables., Comment: Main Paper: 22 pages, 6 figures. Supplementary Material: 11 pages, 1 figure

A Bayesian approach is developed to analyze change points in multivariate time series and space-time data. The methodology is used to assess the impact of extended inundation on the ecosystem of the Gulf Plains bioregion in northern Australia. The proposed approach can be implemented for dynamic mixture models that have a conditionally Gaussian state space representation. Details are given on how to efficiently implement the algorithm for a general class of multivariate time series and space-time models. This efficient implementation makes it feasible to analyze high dimensional, but of realistic size, space-time data sets because our approach can be appreciably faster, possibly millions of times, than a standard implementation in such cases., Comment: 24 pages, 4 figures

Observational time series data often exhibit both cyclic temporal trends and autocorrelation and may also depend on covariates. As such, there is a need for flexible regression models that are able to capture these trends and model any residual autocorrelation simultaneously. Modelling the autocorrelation in the residuals leads to more realistic forecasts than an assumption of independence. In this paper we propose a method which combines spline-based semi-parametric regression modelling with the modelling of auto-regressive errors. The method is applied to a simulated data set in order to show its efficacy and to ultrafine particle number concentration in Helsinki, Finland, to show its use in real world problems.

There has been a lively debate in many fields, including statistics and related applied fields such as psychology and biomedical research, on possible reforms of the scholarly publishing system. Currently, referees contribute so much to improve scientific papers, both directly through constructive criticism and indirectly through the threat of rejection. We discuss ways in which new approaches to journal publication could continue to make use of the valuable efforts of peer reviewers., Comment: 13 pages