The SEIQS stochastic epidemic model with external source of infection

This paper deals with a stochastic epidemic model for computer viruses with latent and quarantine periods, and two sources of infection: internal and external. All sojourn times are considered random variables which are assumed to be independent and exponentially distributed. For this model extinction and hazard times are analyzed, giving results for their Laplace transforms and moments. The transient behavior is considered by studying the number of times that computers are susceptible, exposed, infectious and quarantined during a period of time (0, t] and results for their joint and marginal distributions, moments and cross moments are presented. In order to give light this analysis, some numerical examples are showed.

Assessing advertising in a hierarchical decision model

Many destination marketing organizations in the United States and elsewhere are facing budget retrenchment for tourism marketing, especially for advertising. This study evaluates a three-stage model using Random Coefficient Logit (RCL) approach which controls for correlations between different non-independent alternatives and considers heterogeneity within individual’s responses to advertising. The results of this study indicate that the proposed RCL model results in a significantly better fit as compared to traditional logit models, and indicates that tourism advertising significantly influences tourist decisions with several variables (age, income, distance and Internet access) moderating these decisions differently depending on decision stage and product type. These findings suggest that this approach provides a better foundation for assessing, and in turn, designing more effective advertising campaigns.

Three-dimensional planar model estimation using multi-constraint knowledge based on k-means and RANSAC

Plane model extraction from three-dimensional point clouds is a necessary step in many different applications such as planar object reconstruction, indoor mapping and indoor localization. Different RANdom SAmple Consensus (RANSAC)-based methods have been proposed for this purpose in recent years. In this study, we propose a novel method-based on RANSAC called Multiplane Model Estimation, which can estimate multiple plane models simultaneously from a noisy point cloud using the knowledge extracted from a scene (or an object) in order to reconstruct it accurately. This method comprises two steps: first, it clusters the data into planar faces that preserve some constraints defined by knowledge related to the object (e.g., the angles between faces); and second, the models of the planes are estimated based on these data using a novel multi-constraint RANSAC. We performed experiments in the clustering and RANSAC stages, which showed that the proposed method performed better than state-of-the-art methods.

Boston, Massachusetts Region, Digital Elevation Model with Bathymetry

This raster layer represents surface elevation and bathymetry data for the Boston Region, Massachusetts. It was created by merging portions of MassGIS Digital Elevation Model 1:5,000 (2005) data with NOAA Estuarine Bathymetric Digital Elevation Models (30 m.) (1998). DEM data was derived from the digital terrain models that were produced as part of the MassGIS 1:5,000 Black and White Digital Orthophoto imagery project. Cellsize is 5 meters by 5 meters. Each cell has a floating point value, in meters, which represents its elevation above or below sea level.

On ANOVA Decompositions of Kernels and Gaussian Random Field Paths

The FANOVA (or “Sobol’-Hoeffding”) decomposition of multivariate functions has been used for high-dimensional model representation and global sensitivity analysis. When the objective function f has no simple analytic form and is costly to evaluate, computing FANOVA terms may be unaffordable due to numerical integration costs. Several approximate approaches relying on Gaussian random field (GRF) models have been proposed to alleviate these costs, where f is substituted by a (kriging) predictor or by conditional simulations. Here we focus on FANOVA decompositions of GRF sample paths, and we notably introduce an associated kernel decomposition into 4 d 4d terms called KANOVA. An interpretation in terms of tensor product projections is obtained, and it is shown that projected kernels control both the sparsity of GRF sample paths and the dependence structure between FANOVA effects. Applications on simulated data show the relevance of the approach for designing new classes of covariance kernels dedicated to high-dimensional kriging.

Age model of ODP Site 184-1146 (Table 1)

Clay mineral assemblages at ODP Site 1146 in the northern South China Sea are used to investigate sediment source and transport processes and to evaluate the evolution of the East Asian monsoon over the past 2 Myr. Clay minerals consist mainly of illite (22-43%) and smectite (12-48%), with associated chlorite (10-30%), kaolinite (2-18%), and random mixed-layer clays (5-22%). Hydrodynamic and mineralogical studies indicate that illite and chlorite sources include Taiwan and the Yangtze River, that smectite and mixed-layer clays originate predominantly from Luzon and Indonesia, and that kaolinite is primarily derived from the Pearl River. Mineral assemblages indicate strong glacial-interglacial cyclicity, with high illite, chlorite, and kaolinite content during glacials and high smectite and mixed-layer clay content during interglacials. During interglacials, summer enhanced monsoon (southwesterly) currents transport more smectite and mixed-layer clays to Site 1146 whereas during glacials, enhanced winter monsoon (northerly) currents transport more illite and chlorite from Taiwan and the Yangtze River. The ratio (smectite+mixed layers)/(illite+chlorite) was adopted as a proxy for East Asian monsoon variability. Higher ratios indicate strengthened summer-monsoon winds and weakened winter-monsoon winds during interglacials. In contrast, lower ratios indicate a strongly intensified winter monsoon and weakened summer monsoon during glacials. Spectral analysis indicates the mineral ratio was dominantly forced by monsoon variability prior to the development of large-scale glaciation at 1.2 Myr and by both monsoon variability and the effects of changing sea level in the interval 1.2 Myr to present.

Random recursion

Thesis (Ph.D.)--University of Washington, 2016-06

Speeding up the EM algorithm for mixture model-based segmentation of magnetic resonance images

Mixture models implemented via the expectation-maximization (EM) algorithm are being increasingly used in a wide range of problems in pattern recognition such as image segmentation. However, the EM algorithm requires considerable computational time in its application to huge data sets such as a three-dimensional magnetic resonance (MR) image of over 10 million voxels. Recently, it was shown that a sparse, incremental version of the EM algorithm could improve its rate of convergence. In this paper, we show how this modified EM algorithm can be speeded up further by adopting a multiresolution kd-tree structure in performing the E-step. The proposed algorithm outperforms some other variants of the EM algorithm for segmenting MR images of the human brain. (C) 2004 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved.

Analysis of Melanoma Onset: Assessing Familial Aggregation by Using Estimating Equations and Fitting Variance Components via Bayesian Random Effects Models

We investigate whether relative contributions of genetic and shared environmental factors are associated with an increased risk in melanoma. Data from the Queensland Familial Melanoma Project comprising 15,907 subjects arising from 1912 families were analyzed to estimate the additive genetic, common and unique environmental contributions to variation in the age at onset of melanoma. Two complementary approaches for analyzing correlated time-to-onset family data were considered: the generalized estimating equations (GEE) method in which one can estimate relationship-specific dependence simultaneously with regression coefficients that describe the average population response to changing covariates; and a subject-specific Bayesian mixed model in which heterogeneity in regression parameters is explicitly modeled and the different components of variation may be estimated directly. The proportional hazards and Weibull models were utilized, as both produce natural frameworks for estimating relative risks while adjusting for simultaneous effects of other covariates. A simple Markov Chain Monte Carlo method for covariate imputation of missing data was used and the actual implementation of the Bayesian model was based on Gibbs sampling using the free ware package BUGS. In addition, we also used a Bayesian model to investigate the relative contribution of genetic and environmental effects on the expression of naevi and freckles, which are known risk factors for melanoma.

Mixed model formulations for multi-environment trials

When studying genotype X environment interaction in multi-environment trials, plant breeders and geneticists often consider one of the effects, environments or genotypes, to be fixed and the other to be random. However, there are two main formulations for variance component estimation for the mixed model situation, referred to as the unconstrained-parameters (UP) and constrained-parameters (CP) formulations. These formulations give different estimates of genetic correlation and heritability as well as different tests of significance for the random effects factor. The definition of main effects and interactions and the consequences of such definitions should be clearly understood, and the selected formulation should be consistent for both fixed and random effects. A discussion of the practical outcomes of using the two formulations in the analysis of balanced data from multi-environment trials is presented. It is recommended that the CP formulation be used because of the meaning of its parameters and the corresponding variance components. When managed (fixed) environments are considered, users will have more confidence in prediction for them but will not be overconfident in prediction in the target (random) environments. Genetic gain (predicted response to selection in the target environments from the managed environments) is independent of formulation.

A Bayesian hierarchical model for categorical longitudinal data from a social survey of immigrants

The paper investigates a Bayesian hierarchical model for the analysis of categorical longitudinal data from a large social survey of immigrants to Australia. Data for each subject are observed on three separate occasions, or waves, of the survey. One of the features of the data set is that observations for some variables are missing for at least one wave. A model for the employment status of immigrants is developed by introducing, at the first stage of a hierarchical model, a multinomial model for the response and then subsequent terms are introduced to explain wave and subject effects. To estimate the model, we use the Gibbs sampler, which allows missing data for both the response and the explanatory variables to be imputed at each iteration of the algorithm, given some appropriate prior distributions. After accounting for significant covariate effects in the model, results show that the relative probability of remaining unemployed diminished with time following arrival in Australia.

A generative model for separating illumination and reflectance from images

It is well known that even slight changes in nonuniform illumination lead to a large image variability and are crucial for many visual tasks. This paper presents a new ICA related probabilistic model where the number of sources exceeds the number of sensors to perform an image segmentation and illumination removal, simultaneously. We model illumination and reflectance in log space by a generalized autoregressive process and Hidden Gaussian Markov random field, respectively. The model ability to deal with segmentation of illuminated images is compared with a Canny edge detector and homomorphic filtering. We apply the model to two problems: synthetic image segmentation and sea surface pollution detection from intensity images.

Emulation of random output simulators

Computer models, or simulators, are widely used in a range of scientific fields to aid understanding of the processes involved and make predictions. Such simulators are often computationally demanding and are thus not amenable to statistical analysis. Emulators provide a statistical approximation, or surrogate, for the simulators accounting for the additional approximation uncertainty. This thesis develops a novel sequential screening method to reduce the set of simulator variables considered during emulation. This screening method is shown to require fewer simulator evaluations than existing approaches. Utilising the lower dimensional active variable set simplifies subsequent emulation analysis. For random output, or stochastic, simulators the output dispersion, and thus variance, is typically a function of the inputs. This work extends the emulator framework to account for such heteroscedasticity by constructing two new heteroscedastic Gaussian process representations and proposes an experimental design technique to optimally learn the model parameters. The design criterion is an extension of Fisher information to heteroscedastic variance models. Replicated observations are efficiently handled in both the design and model inference stages. Through a series of simulation experiments on both synthetic and real world simulators, the emulators inferred on optimal designs with replicated observations are shown to outperform equivalent models inferred on space-filling replicate-free designs in terms of both model parameter uncertainty and predictive variance.

Noisy random Boolean formulae:a statistical physics perspective

Properties of computing Boolean circuits composed of noisy logical gates are studied using the statistical physics methodology. A formula-growth model that gives rise to random Boolean functions is mapped onto a spin system, which facilitates the study of their typical behavior in the presence of noise. Bounds on their performance, derived in the information theory literature for specific gates, are straightforwardly retrieved, generalized and identified as the corresponding macroscopic phase transitions. The framework is employed for deriving results on error-rates at various function-depths and function sensitivity, and their dependence on the gate-type and noise model used. These are difficult to obtain via the traditional methods used in this field.

Web based expert elicitation of uncertainties in environmental model inputs

When constructing and using environmental models, it is typical that many of the inputs to the models will not be known perfectly. In some cases, it will be possible to make observations, or occasionally physics-based uncertainty propagation, to ascertain the uncertainty on these inputs. However, such observations are often either not available or even possible, and another approach to characterising the uncertainty on the inputs must be sought. Even when observations are available, if the analysis is being carried out within a Bayesian framework then prior distributions will have to be specified. One option for gathering or at least estimating this information is to employ expert elicitation. Expert elicitation is well studied within statistics and psychology and involves the assessment of the beliefs of a group of experts about an uncertain quantity, (for example an input / parameter within a model), typically in terms of obtaining a probability distribution. One of the challenges in expert elicitation is to minimise the biases that might enter into the judgements made by the individual experts, and then to come to a consensus decision within the group of experts. Effort is made in the elicitation exercise to prevent biases clouding the judgements through well-devised questioning schemes. It is also important that, when reaching a consensus, the experts are exposed to the knowledge of the others in the group. Within the FP7 UncertWeb project (http://www.uncertweb.org/), there is a requirement to build a Webbased tool for expert elicitation. In this paper, we discuss some of the issues of building a Web-based elicitation system - both the technological aspects and the statistical and scientific issues. In particular, we demonstrate two tools: a Web-based system for the elicitation of continuous random variables and a system designed to elicit uncertainty about categorical random variables in the setting of landcover classification uncertainty. The first of these examples is a generic tool developed to elicit uncertainty about univariate continuous random variables. It is designed to be used within an application context and extends the existing SHELF method, adding a web interface and access to metadata. The tool is developed so that it can be readily integrated with environmental models exposed as web services. The second example was developed for the TREES-3 initiative which monitors tropical landcover change through ground-truthing at confluence points. It allows experts to validate the accuracy of automated landcover classifications using site-specific imagery and local knowledge. Experts may provide uncertainty information at various levels: from a general rating of their confidence in a site validation to a numerical ranking of the possible landcover types within a segment. A key challenge in the web based setting is the design of the user interface and the method of interacting between the problem owner and the problem experts. We show the workflow of the elicitation tool, and show how we can represent the final elicited distributions and confusion matrices using UncertML, ready for integration into uncertainty enabled workflows.We also show how the metadata associated with the elicitation exercise is captured and can be referenced from the elicited result, providing crucial lineage information and thus traceability in the decision making process.