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.

Challenges in improving chronic disease survivorship outcomes using tele-health and self-managed online solutions

The advances in modern information and communication (ICT) technology continue to address the challenges and improve` health outcomes for the survivors of chronic disease such as prostate cancer. The management of survivorship is increasingly becoming an important need for the survivors to manage their chronic conditions. The technology interventions such as tele-health as well as self-managed technology applications have shown a potential to improve survivorship outcomes. However, the application of these tools should be supported by strong health economics evidence. This work discusses the challenges of technology led survivorship care models and presents an integrated approach to address these challenges.

Detecting approximate clones in business process model repositories

Empirical evidence shows that repositories of business process models used in industrial practice contain significant amounts of duplication. This duplication arises for example when the repository covers multiple variants of the same processes or due to copy-pasting. Previous work has addressed the problem of efficiently retrieving exact clones that can be refactored into shared subprocess models. This article studies the broader problem of approximate clone detection in process models. The article proposes techniques for detecting clusters of approximate clones based on two well-known clustering algorithms: DBSCAN and Hi- erarchical Agglomerative Clustering (HAC). The article also defines a measure of standardizability of an approximate clone cluster, meaning the potential benefit of replacing the approximate clones with a single standardized subprocess. Experiments show that both techniques, in conjunction with the proposed standardizability measure, accurately retrieve clusters of approximate clones that originate from copy-pasting followed by independent modifications to the copied fragments. Additional experiments show that both techniques produce clusters that match those produced by human subjects and that are perceived to be standardizable.

Complementary surface-enhanced resonance raman spectroscopic biodetection of mixed protein solutions by chitosan- and silica-coated plasmon-tuned silver nanoparticles

Silver nanoparticles with identical plasmonic properties but different surface functionalities are synthesized and tested as chemically selective surface-enhanced resonance Raman (SERR) amplifiers in a two-component protein solution. The surface plasmon resonances of the particles are tuned to 413 nm to match the molecular resonance of protein heme cofactors. Biocompatible functionalization of the nanoparticles with a thin film of chitosan yields selective SERR enhancement of the anionic protein cytochrome b5, whereas functionalization with SiO2 amplifies only the spectra of the cationic protein cytochrome c. As a result, subsequent addition of the two differently functionalized particles yields complementary information on the same mixed protein sample solution. Finally, the applicability of chitosan-coated Ag nanoparticles for protein separation was tested by in situ resonance Raman spectroscopy.

Novel solutions for a model of wound healing angiogenesis

We prove the existence of novel, shock-fronted travelling wave solutions to a model of wound healing angiogenesis studied in Pettet et al (2000 IMA J. Math. App. Med. 17 395–413) assuming two conjectures hold. In the previous work, the authors showed that for certain parameter values, a heteroclinic orbit in the phase plane representing a smooth travelling wave solution exists. However, upon varying one of the parameters, the heteroclinic orbit was destroyed, or rather cut-off, by a wall of singularities in the phase plane. As a result, they concluded that under this parameter regime no travelling wave solutions existed. Using techniques from geometric singular perturbation theory and canard theory, we show that a travelling wave solution actually still exists for this parameter regime. We construct a heteroclinic orbit passing through the wall of singularities via a folded saddle canard point onto a repelling slow manifold. The orbit leaves this manifold via the fast dynamics and lands on the attracting slow manifold, finally connecting to its end state. This new travelling wave is no longer smooth but exhibits a sharp front or shock. Finally, we identify regions in parameter space where we expect that similar solutions exist. Moreover, we discuss the possibility of more exotic solutions.

Contributions to Bayesian experimental design

This thesis progresses Bayesian experimental design by developing novel methodologies and extensions to existing algorithms. Through these advancements, this thesis provides solutions to several important and complex experimental design problems, many of which have applications in biology and medicine. This thesis consists of a series of published and submitted papers. In the first paper, we provide a comprehensive literature review on Bayesian design. In the second paper, we discuss methods which may be used to solve design problems in which one is interested in finding a large number of (near) optimal design points. The third paper presents methods for finding fully Bayesian experimental designs for nonlinear mixed effects models, and the fourth paper investigates methods to rapidly approximate the posterior distribution for use in Bayesian utility functions.

Pre-processing for approximate Bayesian computation in image analysis

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.

The Sawa World model : addressing extreme poverty through local solutions and youth empowerment

With an estimated 1.2 billion people worldwide living in extreme poverty, it is critical to find effective long-term solutions. Sawa World is a non-profit organization founded by Daphne Nederhorst in 2005 to empower marginalized youth to document simple, locally created solutions that address this pressing issue. Currently working primarily in Uganda, Sawa World has created a unique model that celebrates powerful solutions generated from within the community to help people living in poverty help themselves. Using inspiring local leaders who themselves come from extreme poverty, Sawa World aims to end extreme poverty from the ground up.

Stigmatization of failed entrepreneurs : prevalence and solutions

This paper investigates why entrepreneurs experience stigma after firm failure and what can be done to reduce it. We use attribution theory as an overarching theoretical framework and hypothesize that entrepreneurs are held more accountable than employees for their unemployment after firm failure irrespective of the circumstances causing the failure. To test this hypothesis we conduct a between group, 2x2 full factorial experiment where the cause of the failure is manipulated. We find that entrepreneurs are held more accountable for firm failure irrespective of the circumstances causing the failure and that respondents who view failure as an inherent risk of firm ownership are less likely to stigmatize failed entrepreneurs.

Revisiting borehole stresses in anisotropic elastic media : comparison of analytical versus numerical solutions

We present a rigorous validation of the analyticalAmadei solution for the stress concentration around arbitrarily orientated borehole in general anisotropic elastic media. First, we revisit the theoretical framework of the Amadei solution and present analytical insights that show that the solution does indeed contain all special cases of symmetry, contrary to previous understanding, provided that the reduced strain coefficients β11 and β55 are not equal. It is shown from theoretical considerations and published experimental data that the β11 and β55 are not equal for realistic rocks. Second, we develop a 3D finite-element elastic model within a hybrid analyticalnumerical workflow that circumvents the need to rebuild and remesh the model for every borehole and material orientation. Third, we show that the borehole stresses computed from the numerical model and the analytical solution match almost perfectly for different borehole orientations (vertical, deviated and horizontal) and for several cases involving isotropic and transverse isotropic symmetries. It is concluded that the analytical Amadei solution is valid with no restrictions on the borehole orientation or elastic anisotropy symmetry.

Degradation of hydroxycinnamic acid mixtures in aqueous sucrose solutions by the Fenton process

The degradation efficiencies and behaviors of caffeic acid (CaA), p-coumaric acid (pCoA) and ferulic acid (FeA) in aqueous sucrose solutions containing the mixture of these hydroxycinnamic acids (HCAs) mixtures were studied by the Fenton oxidation process. Central composite design and multi-response surface methodology were used to evaluate and optimize the interactive effects of process parameters. Four quadratic polynomial models were developed for the degradation of each individual acid in the mixture and the total HCAs degraded. Sucrose was the most influential parameter that significantly affected the total amount of HCA degraded. Under the conditions studied there was < 0.01% loss of sucrose in all reactions. The optimal values of the process parameters for a 200 mg/L HCA mixture in water (pH 4.73, 25.15 °C) and sucrose solution (13 mass%, pH 5.39, 35.98 °C) were 77% and 57% respectively. Regression analysis showed goodness of fit between the experimental results and the predicted values. The degradation behavior of CaA differed from those of pCoA and FeA, where further CaA degradation is observed at increasing sucrose and decreasing solution pH. The differences (established using UV/Vis and ATR-FTIR spectroscopy) were because, unlike the other acids, CaA formed a complex with Fe(III) or with Fe(III) hydrogen-bonded to sucrose, and coprecipitated with lepidocrocite, an iron oxyhydroxide.

Transmittance properties of contact lens multipurpose solutions and their effects on a hydrogel lens

Purpose The aim was to assess the compatibility of different multipurpose solutions (MPSs) with one type of silicone hydrogel (SiH) contact lens by, assessing the changes in both ultraviolet (UV) and visible light transmissibility of the hydrogel lens caused by the MPSs. Methods The light transmittance from 200-700 nm were measured for the lotrafilcon B blister pack solution (BPS), six MPSs namely, ReNuMultiPlus Multi-Purpose Solution (Bausch and Lomb Inc., Rochester NY, USA.); Complete RevitaLens Multi-Purpose (Abbott Medical Optics Inc., Quarryvale Co. Dublin, Ireland); All In One Light (Sauflon Pharmaceuticals Ltd., Twickenham, England); SOLO-care AQUA™ (Ciba Vision Corporation Duluth, Georgia, USA.); Biomedics All-in-one solution (CooperVision, Hamble, UK); and HippiaMultiPlus All-in-one solution (Interojo Inc., Kyeonggi-do, Korea), and a lotrafilcon B SiH lens (before and after storage), using a spectrophotometer. Results The UV transmitted through the BPS and the MPS were similar (p >.05, for all), except for the HippiaMultiPlus which was lower (p < 0.001) by 19.8%. Mean transparency values were statistically (p<.001) significantly different between the BPS and the MPSs. All MP solution/SiH lens combinations resulted in relatively high UV transmittance values especially in the UVC spectrum, and significantly increased (p <.001) the visible light transmittance values of the SiH lens. Greater changes in transparency were observed in the ReNu/SiH lens (28.5%) and the Complete RevitaLens/SiH lens (24.9%) combinations. Conclusion The six MPSs showed significant variations in the transmitted UV and visible light. Similar to the BPS, all MPSs were equally transparent, but showed very poor UVA & UVB attenuation, except for the Hippia MultiPlus. The MPS/SiH lens combinations did not significantly affect the lens transparency but it significant increased the lens transmittance of UV radiation, after storage. Further in-vivo studies are needed to validate if this effect is constant.

Quantifying uncertainty in parameter estimates for stochastic models of collective cell spreading using approximate Bayesian computation

Wound healing and tumour growth involve collective cell spreading, which is driven by individual motility and proliferation events within a population of cells. Mathematical models are often used to interpret experimental data and to estimate the parameters so that predictions can be made. Existing methods for parameter estimation typically assume that these parameters are constants and often ignore any uncertainty in the estimated values. We use approximate Bayesian computation (ABC) to estimate the cell diffusivity, D, and the cell proliferation rate, λ, from a discrete model of collective cell spreading, and we quantify the uncertainty associated with these estimates using Bayesian inference. We use a detailed experimental data set describing the collective cell spreading of 3T3 fibroblast cells. The ABC analysis is conducted for different combinations of initial cell densities and experimental times in two separate scenarios: (i) where collective cell spreading is driven by cell motility alone, and (ii) where collective cell spreading is driven by combined cell motility and cell proliferation. We find that D can be estimated precisely, with a small coefficient of variation (CV) of 2–6%. Our results indicate that D appears to depend on the experimental time, which is a feature that has been previously overlooked. Assuming that the values of D are the same in both experimental scenarios, we use the information about D from the first experimental scenario to obtain reasonably precise estimates of λ, with a CV between 4 and 12%. Our estimates of D and λ are consistent with previously reported values; however, our method is based on a straightforward measurement of the position of the leading edge whereas previous approaches have involved expensive cell counting techniques. Additional insights gained using a fully Bayesian approach justify the computational cost, especially since it allows us to accommodate information from different experiments in a principled way.