Mathematical modeling has been instrumental to the development of natural sciences over the last half-century. Through iterated interactions between modeling and real-world exper- imentation, these models have furthered our understanding of the processes in biology and chemistry that they seek to represent. In certain application domains, such as the field of car- diac biology, communities of modelers with common interests have emerged, leading to the development of many models that attempt to explain the same or similar phenomena. As these communities have developed, however, reporting standards for modeling studies have been in- consistent, often focusing on the final parameterized result, and obscuring the assumptions and data used during their creation. These practices make it difficult for researchers to adapt exist- ing models to new systems or newly available data, and also to assess the identifiability of said models - the degree to which their optimal parameters are constrained by data - which is a key step in building trust that their formulation captures truth about the system of study. In this thesis, we develop tools that allow modelers working with biological or chemical time series data to assess identifiability in an automated fashion, and embed these tools within a novel online community resource that enforces reproducible standards of reporting and facilitates exchange of models and data. We begin by exploring the application of Bayesian and approximate Bayesian inference methods, which parameterize models while simultaneously assessing uncertainty about these estimates, to assess the identifiability of models of the cardiac action potential. We then demon- strate how the side-by-side application of these Bayesian and approximate Bayesian methods can be used to assess the information content of experiments where system observability is limited to "summary statistics" - low-dimensional representations of full time-series data. We next investigate how a posteriori methods of identifiability assessment, such as the above inference techniques, compare against a priori methods based on model structure. We compare these two approaches over a range of biologically relevant experimental conditions, and high- light the cases under which each strategy is preferable. We also explore the concept of optimal experimental design, in which measurements are chosen in order to maximize model identifia- bility, and compare the feasibility of established a priori approaches against a novel a posteriori approach. Finally, we propose a framework for representing and executing modeling experiments in a reproducible manner, and use this as the foundation for a prototype "Modeling Web Lab" where researchers may upload specifications for and share the results of the types of inference explored in this thesis. We demonstrate the Modeling Web Lab's utility across multiple mod- eling domains by re-creating the results of a contemporary modeling study of the hERG ion channel model, as well as the results of an original study of electrochemical redox reactions. We hope that this works serves to highlight the importance of both reproducible standards of model reporting, as well as identifiability assessment, which are inherently linked by the desire to foster trust in community-developed models in disciplines across the natural sciences.

Knowledge Space Theory (KST) links in several ways to Formal Concept Analysis (FCA). Recently, the probabilistic and statistical aspects of KST have been further developed by several authors. We review part of the recent results, and describe some of the open problems. The question of whether the outcomes can be useful in FCA remains to be investigated.

Knowledge Space Theory (KST) links in several ways to Formal Concept Analysis (FCA). Recently, the probabilistic and statistical aspects of KST have been further developed by several authors. We review part of the recent results, and describe some of the open problems. The question of whether the outcomes can be useful in FCA remains to be investigated.

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[pt] Nesta tese apresenta-se o Modelo de Redes Neurais Globais- Locais (RNGL) dentro do contexto de modelos de séries temporais. Esta formulação abrange alguns modelos não- lineares já existentes e admite também o enfoque de Mistura de Especialistas. Dedica-se especial atenção ao caso de especialistas lineares, e são discutidos extensivamente aspectos teóricos do modelo: condições de estacionariedade, identificabilidade do modelo, existência, consistência e normalidade assintótica dos estimadores dos parâmetros. Considera-se também uma estratégia de construção do modelo e são discutidos os procedimentos numéricos de estimação, apresentando uma solução para o cálculo de valores iniciais. Finalmente, ilustra-se a metodologia apresentada em duas séries temporais reais, amplamente utilizada na literatura de modelos não lineares. / [en] In this thesis, the Local Global Neural Networks model is proposed within the context of time series models. This formulation encompasses some already existing nonlinear models and also admits the Mixture of Experts approach. We place emphasis on the linear expert case and extensively discuss the theoretical aspects of the model: stationary conditions, existence, consistency and asymptotic normality of the parameter estimates, and model identifiability. A model building strategy is also considered and the whole procedure is illustrated with two real time-series.