Hierarchical modelling of timber reference properties using probabilistic methods: Maximum Likelihood Method, Bayesian Methods and Probability Networks

In recent decades, an increased interest has been evidenced in the research on multi-scale hierarchical modelling in the field of mechanics, and also in the field of wood products and timber engineering. One of the main motivations for hierar-chical modelling is to understand how properties, composition and structure at lower scale levels may influence and be used to predict the material properties on a macroscopic and structural engineering scale. This chapter presents the applicability of statistic and probabilistic methods, such as the Maximum Likelihood method and Bayesian methods, in the representation of timber’s mechanical properties and its inference accounting to prior information obtained in different importance scales. These methods allow to analyse distinct timber’s reference properties, such as density, bending stiffness and strength, and hierarchically consider information obtained through different non, semi or destructive tests. The basis and fundaments of the methods are described and also recommendations and limitations are discussed. The methods may be used in several contexts, however require an expert’s knowledge to assess the correct statistic fitting and define the correlation arrangement between properties.

An empirical hierarchical Bayesian unification of occupational exposure assessment methods.

In occupational exposure assessment of airborne contaminants, exposure levels can either be estimated through repeated measurements of the pollutant concentration in air, expert judgment or through exposure models that use information on the conditions of exposure as input. In this report, we propose an empirical hierarchical Bayesian model to unify these approaches. Prior to any measurement, the hygienist conducts an assessment to generate prior distributions of exposure determinants. Monte-Carlo samples from these distributions feed two level-2 models: a physical, two-compartment model, and a non-parametric, neural network model trained with existing exposure data. The outputs of these two models are weighted according to the expert's assessment of their relevance to yield predictive distributions of the long-term geometric mean and geometric standard deviation of the worker's exposure profile (level-1 model). Bayesian inferences are then drawn iteratively from subsequent measurements of worker exposure. Any traditional decision strategy based on a comparison with occupational exposure limits (e.g. mean exposure, exceedance strategies) can then be applied. Data on 82 workers exposed to 18 contaminants in 14 companies were used to validate the model with cross-validation techniques. A user-friendly program running the model is available upon request.

The seasonal forecast of electricity demand: A hierarchical Bayesian model with climatological weather generator

In this paper we focus on the one year ahead prediction of the electricity peak-demand daily trajectory during the winter season in Central England and Wales. We define a Bayesian hierarchical model for predicting the winter trajectories and present results based on the past observed weather. Thanks to the flexibility of the Bayesian approach, we are able to produce the marginal posterior distributions of all the predictands of interest. This is a fundamental progress with respect to the classical methods. The results are encouraging in both skill and representation of uncertainty. Further extensions are straightforward at least in principle. The main two of those consist in conditioning the weather generator model with respect to additional information like the knowledge of the first part of the winter and/or the seasonal weather forecast. Copyright (C) 2006 John Wiley & Sons, Ltd.

A hierarchical Bayesian model for predicting the functional consequences of amino-acid polymorphisms

Genetic polymorphisms in deoxyribonucleic acid coding regions may have a phenotypic effect on the carrier, e.g. by influencing susceptibility to disease. Detection of deleterious mutations via association studies is hampered by the large number of candidate sites; therefore methods are needed to narrow down the search to the most promising sites. For this, a possible approach is to use structural and sequence-based information of the encoded protein to predict whether a mutation at a particular site is likely to disrupt the functionality of the protein itself. We propose a hierarchical Bayesian multivariate adaptive regression spline (BMARS) model for supervised learning in this context and assess its predictive performance by using data from mutagenesis experiments on lac repressor and lysozyme proteins. In these experiments, about 12 amino-acid substitutions were performed at each native amino-acid position and the effect on protein functionality was assessed. The training data thus consist of repeated observations at each position, which the hierarchical framework is needed to account for. The model is trained on the lac repressor data and tested on the lysozyme mutations and vice versa. In particular, we show that the hierarchical BMARS model, by allowing for the clustered nature of the data, yields lower out-of-sample misclassification rates compared with both a BMARS and a frequen-tist MARS model, a support vector machine classifier and an optimally pruned classification tree.

The seasonal forecast of electricity demand: A hierarchical Bayesian model with climatological weather generator

In this paper we focus on the one year ahead prediction of the electricity peak-demand daily trajectory during the winter season in Central England and Wales. We define a Bayesian hierarchical model for predicting the winter trajectories and present results based on the past observed weather. Thanks to the flexibility of the Bayesian approach, we are able to produce the marginal posterior distributions of all the predictands of interest. This is a fundamental progress with respect to the classical methods. The results are encouraging in both skill and representation of uncertainty. Further extensions are straightforward at least in principle. The main two of those consist in conditioning the weather generator model with respect to additional information like the knowledge of the first part of the winter and/or the seasonal weather forecast. Copyright (C) 2006 John Wiley & Sons, Ltd.

Global trends and factors associated with the illegal killing of elephants: a hierarchical bayesian analysis of carcass encounter data

Elephant poaching and the ivory trade remain high on the agenda at meetings of the Convention on International Trade in Endangered Species of Wild Fauna and Flora (CITES). Well-informed debates require robust estimates of trends, the spatial distribution of poaching, and drivers of poaching. We present an analysis of trends and drivers of an indicator of elephant poaching of all elephant species. The site-based monitoring system known as Monitoring the Illegal Killing of Elephants (MIKE), set up by the 10th Conference of the Parties of CITES in 1997, produces carcass encounter data reported mainly by anti-poaching patrols. Data analyzed were site by year totals of 6,337 carcasses from 66 sites in Africa and Asia from 2002–2009. Analysis of these observational data is a serious challenge to traditional statistical methods because of the opportunistic and non-random nature of patrols, and the heterogeneity across sites. Adopting a Bayesian hierarchical modeling approach, we used the proportion of carcasses that were illegally killed (PIKE) as a poaching index, to estimate the trend and the effects of site- and country-level factors associated with poaching. Important drivers of illegal killing that emerged at country level were poor governance and low levels of human development, and at site level, forest cover and area of the site in regions where human population density is low. After a drop from 2002, PIKE remained fairly constant from 2003 until 2006, after which it increased until 2008. The results for 2009 indicate a decline. Sites with PIKE ranging from the lowest to the highest were identified. The results of the analysis provide a sound information base for scientific evidence-based decision making in the CITES process.

Sparse hierarchical Bayesian models for detecting relevant antigenic sites in virus evolution

Understanding how virus strains offer protection against closely related emerging strains is vital for creating effective vaccines. For many viruses, including Foot-and-Mouth Disease Virus (FMDV) and the Influenza virus where multiple serotypes often co-circulate, in vitro testing of large numbers of vaccines can be infeasible. Therefore the development of an in silico predictor of cross-protection between strains is important to help optimise vaccine choice. Vaccines will offer cross-protection against closely related strains, but not against those that are antigenically distinct. To be able to predict cross-protection we must understand the antigenic variability within a virus serotype, distinct lineages of a virus, and identify the antigenic residues and evolutionary changes that cause the variability. In this thesis we present a family of sparse hierarchical Bayesian models for detecting relevant antigenic sites in virus evolution (SABRE), as well as an extended version of the method, the extended SABRE (eSABRE) method, which better takes into account the data collection process. The SABRE methods are a family of sparse Bayesian hierarchical models that use spike and slab priors to identify sites in the viral protein which are important for the neutralisation of the virus. In this thesis we demonstrate how the SABRE methods can be used to identify antigenic residues within different serotypes and show how the SABRE method outperforms established methods, mixed-effects models based on forward variable selection or l1 regularisation, on both synthetic and viral datasets. In addition we also test a number of different versions of the SABRE method, compare conjugate and semi-conjugate prior specifications and an alternative to the spike and slab prior; the binary mask model. We also propose novel proposal mechanisms for the Markov chain Monte Carlo (MCMC) simulations, which improve mixing and convergence over that of the established component-wise Gibbs sampler. The SABRE method is then applied to datasets from FMDV and the Influenza virus in order to identify a number of known antigenic residue and to provide hypotheses of other potentially antigenic residues. We also demonstrate how the SABRE methods can be used to create accurate predictions of the important evolutionary changes of the FMDV serotypes. In this thesis we provide an extended version of the SABRE method, the eSABRE method, based on a latent variable model. The eSABRE method takes further into account the structure of the datasets for FMDV and the Influenza virus through the latent variable model and gives an improvement in the modelling of the error. We show how the eSABRE method outperforms the SABRE methods in simulation studies and propose a new information criterion for selecting the random effects factors that should be included in the eSABRE method; block integrated Widely Applicable Information Criterion (biWAIC). We demonstrate how biWAIC performs equally to two other methods for selecting the random effects factors and combine it with the eSABRE method to apply it to two large Influenza datasets. Inference in these large datasets is computationally infeasible with the SABRE methods, but as a result of the improved structure of the likelihood, we are able to show how the eSABRE method offers a computational improvement, leading it to be used on these datasets. The results of the eSABRE method show that we can use the method in a fully automatic manner to identify a large number of antigenic residues on a variety of the antigenic sites of two Influenza serotypes, as well as making predictions of a number of nearby sites that may also be antigenic and are worthy of further experiment investigation.

Bayesian methods for estimation, optimization and experimental design

Mathematical models often contain parameters that need to be calibrated from measured data. The emergence of efficient Markov Chain Monte Carlo (MCMC) methods has made the Bayesian approach a standard tool in quantifying the uncertainty in the parameters. With MCMC, the parameter estimation problem can be solved in a fully statistical manner, and the whole distribution of the parameters can be explored, instead of obtaining point estimates and using, e.g., Gaussian approximations. In this thesis, MCMC methods are applied to parameter estimation problems in chemical reaction engineering, population ecology, and climate modeling. Motivated by the climate model experiments, the methods are developed further to make them more suitable for problems where the model is computationally intensive. After the parameters are estimated, one can start to use the model for various tasks. Two such tasks are studied in this thesis: optimal design of experiments, where the task is to design the next measurements so that the parameter uncertainty is minimized, and model-based optimization, where a model-based quantity, such as the product yield in a chemical reaction model, is optimized. In this thesis, novel ways to perform these tasks are developed, based on the output of MCMC parameter estimation. A separate topic is dynamical state estimation, where the task is to estimate the dynamically changing model state, instead of static parameters. For example, in numerical weather prediction, an estimate of the state of the atmosphere must constantly be updated based on the recently obtained measurements. In this thesis, a novel hybrid state estimation method is developed, which combines elements from deterministic and random sampling methods.

Use of Bayesian Methods for Multivariate Bioequivalence Measures

In this paper, we introduce a Bayesian analysis for bioequivalence data assuming multivariate pharmacokinetic measures. With the introduction of correlation parameters between the pharmacokinetic measures or between the random effects in the bioequivalence models, we observe a good improvement in the bioequivalence results. These results are of great practical interest since they can yield higher accuracy and reliability for the bioequivalence tests, usually assumed by regulatory offices. An example is introduced to illustrate the proposed methodology by comparing the usual univariate bioequivalence methods with multivariate bioequivalence. We also consider some usual existing discrimination Bayesian methods to choose the best model to be used in bioequivalence studies.

A Hierarchical Bayesian Model for Measuring Motion Adaptation

Previous research has shown that motion imagery draws on the same neural circuits that are involved in perception of motion, thus leading to a motion aftereffect (Winawer et al., 2010). Imagined stimuli can induce a similar shift in participants’ psychometric functions as neural adaptation due to a perceived stimulus. However, these studies have been criticized on the grounds that they fail to exclude the possibility that the subjects might have guessed the experimental hypothesis, and behaved accordingly (Morgan et al., 2012). In particular, the authors claim that participants can adopt arbitrary response criteria, which results in similar changes of the central tendency μ of psychometric curves as those shown by Winawer et al. (2010).

Simultaneous 3D object tracking and camera parameter estimation by Bayesian methods and transdimensional MCMC sampling

Multi-camera 3D tracking systems with overlapping cameras represent a powerful mean for scene analysis, as they potentially allow greater robustness than monocular systems and provide useful 3D information about object location and movement. However, their performance relies on accurately calibrated camera networks, which is not a realistic assumption in real surveillance environments. Here, we introduce a multi-camera system for tracking the 3D position of a varying number of objects and simultaneously refin-ing the calibration of the network of overlapping cameras. Therefore, we introduce a Bayesian framework that combines Particle Filtering for tracking with recursive Bayesian estimation methods by means of adapted transdimensional MCMC sampling. Addi-tionally, the system has been designed to work on simple motion detection masks, making it suitable for camera networks with low transmission capabilities. Tests show that our approach allows a successful performance even when starting from clearly inaccurate camera calibrations, which would ruin conventional approaches.

Bayesian methods for neural networks

Bayesian techniques have been developed over many years in a range of different fields, but have only recently been applied to the problem of learning in neural networks. As well as providing a consistent framework for statistical pattern recognition, the Bayesian approach offers a number of practical advantages including a potential solution to the problem of over-fitting. This chapter aims to provide an introductory overview of the application of Bayesian methods to neural networks. It assumes the reader is familiar with standard feed-forward network models and how to train them using conventional techniques.

Bayesian methods for neural networks

Bayesian techniques have been developed over many years in a range of different fields, but have only recently been applied to the problem of learning in neural networks. As well as providing a consistent framework for statistical pattern recognition, the Bayesian approach offers a number of practical advantages including a potential solution to the problem of over-fitting. This chapter aims to provide an introductory overview of the application of Bayesian methods to neural networks. It assumes the reader is familiar with standard feed-forward network models and how to train them using conventional techniques.

Cascaded Bayesian processes: an account of bias in orientation perception

Following adaptation to an oriented (1-d) signal in central vision, the orientation of subsequently viewed test signals may appear repelled away from or attracted towards the adapting orientation. Small angular differences between the adaptor and test yield 'repulsive' shifts, while large angular differences yield 'attractive' shifts. In peripheral vision, however, both small and large angular differences yield repulsive shifts. To account for these tilt after-effects (TAEs), a cascaded model of orientation estimation that is optimized using hierarchical Bayesian methods is proposed. The model accounts for orientation bias through adaptation-induced losses in information that arise because of signal uncertainties and neural constraints placed upon the propagation of visual information. Repulsive (direct) TAEs arise at early stages of visual processing from adaptation of orientation-selective units with peak sensitivity at the orientation of the adaptor (theta). Attractive (indirect) TAEs result from adaptation of second-stage units with peak sensitivity at theta and theta+90 degrees , which arise from an efficient stage of linear compression that pools across the responses of the first-stage orientation-selective units. A spatial orientation vector is estimated from the transformed oriented unit responses. The change from attractive to repulsive TAEs in peripheral vision can be explained by the differing harmonic biases resulting from constraints on signal power (in central vision) versus signal uncertainties in orientation (in peripheral vision). The proposed model is consistent with recent work by computational neuroscientists in supposing that visual bias reflects the adjustment of a rational system in the light of uncertain signals and system constraints.