Computing the Stochastic Complexity of Simple Probabilistic Graphical Models

Minimum Description Length (MDL) is an information-theoretic principle that can be used for model selection and other statistical inference tasks. There are various ways to use the principle in practice. One theoretically valid way is to use the normalized maximum likelihood (NML) criterion. Due to computational difficulties, this approach has not been used very often. This thesis presents efficient floating-point algorithms that make it possible to compute the NML for multinomial, Naive Bayes and Bayesian forest models. None of the presented algorithms rely on asymptotic analysis and with the first two model classes we also discuss how to compute exact rational number solutions.

Factors influencing kinetic and equilibrium behaviour of sodium ion exchange with strong acid cation resin

This study reports an investigation of the ion exchange treatment of sodium chloride solutions in relation to use of resin technology for applications such as desalination of brackish water. In particular, a strong acid cation (SAC) resin (DOW Marathon C) was studied to determine its capacity for sodium uptake and to evaluate the fundamentals of the ion exchange process involved. Key questions to answer included: impact of resin identity; best models to simulate the kinetics and equilibrium exchange behaviour of sodium ions; difference between using linear least squares (LLS) and non-linear least squares (NLLS) methods for data interpretation; and, effect of changing the type of anion in solution which accompanied the sodium species. Kinetic studies suggested that the exchange process was best described by a pseudo first order rate expression based upon non-linear least squares analysis of the test data. Application of the Langmuir Vageler isotherm model was recommended as it allowed confirmation that experimental conditions were sufficient for maximum loading of sodium ions to occur. The Freundlich expression best fitted the equilibrium data when analysing the information by a NLLS approach. In contrast, LLS methods suggested that the Langmuir model was optimal for describing the equilibrium process. The Competitive Langmuir model which considered the stoichiometric nature of ion exchange process, estimated the maximum loading of sodium ions to be 64.7 g Na/kg resin. This latter value was comparable to sodium ion capacities for SAC resin published previously. Inherent discrepancies involved when using linearized versions of kinetic and isotherm equations were illustrated, and despite their widespread use, the value of this latter approach was questionable. The equilibrium behaviour of sodium ions form sodium fluoride solution revealed that the sodium ions were now more preferred by the resin compared to the situation with sodium chloride. The solution chemistry of hydrofluoric acid was suggested as promoting the affinity of the sodium ions to the resin.

Effects of environmental variation on ecological and evolutionary dynamics

Environmental variation is a fact of life for all the species on earth: for any population of any particular species, the local environmental conditions are liable to vary in both time and space. In today's world, anthropogenic activity is causing habitat loss and fragmentation for many species, which may profoundly alter the characteristics of environmental variation in remaining habitat. Previous research indicates that, as habitat is lost, the spatial configuration of remaining habitat will increasingly affect the dynamics by which populations are governed. Through the use of mathematical models, this thesis asks how environmental variation interacts with species properties to influence population dynamics, local adaptation, and dispersal evolution. More specifically, we couple continuous-time continuous-space stochastic population dynamic models to landscape models. We manipulate environmental variation via parameters such as mean patch size, patch density, and patch longevity. Among other findings, we show that a mixture of high and low quality habitat is commonly better for a population than uniformly mediocre habitat. This conclusion is justified by purely ecological arguments, yet the positive effects of landscape heterogeneity may be enhanced further by local adaptation, and by the evolution of short-ranged dispersal. The predicted evolutionary responses to environmental variation are complex, however, since they involve numerous conflicting factors. We discuss why the species that have high levels of local adaptation within their ranges may not be the same species that benefit from local adaptation during range expansion. We show how habitat loss can lead to either increased or decreased selection for dispersal depending on the type of habitat and the manner in which it is lost. To study the models, we develop a recent analytical method, Perturbation expansion, to enable the incorporation of environmental variation. Within this context, we use two methods to address evolutionary dynamics: Adaptive dynamics, which assumes mutations occur infrequently so that the ecological and evolutionary timescales can be separated, and via Genotype distributions, which assume mutations are more frequent. The two approaches generally lead to similar predictions yet, exceptionally, we show how the evolutionary response of dispersal behaviour to habitat turnover may qualitatively depend on the mutation rate.

Evaluation of methods and applications for behavioural profiling of transgenic mice

During the last 10-15 years interest in mouse behavioural analysis has evolved considerably. The driving force is development in molecular biological techniques that allow manipulation of the mouse genome by changing the expression of genes. Therefore, with some limitations it is possible to study how genes participate in regulation of physiological functions and to create models explaining genetic contribution to various pathological conditions. The first aim of our study was to establish a framework for behavioural phenotyping of genetically modified mice. We established comprehensive battery of tests for the initial screening of mutant mice. These included tests for exploratory and locomotor activity, emotional behaviour, sensory functions, and cognitive performance. Our interest was in the behavioural patterns of common background strains used for genetic manipulations in mice. Additionally we studied the behavioural effect of sex differences, test history, and individual housing. Our findings highlight the importance of careful consideration of genetic background for analysis of mutant mice. It was evident that some backgrounds may mask or modify the behavioural phenotype of mutants and thereby lead to false positive or negative findings. Moreover, there is no universal strain that is equally suitable for all tests, and using different backgrounds allows one to address possible phenotype modifying factors. We discovered that previous experience affected performance in several tasks. The most sensitive traits were the exploratory and emotional behaviour, as well as motor and nociceptive functions. Therefore, it may be essential to repeat some of the tests in naïve animals for assuring the phenotype. Social isolation for a long time period had strong effects on exploratory behaviour, but also on learning and memory. All experiments revealed significant interactions between strain and environmental factors (test history or housing condition) indicating genotype-dependent effects of environmental manipulations. Several mutant line analyses utilize this information. For example, we studied mice overexpressing as well as those lacking extracellular matrix protein heparin-binding growth-associated molecule (HB-GAM), and mice lacking N-syndecan (a receptor for HB-GAM). All mutant mice appeared to be fertile and healthy, without any apparent neurological or sensory defects. The lack of HB-GAM and N-syndecan, however, significantly reduced the learning capacity of the mice. On the other hand, overexpression of HB-GAM resulted in facilitated learning. Moreover, HB-GAM knockout mice displayed higher anxiety-like behaviour, whereas anxiety was reduced in HB-GAM overexpressing mice. Changes in hippocampal plasticity accompanied the behavioural phenotypes. We conclude that HB-GAM and N-syndecan are involved in the modulation of synaptic plasticity in hippocampus and play a role in regulation of anxiety- and learning-related behaviour.

Deformation and stability regression models for soil nail walls

Lateral displacement and global stability are the two main stability criteria for soil nail walls. Conventional design methods do not adequately address the deformation behaviour of soil nail walls, owing to the complexity involved in handling a large number of influencing factors. Consequently, limited methods of deformation estimates based on empirical relationships and in situ performance monitoring are available in the literature. It is therefore desirable that numerical techniques and statistical methods are used in order to gain a better insight into the deformation behaviour of soil nail walls. In the present study numerical experiments are conducted using a 2 4 factorial design method. Based on analysis of the maximum lateral deformation and factor-of-safety observations from the numerical experiments, regression models for maximum lateral deformation and factor-of-safety prediction are developed and checked for adequacy. Selection of suitable design factors for the 2 4 factorial design of numerical experiments enabled the use of the proposed regression models over a practical range of soil nail wall heights and in situ soil variability. It is evident from the model adequacy analyses and illustrative example that the proposed regression models provided a reasonably good estimate of the lateral deformation and global factor of safety of the soil nail walls.

Seismic behaviour of rigid-faced reinforced soil retaining wall models:reinforcement effect

This paper presents the results of shaking table tests on models of rigid-faced reinforced soil retaining walls in which reinforcement materials of different tensile strength were used. The construction of the model retaining walls in a laminar box mounted on a shaking table, the instrumentation and the results from the shaking table tests are described in detail and the effects of the reinforcement parameters on the acceleration response at different elevations of the retaining wall, horizontal soil pressures and face deformations are presented. It was observed from these tests that the horizontal face displacement response of the rigid-faced retaining walls was significantly affected by the inclusion of reinforcement and even low-strength polymer reinforcement was found to be efficient in significantly reducing the deformation of the face. The acceleration amplifications were, however, observed to be less influenced by the reinforcement parameters. The results obtained from this study are helpful in understanding the relative performance of reinforced soil retaining walls under the different test conditions used in the experiments.

Bayesian estimation of small effects in exercise and sports science

The aim of this paper is to provide a Bayesian formulation of the so-called magnitude-based inference approach to quantifying and interpreting effects, and in a case study example provide accurate probabilistic statements that correspond to the intended magnitude-based inferences. The model is described in the context of a published small-scale athlete study which employed a magnitude-based inference approach to compare the effect of two altitude training regimens (live high-train low (LHTL), and intermittent hypoxic exposure (IHE)) on running performance and blood measurements of elite triathletes. The posterior distributions, and corresponding point and interval estimates, for the parameters and associated effects and comparisons of interest, were estimated using Markov chain Monte Carlo simulations. The Bayesian analysis was shown to provide more direct probabilistic comparisons of treatments and able to identify small effects of interest. The approach avoided asymptotic assumptions and overcame issues such as multiple testing. Bayesian analysis of unscaled effects showed a probability of 0.96 that LHTL yields a substantially greater increase in hemoglobin mass than IHE, a 0.93 probability of a substantially greater improvement in running economy and a greater than 0.96 probability that both IHE and LHTL yield a substantially greater improvement in maximum blood lactate concentration compared to a Placebo. The conclusions are consistent with those obtained using a ‘magnitude-based inference’ approach that has been promoted in the field. The paper demonstrates that a fully Bayesian analysis is a simple and effective way of analysing small effects, providing a rich set of results that are straightforward to interpret in terms of probabilistic statements.

Bayesian Analysis of a Superimposed Renewal Process

Stochastic behavior of an aero-engine failure/repair process has been analyzed from a Bayesian perspective. Number of failures/repairs in the component-sockets of this multi-component system are assumed to follow independent renewal processes with Weibull inter-arrival times. Based on the field failure/repair data of a large number of such engines and independent Gamma priors on the scale parameters and log-concave priors on the shape parameters, an exact method of sampling from the resulting posterior distributions of the parameters has been proposed. These generated parameter values are next utilised in obtaining the posteriors of the expected number of system repairs, system failure rate, and the conditional intensity function, which are computed using a recursive formula.

Effect of colostrum feeding method and presence of dam on the sleep, rest and sucking behaviour of newborn calves

"In rats, sucking milk reduces anxiety and promotes non-rapid eye movement (NREM) sleep, and in calves it induces resting but the effect on sleep is unknown. Here, we investigated how calves' sleep was affected by colostrum feeding methods. Forty-one calves were blocked by birth date and randomly allotted within blocks to the experimental treatments. Calves were housed for four days either with their dam (DAM) or individually with warm colostrum feeding (2 L four times a day) from either a teat bucket (TEAT) or an open bucket (BUCKET). DAM calves suckled their dam freely. Calves' sleeping and sucking behaviour was filmed continuously for 48 h at the ages of two and three days. Behavioural sleep (BS) was defined as calves resting at least 30 s with their head still and raised (non-rapid eye movement) or with their head against their body or the ground (rapid eye movement, REM). Latency from the end of colostrum feeding to the start of BS was recorded. We compared behaviour of TEAT calves with that of DAM and BUCKET calves using mixed models. Milk meal duration was significantly longer for TEAT calves than for BUCKET calves (mean +/- S.E.M.; 8.3 +/- 0.6 min vs. 5.2 +/- 0.6 min), but equal to that of DAM calves. We found no effect of feeding method on the duration of daily BS (12 h 59 min I h 38 min) but we found a tendency for the daily amount of NREM sleep; BUCKET calves had less NREM sleep per day than TEAT calves (6 h 18 min vs. 7 h 48 min, S.E.M. = 45 min) and also longer latencies from milk ingestion to BS (21.9 +/- 2.0 min vs. 16.2 +/- 2.0 min). DAM calves slept longer bouts than TEAT calves (10.8 +/- 1.0 min vs. 8.3 +/- 1.0 min) and less often (78 +/- 4 vs. 92 +/- 4). Sucking colostrum from a teat bucket compared with drinking from an open"

Prediction of load-deflection behaviour using fracture energy GF: A comparative study of two fracture models for concrete

Load-deflection curves for a notched beam under three-point load are determined using the Fictitious Crack Model (FCM) and Blunt Crack Model (BCM). Two values of fracture energy GF are used in this analysis: (i) GF obtained from the size effect law and (ii) GF obtained independently of the size effect. The predicted load-deflection diagrams are compared with the experimental ones obtained for the beams tested by Jenq and Shah. In addition, the values of maximum load (Pmax) obtained by the analyses are compared with the experimental ones for beams tested by Jenq and Shah and by Bažant and Pfeiffer. The results indicate that the descending portion of the load-deflection curve is very sensitive to the GF value used.

Experimental determination and activity coefficient based models for mixture solubilities of nitrophenol isomers in supercritical carbon dioxide

The experimental solubilities of the mixture of nitrophenol (m- and p-) isomers were determined at 308, 318 and 328 K over a pressure range of 10-17.55 MPa. Compared to the binary solubilities, the ternary solubilities of m-nitrophenol increased at 308, 318 and 328 K. The ternary solubilities of p-nitrophenol increased at 308 K, while the ternary solubilities decreased at lower pressures and increased at higher pressure at 318 and 328 K. The solubilities of the solid mixtures in supercritical carbon dioxide (SCCO2) were correlated with solution models by incorporating the non-idealities using activity coefficient based models. The Wilson and NRTL activity coefficient models were applied to determine the nature of the interactions between the molecules. The equation developed by using the NRTL model has three parameters and correlates mixture solubilities of solid solutes in terms of temperature and cosolute composition. The equation derived from the Wilson model contains five parameters and correlates solubilities in terms of temperature, density and cosolute composition. These two new equations developed in this work were used to correlate the solubilities of 25 binary solid mixtures including the current data. The average AARDs of the model equations derived using the NRTL and Wilson models for the solid mixtures were found to be 7% and 4%, respectively. (C) 2012 Elsevier B.V. All rights reserved.

Bayesian Accelerated Life Testing under Competing Weibull Causes of Failure

Consider a J-component series system which is put on Accelerated Life Test (ALT) involving K stress variables. First, a general formulation of ALT is provided for log-location-scale family of distributions. A general stress translation function of location parameter of the component log-lifetime distribution is proposed which can accommodate standard ones like Arrhenius, power-rule, log-linear model, etc., as special cases. Later, the component lives are assumed to be independent Weibull random variables with a common shape parameter. A full Bayesian methodology is then developed by letting only the scale parameters of the Weibull component lives depend on the stress variables through the general stress translation function. Priors on all the parameters, namely the stress coefficients and the Weibull shape parameter, are assumed to be log-concave and independent of each other. This assumption is to facilitate Gibbs sampling from the joint posterior. The samples thus generated from the joint posterior is then used to obtain the Bayesian point and interval estimates of the system reliability at usage condition.

Bayesian Accelerated Life Testing under Competing Weibull Causes of Failure

Consider a J-component series system which is put on Accelerated Life Test (ALT) involving K stress variables. First, a general formulation of ALT is provided for log-location-scale family of distributions. A general stress translation function of location parameter of the component log-lifetime distribution is proposed which can accommodate standard ones like Arrhenius, power-rule, log-linear model, etc., as special cases. Later, the component lives are assumed to be independent Weibull random variables with a common shape parameter. A full Bayesian methodology is then developed by letting only the scale parameters of the Weibull component lives depend on the stress variables through the general stress translation function. Priors on all the parameters, namely the stress coefficients and the Weibull shape parameter, are assumed to be log-concave and independent of each other. This assumption is to facilitate Gibbs sampling from the joint posterior. The samples thus generated from the joint posterior is then used to obtain the Bayesian point and interval estimates of the system reliability at usage condition.

ASYMPTOTIC PRESERVING SCHEME FOR A KINETIC MODEL DESCRIBING IN COMPRESSIBLE FLUIDS

The kinetic theory of fluid turbulence modeling developed by Degond and Lemou in 7] is considered for further study, analysis and simulation. Starting with the Boltzmann like equation representation for turbulence modeling, a relaxation type collision term is introduced for isotropic turbulence. In order to describe some important turbulence phenomenology, the relaxation time incorporates a dependency on the turbulent microscopic energy and this makes difficult the construction of efficient numerical methods. To investigate this problem, we focus here on a multi-dimensional prototype model and first propose an appropriate change of frame that makes the numerical study simpler. Then, a numerical strategy to tackle the stiff relaxation source term is introduced in the spirit of Asymptotic Preserving Schemes. Numerical tests are performed in a one-dimensional framework on the basis of the developed strategy to confirm its efficiency.

Nonparametric Bayesian Density Modeling with Gaussian Processes

We present the Gaussian process density sampler (GPDS), an exchangeable generative model for use in nonparametric Bayesian density estimation. Samples drawn from the GPDS are consistent with exact, independent samples from a distribution defined by a density that is a transformation of a function drawn from a Gaussian process prior. Our formulation allows us to infer an unknown density from data using Markov chain Monte Carlo, which gives samples from the posterior distribution over density functions and from the predictive distribution on data space. We describe two such MCMC methods. Both methods also allow inference of the hyperparameters of the Gaussian process.