Searching for a Cure: Health Care Behaviour Among the Q'eqchi' Maya in Southern Belize

This thesis explores the health care behaviour of Q’eqchi’ Maya community members living in the Indian Creek village in southern Belize. Using an ethnographic approach based on three months of participation and interviews, this thesis focuses on how Q’eqchi’ villagers evaluate the effectiveness of practitioners and interventions, how they make treatment decisions, and their overall patterns of health care behaviour when an episode of sickness arises. It contends that members of this Indigenous community equally value the medical practice of both Q’eqchi’ and biomedical practitioners, and that they select between health care alternatives pragmatically, abiding by a cost-effectiveness analysis based on a specific social, cultural, and economic context. By showing how the involvement of local realities is necessary to improve health outcomes, this thesis identifies possible pitfalls of current international and Belizean models of care for Q’eqchi’ communities living in Belize, and provides recommendations that must be addressed in future health care research and planning

Approximate Bayesian techniques for inference in stochastic dynamical systems

This thesis is concerned with approximate inference in dynamical systems, from a variational Bayesian perspective. When modelling real world dynamical systems, stochastic differential equations appear as a natural choice, mainly because of their ability to model the noise of the system by adding a variant of some stochastic process to the deterministic dynamics. Hence, inference in such processes has drawn much attention. Here two new extended frameworks are derived and presented that are based on basis function expansions and local polynomial approximations of a recently proposed variational Bayesian algorithm. It is shown that the new extensions converge to the original variational algorithm and can be used for state estimation (smoothing). However, the main focus is on estimating the (hyper-) parameters of these systems (i.e. drift parameters and diffusion coefficients). The new methods are numerically validated on a range of different systems which vary in dimensionality and non-linearity. These are the Ornstein-Uhlenbeck process, for which the exact likelihood can be computed analytically, the univariate and highly non-linear, stochastic double well and the multivariate chaotic stochastic Lorenz '63 (3-dimensional model). The algorithms are also applied to the 40 dimensional stochastic Lorenz '96 system. In this investigation these new approaches are compared with a variety of other well known methods such as the ensemble Kalman filter / smoother, a hybrid Monte Carlo sampler, the dual unscented Kalman filter (for jointly estimating the systems states and model parameters) and full weak-constraint 4D-Var. Empirical analysis of their asymptotic behaviour as a function of observation density or length of time window increases is provided

Quantifying simulator discrepancy in discrete-time dynamical simulators

When making predictions with complex simulators it can be important to quantify the various sources of uncertainty. Errors in the structural specification of the simulator, for example due to missing processes or incorrect mathematical specification, can be a major source of uncertainty, but are often ignored. We introduce a methodology for inferring the discrepancy between the simulator and the system in discrete-time dynamical simulators. We assume a structural form for the discrepancy function, and show how to infer the maximum likelihood parameter estimates using a particle filter embedded within a Monte Carlo expectation maximization (MCEM) algorithm. We illustrate the method on a conceptual rainfall runoff simulator (logSPM) used to model the Abercrombie catchment in Australia. We assess the simulator and discrepancy model on the basis of their predictive performance using proper scoring rules

Derivations of variational gaussian process approximation framework

Recently, within the VISDEM project (EPSRC funded EP/C005848/1), a novel variational approximation framework has been developed for inference in partially observed, continuous space-time, diffusion processes. In this technical report all the derivations of the variational framework, from the initial work, are provided in detail to help the reader better understand the framework and its assumptions

Variational mean-field algorithm for efficient inference in large systems of stochastic differential equations

This work introduces a Gaussian variational mean-field approximation for inference in dynamical systems which can be modeled by ordinary stochastic differential equations. This new approach allows one to express the variational free energy as a functional of the marginal moments of the approximating Gaussian process. A restriction of the moment equations to piecewise polynomial functions, over time, dramatically reduces the complexity of approximate inference for stochastic differential equation models and makes it comparable to that of discrete time hidden Markov models. The algorithm is demonstrated on state and parameter estimation for nonlinear problems with up to 1000 dimensional state vectors and compares the results empirically with various well-known inference methodologies

Approximate Bayesian techniques for inference in stochastic dynamical systems

This thesis is concerned with approximate inference in dynamical systems, from a variational Bayesian perspective. When modelling real world dynamical systems, stochastic differential equations appear as a natural choice, mainly because of their ability to model the noise of the system by adding a variant of some stochastic process to the deterministic dynamics. Hence, inference in such processes has drawn much attention. Here two new extended frameworks are derived and presented that are based on basis function expansions and local polynomial approximations of a recently proposed variational Bayesian algorithm. It is shown that the new extensions converge to the original variational algorithm and can be used for state estimation (smoothing). However, the main focus is on estimating the (hyper-) parameters of these systems (i.e. drift parameters and diffusion coefficients). The new methods are numerically validated on a range of different systems which vary in dimensionality and non-linearity. These are the Ornstein-Uhlenbeck process, for which the exact likelihood can be computed analytically, the univariate and highly non-linear, stochastic double well and the multivariate chaotic stochastic Lorenz '63 (3-dimensional model). The algorithms are also applied to the 40 dimensional stochastic Lorenz '96 system. In this investigation these new approaches are compared with a variety of other well known methods such as the ensemble Kalman filter / smoother, a hybrid Monte Carlo sampler, the dual unscented Kalman filter (for jointly estimating the systems states and model parameters) and full weak-constraint 4D-Var. Empirical analysis of their asymptotic behaviour as a function of observation density or length of time window increases is provided.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

A new variational radial basis function approximation for inference in multivariate diffusions

In this paper we present a radial basis function based extension to a recently proposed variational algorithm for approximate inference for diffusion processes. Inference, for state and in particular (hyper-) parameters, in diffusion processes is a challenging and crucial task. We show that the new radial basis function approximation based algorithm converges to the original algorithm and has beneficial characteristics when estimating (hyper-)parameters. We validate our new approach on a nonlinear double well potential dynamical system

The docking of synaptic vesicles on the presynaptic membrane induced by α-synuclein is modulated by lipid composition.

α-Synuclein (αS) is a presynaptic disordered protein whose aberrant aggregation is associated with Parkinson's disease. The functional role of αS is still debated, although it has been involved in the regulation of neurotransmitter release via the interaction with synaptic vesicles (SVs). We report here a detailed characterisation of the conformational properties of αS bound to the inner and outer leaflets of the presynaptic plasma membrane (PM), using small unilamellar vesicles. Our results suggest that αS preferentially binds the inner PM leaflet. On the basis of these studies we characterise in vitro a mechanism by which αS stabilises, in a concentration-dependent manner, the docking of SVs on the PM by establishing a dynamic link between the two membranes. The study then provides evidence that changes in the lipid composition of the PM, typically associated with neurodegenerative diseases, alter the modes of binding of αS, specifically in a segment of the sequence overlapping with the non-amyloid component region. Taken together, these results reveal how lipid composition modulates the interaction of αS with the PM and underlie its functional and pathological behaviours in vitro

Quantifying simulator discrepancy in discrete-time dynamical simulators

When making predictions with complex simulators it can be important to quantify the various sources of uncertainty. Errors in the structural specification of the simulator, for example due to missing processes or incorrect mathematical specification, can be a major source of uncertainty, but are often ignored. We introduce a methodology for inferring the discrepancy between the simulator and the system in discrete-time dynamical simulators. We assume a structural form for the discrepancy function, and show how to infer the maximum likelihood parameter estimates using a particle filter embedded within a Monte Carlo expectation maximization (MCEM) algorithm. We illustrate the method on a conceptual rainfall runoff simulator (logSPM) used to model the Abercrombie catchment in Australia. We assess the simulator and discrepancy model on the basis of their predictive performance using proper scoring rules