Bayesian Inference for Diffusion Processes with Applications in Life Sciences

Diffusion processes are a promising instrument to realistically model the time-continuous evolution of natural phenomena in life sciences. However, approximation of a given system is often carried out heuristically, leading to diffusions that do not correctly reflect the true dynamics of the original process. Moreover, statistical inference for diffusions proves to be challenging in practice as the likelihood function is typically intractable. This thesis contributes to stochastic modelling and statistical estimation of real problems in life sciences by means of diffusion processes. In particular, it creates a framework from existing and novel techniques for the correct approximation of pure Markov jump processes by diffusions. Concerning statistical inference, the thesis reviews existing practices and analyses and further develops a well-known Bayesian approach which introduces auxiliary observations by means of Markov chain Monte Carlo (MCMC) techniques. This procedure originally suffers from convergence problems which stem from a deterministic link between the model parameters and the quadratic variation of a continuously observed diffusion path. This thesis formulates a neat modification of the above approach for general multi-dimensional diffusions and provides the mathematical and empirical proof that the so-constructed MCMC scheme converges. The potential of the newly developed modelling and estimation methods is demonstrated in two real-data application studies: the spatial spread of human influenza in Germany and the in vivo binding behaviour of proteins in cell nuclei

VII Workshop on Computational Data Analysis and Numerical Methods

Dear participants, colleagues and friends, it is a great honour and a privilege to give you all a warmest welcome to the VII Workshop on Computational Data Analysis and Numerical Methods (VII WCDANM), which is organized by the Polytechnic Institute of Tomar (located in the center of Portugal in the beautiful city of Tomar), with the support of some Portuguese research centers, hoping that the final result may exceed the expectations of the participants, sponsors and organizers. Due to the worldwide pandemic caused by the COVID-19 virus, for the first time, this meeting will be transmitted through videoconference (webminar). Nevertheless, the important contributions of Adélia Sequeira (University of Lisbon, Portugal), Sílvia Barbeiro (University of Coimbra, Portugal), Malay Banerjee (Indian Instituto of Techonology Kampur, India) and Indranhil Ghosh (University of North Carolina at Wilmington, USA) as Plenary Speakers, the high scientific level of oral and poster presentations and an active audience will certainly contribute to the success of the meeting. Part of the accepted papers (theoretical and applied) by the VII WCDANM involve big data, data mining, data science and machine learning, in different areas of research, some giving emphasis to coronavirus. A very special thanks to this small, yet important, scientific community, since this event could not be possible without any of these essential and complementary parts. This year, there is also the possibility to attend a course on ŞModeling Partial Least Squares Structural Equations (PLS-SEM) using SmartPLSŤ given by Christian M. Ringle ((TUHH) Hamburg University of Technology, Germany), who kindly and readily accepted our invitation and to whom we are very grateful. A special acknowledgment is also due to the Members of the Executive, Scientific and Organizing Committees. In particular, Anuj Mubayi (Arizona StateUniversity,USA),MilanStehlík(Johannes KeplerUniversity,Austria), AnaNata,IsabelPitacasandManuelaFernandes(hostsfromthePolytechnic Institute of Tomar, Portugal), A. Manuela Gonçalves (University of Minho, Portugal), Teresa Oliveira (Aberta University) and Fernando Carapau (University of Évora, Portugal) have been relentless in search for a balanced, broad and interesting program, having achieved an excellent result. For the third consecutive year, the Journal of Applied Statistics (Taylor & Francis) and Neural Computing and Applications (Springer) are also associated to the event, being extremely important in the dissemination of the scientific results achieved at the meeting. Given the above, it is a pleasure to be ”together” with all of you in this web conference, hoping it may provide an intellectual stimulus and an opportunity for the scientific community to jointly work and disseminate scientific research, namely presenting approaches that may contribute to the solution of the pandemic we are experiencing in the expectation that the present might be past in the near future

International Conference on Mathematical Analysis and Applications in Science and Engineering – Book of Extended Abstracts

The present volume on Mathematical Analysis and Applications in Science and Engineering - Book of Extended Abstracts of the ICMASC’2022 collects the extended abstracts of the talks presented at the International Conference on Mathematical Analysis and Applications in Science and Engineering – ICMA2SC'22 that took place at the beautiful city of Porto, Portugal, in June 27th-June 29th 2022 (3 days). Its aim was to bring together researchers in every discipline of applied mathematics, science, engineering, industry, and technology, to discuss the development of new mathematical models, theories, and applications that contribute to the advancement of scientific knowledge and practice. Authors proposed research in topics including partial and ordinary differential equations, integer and fractional order equations, linear algebra, numerical analysis, operations research, discrete mathematics, optimization, control, probability, computational mathematics, amongst others. The conference was designed to maximize the involvement of all participants and will present the state-of- the-art research and the latest achievements.info:eu-repo/semantics/publishedVersio

Mathematical Methods, Modelling and Applications

This volume deals with novel high-quality research results of a wide class of mathematical models with applications in engineering, nature, and social sciences. Analytical and numeric, deterministic and uncertain dimensions are treated. Complex and multidisciplinary models are treated, including novel techniques of obtaining observation data and pattern recognition. Among the examples of treated problems, we encounter problems in engineering, social sciences, physics, biology, and health sciences. The novelty arises with respect to the mathematical treatment of the problem. Mathematical models are built, some of them under a deterministic approach, and other ones taking into account the uncertainty of the data, deriving random models. Several resulting mathematical representations of the models are shown as equations and systems of equations of different types: difference equations, ordinary differential equations, partial differential equations, integral equations, and algebraic equations. Across the chapters of the book, a wide class of approaches can be found to solve the displayed mathematical models, from analytical to numeric techniques, such as finite difference schemes, finite volume methods, iteration schemes, and numerical integration methods

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Balancing model complexity and inferential capability for disease modelling

Mathematical models for study of infectious diseases have a rich history but it is only in recent years that directly fitting highly complex models to data has become possible. This has lead to a quantum leap in the capabilities of mathematical modelling for contributing to an evidence base for policy decisions. There still remains a large gap between the most complex models we can simulate and the most complex models we can perform inference on resulting in a trade-off between model complexity and inferential capability. This thesis tackles three separate problems with this trade-off in mind. First, we study the dynamics of epidemics on degree heterogeneous clustered networks. Network models have many attractions but possess drawbacks such as one must generally resort to stochastic simulation for clustered networks, which represent realistic societal structure, as closed-form approximations of the dynamics do not hold in the highly clustered regime. Furthermore, data for these systems are hard to collect as they must measure the pairwise interactions of each individual - this lack of data limits the possibilities for applying inference. We develop a new model not requiring extensive simulations that approximates these dynamics more accurately than previous approaches, thus improving on the first problem mentioned. Second, across several chapters we analyse the role of household structure in the transmission and control of soil-transmitted helminths (STH). Starting with a hierarchical negative binomial regression for which inference can easily be performed but which neglects the non-independence of observations, we move on to develop a general methodology for constructing and performing Bayesian inference on stochastic household models that consider different transmission dynamics within and between the households in a population. This permits us to estimate the extent to which transmission occurs within, compared to between, households and simulate the effectiveness of various control strategies – with some exploiting the household structure. The limits to which this general methodology may be extended to arbitrary demographic classes and infection levels before inference with exact-likelihood methods no longer become computationally feasible is explored. Finally, we build a model of the global control programme for lymphatic filariasis at a regional level, forecasting the number of treatments required each year and their costs in order to reach elimination. A scenario where existing guidelines remained in place and a scenario where proposed guidelines incorporating a new treatment were considered. Our analysis was used by WHO as part of the evidence base for adopting precisely these new guidelines