The Bayesian conditional independence model for measurement error: applications in ecology

The measurement error model is a well established statistical method for regression problems in medical sciences, although rarely used in ecological studies. While the situations in which it is appropriate may be less common in ecology, there are instances in which there may be benefits in its use for prediction and estimation of parameters of interest. We have chosen to explore this topic using a conditional independence model in a Bayesian framework using a Gibbs sampler, as this gives a great deal of flexibility, allowing us to analyse a number of different models without losing generality. Using simulations and two examples, we show how the conditional independence model can be used in ecology, and when it is appropriate.

A sequential Monte Carlo algorithm to incorporate model uncertainty in Bayesian sequential design

Here we present a sequential Monte Carlo (SMC) algorithm that can be used for any one-at-a-time Bayesian sequential design problem in the presence of model uncertainty where discrete data are encountered. Our focus is on adaptive design for model discrimination but the methodology is applicable if one has a different design objective such as parameter estimation or prediction. An SMC algorithm is run in parallel for each model and the algorithm relies on a convenient estimator of the evidence of each model which is essentially a function of importance sampling weights. Other methods for this task such as quadrature, often used in design, suffer from the curse of dimensionality. Approximating posterior model probabilities in this way allows us to use model discrimination utility functions derived from information theory that were previously difficult to compute except for conjugate models. A major benefit of the algorithm is that it requires very little problem specific tuning. We demonstrate the methodology on three applications, including discriminating between models for decline in motor neuron numbers in patients suffering from neurological diseases such as Motor Neuron disease.

Using a Bayesian network to model colonisation with Vancomycin Resistant Enterococcus (VRE)

Objective: Effective management of multi-resistant organisms is an important issue for hospitals both in Australia and overseas. This study investigates the utility of using Bayesian Network (BN) analysis to examine relationships between risk factors and colonization with Vancomycin Resistant Enterococcus (VRE). Design: Bayesian Network Analysis was performed using infection control data collected over a period of 36 months (2008-2010). Setting: Princess Alexandra Hospital (PAH), Brisbane. Outcome of interest: Number of new VRE Isolates Methods: A BN is a probabilistic graphical model that represents a set of random variables and their conditional dependencies via a directed acyclic graph (DAG). BN enables multiple interacting agents to be studied simultaneously. The initial BN model was constructed based on the infectious disease physician‟s expert knowledge and current literature. Continuous variables were dichotomised by using third quartile values of year 2008 data. BN was used to examine the probabilistic relationships between VRE isolates and risk factors; and to establish which factors were associated with an increased probability of a high number of VRE isolates. Software: Netica (version 4.16). Results: Preliminary analysis revealed that VRE transmission and VRE prevalence were the most influential factors in predicting a high number of VRE isolates. Interestingly, several factors (hand hygiene and cleaning) known through literature to be associated with VRE prevalence, did not appear to be as influential as expected in this BN model. Conclusions: This preliminary work has shown that Bayesian Network Analysis is a useful tool in examining clinical infection prevention issues, where there is often a web of factors that influence outcomes. This BN model can be restructured easily enabling various combinations of agents to be studied.

A Bayesian approach to the determination of ignition delay

A novel in-cylinder pressure method for determining ignition delay has been proposed and demonstrated. This method proposes a new Bayesian statistical model to resolve the start of combustion, defined as being the point at which the band-pass in-cylinder pressure deviates from background noise and the combustion resonance begins. Further, it is demonstrated that this method is still accurate in situations where there is noise present. The start of combustion can be resolved for each cycle without the need for ad hoc methods such as cycle averaging. Therefore, this method allows for analysis of consecutive cycles and inter-cycle variability studies. Ignition delay obtained by this method and by the net rate of heat release have been shown to give good agreement. However, the use of combustion resonance to determine the start of combustion is preferable over the net rate of heat release method because it does not rely on knowledge of heat losses and will still function accurately in the presence of noise. Results for a six-cylinder turbo-charged common-rail diesel engine run with neat diesel fuel at full, three quarters and half load have been presented. Under these conditions the ignition delay was shown to increase as the load was decreased with a significant increase in ignition delay at half load, when compared with three quarter and full loads.

Bayesian indirect inference using a parametric auxiliary model

Indirect inference (II) is a methodology for estimating the parameters of an intractable (generative) model on the basis of an alternative parametric (auxiliary) model that is both analytically and computationally easier to deal with. Such an approach has been well explored in the classical literature but has received substantially less attention in the Bayesian paradigm. The purpose of this paper is to compare and contrast a collection of what we call parametric Bayesian indirect inference (pBII) methods. One class of pBII methods uses approximate Bayesian computation (referred to here as ABC II) where the summary statistic is formed on the basis of the auxiliary model, using ideas from II. Another approach proposed in the literature, referred to here as parametric Bayesian indirect likelihood (pBIL), we show to be a fundamentally different approach to ABC II. We devise new theoretical results for pBIL to give extra insights into its behaviour and also its differences with ABC II. Furthermore, we examine in more detail the assumptions required to use each pBII method. The results, insights and comparisons developed in this paper are illustrated on simple examples and two other substantive applications. The first of the substantive examples involves performing inference for complex quantile distributions based on simulated data while the second is for estimating the parameters of a trivariate stochastic process describing the evolution of macroparasites within a host based on real data. We create a novel framework called Bayesian indirect likelihood (BIL) which encompasses pBII as well as general ABC methods so that the connections between the methods can be established.

The impact of spatial scales and spatial smoothing on the outcome of Bayesian spatial model

Discretization of a geographical region is quite common in spatial analysis. There have been few studies into the impact of different geographical scales on the outcome of spatial models for different spatial patterns. This study aims to investigate the impact of spatial scales and spatial smoothing on the outcomes of modelling spatial point-based data. Given a spatial point-based dataset (such as occurrence of a disease), we study the geographical variation of residual disease risk using regular grid cells. The individual disease risk is modelled using a logistic model with the inclusion of spatially unstructured and/or spatially structured random effects. Three spatial smoothness priors for the spatially structured component are employed in modelling, namely an intrinsic Gaussian Markov random field, a second-order random walk on a lattice, and a Gaussian field with Matern correlation function. We investigate how changes in grid cell size affect model outcomes under different spatial structures and different smoothness priors for the spatial component. A realistic example (the Humberside data) is analyzed and a simulation study is described. Bayesian computation is carried out using an integrated nested Laplace approximation. The results suggest that the performance and predictive capacity of the spatial models improve as the grid cell size decreases for certain spatial structures. It also appears that different spatial smoothness priors should be applied for different patterns of point data.

Approximate Bayesian computation using auxiliary model based estimates

We present a novel approach for developing summary statistics for use in approximate Bayesian computation (ABC) algorithms using indirect infer- ence. We embed this approach within a sequential Monte Carlo algorithm that is completely adaptive. This methodological development was motivated by an application involving data on macroparasite population evolution modelled with a trivariate Markov process. The main objective of the analysis is to compare inferences on the Markov process when considering two di®erent indirect mod- els. The two indirect models are based on a Beta-Binomial model and a three component mixture of Binomials, with the former providing a better ¯t to the observed data.

A Bayesian hurdle model for analysis of an insect resistance monitoring database

Motivated by the analysis of the Australian Grain Insect Resistance Database (AGIRD), we develop a Bayesian hurdle modelling approach to assess trends in strong resistance of stored grain insects to phosphine over time. The binary response variable from AGIRD indicating presence or absence of strong resistance is characterized by a majority of absence observations and the hurdle model is a two step approach that is useful when analyzing such a binary response dataset. The proposed hurdle model utilizes Bayesian classification trees to firstly identify covariates and covariate levels pertaining to possible presence or absence of strong resistance. Secondly, generalized additive models (GAMs) with spike and slab priors for variable selection are fitted to the subset of the dataset identified from the Bayesian classification tree indicating possibility of presence of strong resistance. From the GAM we assess trends, biosecurity issues and site specific variables influencing the presence of strong resistance using a variable selection approach. The proposed Bayesian hurdle model is compared to its frequentist counterpart, and also to a naive Bayesian approach which fits a GAM to the entire dataset. The Bayesian hurdle model has the benefit of providing a set of good trees for use in the first step and appears to provide enough flexibility to represent the influence of variables on strong resistance compared to the frequentist model, but also captures the subtle changes in the trend that are missed by the frequentist and naive Bayesian models.

Approximate Bayesian Computation for astronomical model analysis : a case study in galaxy demographics and morphological transformation at high redshift

Approximate Bayesian Computation’ (ABC) represents a powerful methodology for the analysis of complex stochastic systems for which the likelihood of the observed data under an arbitrary set of input parameters may be entirely intractable – the latter condition rendering useless the standard machinery of tractable likelihood-based, Bayesian statistical inference [e.g. conventional Markov chain Monte Carlo (MCMC) simulation]. In this paper, we demonstrate the potential of ABC for astronomical model analysis by application to a case study in the morphological transformation of high-redshift galaxies. To this end, we develop, first, a stochastic model for the competing processes of merging and secular evolution in the early Universe, and secondly, through an ABC-based comparison against the observed demographics of massive (Mgal > 1011 M⊙) galaxies (at 1.5 < z < 3) in the Cosmic Assembly Near-IR Deep Extragalatic Legacy Survey (CANDELS)/Extended Groth Strip (EGS) data set we derive posterior probability densities for the key parameters of this model. The ‘Sequential Monte Carlo’ implementation of ABC exhibited herein, featuring both a self-generating target sequence and self-refining MCMC kernel, is amongst the most efficient of contemporary approaches to this important statistical algorithm. We highlight as well through our chosen case study the value of careful summary statistic selection, and demonstrate two modern strategies for assessment and optimization in this regard. Ultimately, our ABC analysis of the high-redshift morphological mix returns tight constraints on the evolving merger rate in the early Universe and favours major merging (with disc survival or rapid reformation) over secular evolution as the mechanism most responsible for building up the first generation of bulges in early-type discs.

Model choice problems using approximate Bayesian computation with applications to pathogen transmission data sets

Analytically or computationally intractable likelihood functions can arise in complex statistical inferential problems making them inaccessible to standard Bayesian inferential methods. Approximate Bayesian computation (ABC) methods address such inferential problems by replacing direct likelihood evaluations with repeated sampling from the model. ABC methods have been predominantly applied to parameter estimation problems and less to model choice problems due to the added difficulty of handling multiple model spaces. The ABC algorithm proposed here addresses model choice problems by extending Fearnhead and Prangle (2012, Journal of the Royal Statistical Society, Series B 74, 1–28) where the posterior mean of the model parameters estimated through regression formed the summary statistics used in the discrepancy measure. An additional stepwise multinomial logistic regression is performed on the model indicator variable in the regression step and the estimated model probabilities are incorporated into the set of summary statistics for model choice purposes. A reversible jump Markov chain Monte Carlo step is also included in the algorithm to increase model diversity for thorough exploration of the model space. This algorithm was applied to a validating example to demonstrate the robustness of the algorithm across a wide range of true model probabilities. Its subsequent use in three pathogen transmission examples of varying complexity illustrates the utility of the algorithm in inferring preference of particular transmission models for the pathogens.

Application of a Bayesian Network complex system model to a successful community electricity demand reduction program

Utilities worldwide are focused on supplying peak electricity demand reliably and cost effectively, requiring a thorough understanding of all the factors influencing residential electricity use at peak times. An electricity demand reduction project based on comprehensive residential consumer engagement was established within an Australian community in 2008, and by 2011, peak demand had decreased to below pre-intervention levels. This paper applied field data discovered through qualitative in-depth interviews of 22 residential households at the community to a Bayesian Network complex system model to examine whether the system model could explain successful peak demand reduction in the case study location. The knowledge and understanding acquired through insights into the major influential factors and the potential impact of changes to these factors on peak demand would underpin demand reduction intervention strategies for a wider target group.