Differential geometric MCMC methods and applications

This thesis presents novel Markov chain Monte Carlo methodology that exploits the natural representation of a statistical model as a Riemannian manifold. The methods developed provide generalisations of the Metropolis-adjusted Langevin algorithm and the Hybrid Monte Carlo algorithm for Bayesian statistical inference, and resolve many shortcomings of existing Monte Carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlation structure. The performance of these Riemannian manifold Markov chain Monte Carlo algorithms is rigorously assessed by performing Bayesian inference on logistic regression models, log-Gaussian Cox point process models, stochastic volatility models, and both parameter and model level inference of dynamical systems described by nonlinear differential equations

A study of Population MCMC for estimating Bayes Factors over nonlinear ODE models

Higher resolution biological data is now becoming available in ever greater quantities, allowing the complex behaviour of fundamental biological processes to be studied in much more detail. The area of Systems Biology is in desperate need of methods for inferring the most likely topology of the underlying genetic networks from this oftentimes noisy and poorly sampled data, to support the construction and testing of new model hypotheses. Towards that end, Bayesian methodology provides an ideal framework for tackling such challenges, and in particular offers a means of objectively comparing competing plausible models through the estimation of Bayes factors. There are, however, formidable obstacles which must be overcome to allow model inference using Bayes factors to be of practical use. Many important biological processes may be most accurately represented using nonlinear models based on systems of ordinary differential equations (ODEs), however parameter inference over these models often produces correspondingly nonlinear posterior distributions, which are very challenging to sample from, often resulting in biased marginal likelihood estimates with large variances. Such problems are commonly encountered when modelling circardian rhythms, which exhibit highly nonlinear oscillatory dynamics and play a central role in the overall functioning of most organisms. In this thesis I investigate tools for calculating Bayes factors to distinguish between ODE-based Goodwin oscillator models of varying complexity, which form the basic building blocks for describing this ubiquitous circadian behaviour. The main result in Chapter 3 of this thesis demonstrates how Population Markov Chain Monte Carlo may be employed in conjunction with thermodynamic integration methods to estimate Bayes factors which may accurately distinguish between two nonlinear oscillator models of varying complexity, given noisy experimental data generated from each of the models. In addition, it is shown how alternative methods may fail drastically in this setting, in particular harmonic mean based estimates. Suggestions are given regarding the optimal temperature schedule which should be employed for Population MCMC, and several ideas for future research extending this work are also discussed

Probabilistic Linear Multistep Methods

We present a derivation and theoretical investigation of the Adams-Bashforth and Adams-Moulton family of linear multistep methods for solving ordinary differential equations, starting from a Gaussian process (GP) framework. In the limit, this formulation coincides with the classical deterministic methods, which have been used as higher-order initial value problem solvers for over a century. Furthermore, the natural probabilistic framework provided by the GP formulation allows us to derive probabilistic versions of these methods, in the spirit of a number of other probabilistic ODE solvers presented in the recent literature. In contrast to higher-order Runge-Kutta methods, which require multiple intermediate function evaluations per step, Adams family methods make use of previous function evaluations, so that increased accuracy arising from a higher-order multistep approach comes at very little additional computational cost. We show that through a careful choice of covariance function for the GP, the posterior mean and standard deviation over the numerical solution can be made to exactly coincide with the value given by the deterministic method and its local truncation error respectively. We provide a rigorous proof of the convergence of these new methods, as well as an empirical investigation (up to fifth order) demonstrating their convergence rates in practice

Ten Simple Rules for Effective Computational Research

<p>Ten Simple Rules for Effective Computational Research</p

The initial education of high school teachers : a critical review of major issues and trends

This paper draws on major research findings in international literature in order to provide a critical review of a number of key issues and trends in the initial education of high school teachers. Firstly, this paper contextualizes the prevalent discourse surrounding the field of initial teacher education (ITE) and explores the effect that this discourse has on the conceptualization of teachers’ work. Secondly, this paper focuses on the debates regarding the most propitious site for the teacher education enterprise, the programme structure for ITE, the field placement or practicum, the relationship between subject study and pedagogy, and the overall effectiveness of teacher education. The paper concludes by considering the new challenges that the field of initial teacher education must confront and the implications of such challenges for the ITE curriculum.peer-reviewe

Diez reglas sencillas para una exitosa colaboración transdisciplinar

El presente artículo es la versión en castellano de la publicación: KNAPP, B.; BARDENET, R.; BERNABEU, M.O.; BORDAS, R.; BRUNA, M.; CALDERHEAD, B. ET AL. (2015) “Ten Simple Rules for a Successful Cross-Disciplinary Collaboration”. PLoS Comput Biol 11(4): e1004214, disponible en: https://doi.org/10.1371/journal.pcbi.1004214. La traducción, autorizada por la entidad editora, ha sido llevada a cabo por Ona Lorda Roure y Leila Adim, colaboradoras del Instituto de Investigación TransJus y supervisada por el Dr. Juli Ponce Solé, Director del TransJus. En la misma se han incluido algunas notas aclaratorias para el lector en español, así como bibliografía complementaria en español.[spa] En el auge de las colaboraciones interdisciplinarias entre los distintos campos científicos, la transdisciplinariedad se presenta como la clave para encontrar soluciones a una variedad de problemas globales. Este trabajo, situado en el marco de la biología informática, se centra en exponer una lista extensa de reglas y consejos útiles para lograr una exitosa sinergia entre los varios colaboradores de un proyecto transdisciplinar. Se trata, de hecho, de una guía que pretende dirigirse tanto a investigadores noveles como a aquellos investigadores consolidados que se adentran en un espacio transdisciplinar por primera vez. En particular, este trabajo expone los beneficios principales de establecer una colaboración transdisciplinar, así como los problemas que de ella puedan surgir.[cat] En l'auge de les col·laboracions interdisciplinàries entre els diferents camps científics, la transdisciplinarietat es presenta com la clau per trobar solucions a una varietat de problemes globals. Aquest treball, situat en el marc de la biologia informàtica, es centra en exposar una llista extensa de regles i consells útils per aconseguir una reeixida sinergia entre els varis col·laboradors d'un projecte transdisciplinar. Es tracta, de fet, d'una guia que pretén dirigir-se tant a recercadors novells com a aquells recercadors consolidats que s'endinsen en un espai transdisciplinar per primera vegada. En particular, aquest treball exposa els beneficis principals d'establir una col·laboració transdisciplinar, així com els problemes que d'ella puguin sorgir.[eng] At a time of increasing interdisciplinary collaboration between different scientific fields, cross-disciplinarity represents a key for finding solutions to a variety of global problems. This work, located within the framework of computer biology, focuses on exposing an extensive list of rules and useful tips to achieve a successful synergy among the various collaborators of a transdisciplinary project. It is, in fact, a guide aimed at addressing both first-time researchers and consolidated researchers who enter a transdisciplinary space for the first time. In particular, this work exposes the main benefits of establishing a cross-disciplinary collaboration, as well as the problems that may arise from it