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Several recent empirical studies, particularly in the regional economic growth literature, emphasize the importance of explicitly accounting for uncertainty surrounding model specification. Standard approaches to deal with the problem of model uncertainty involve the use of Bayesian model-averaging techniques. However, Bayesian model-averaging for spatial autoregressive models suffers from severe drawbacks both in terms of computational time and possible extensions to more flexible econometric frameworks. To alleviate these problems, this paper presents two global-local shrinkage priors in the context of high-dimensional matrix exponential spatial specifications. A simulation study is conducted to evaluate the performance of the shrinkage priors. Results suggest that they perform particularly well in high-dimensional environments, especially when the number of parameters to estimate exceeds the number of observations. Moreover, we use pan-European regional economic growth data to illustrate the performance of the proposed shrinkage priors.

Process algebra, formal specification, and model checking are all well studied techniques in the analysis of concurrent computer systems. More recently these techniques have been applied to the analysis of biochemical systems which, at an abstract level, have similar patterns of behaviour to concurrent processes. Process algebraic models and temporal logic specifications, along with their associated model-checking techniques, have been used to analyse biochemical systems. In this thesis we develop a spatio-temporal logic, the Logic of Behaviour in Context (LBC), for the analysis of biochemical models. That is, we define and study the application of a formal specification language which not only expresses temporal properties of biochemical models, but expresses spatial or contextual properties as well. The logic can be used to express, or specify, the behaviour of a model when it is placed into the context of another model. We also explore the types of properties which can be expressed in LBC, various algorithms for model checking LBC - each an improvement on the last, the implementation of the computational tools to support model checking LBC, and a case study on the analysis of models of post-translational biochemical oscillators using LBC. We show that a number of interesting and useful properties can be expressed in LBC and that it is possible to express highly useful properties of real models in the biochemistry domain, with practical application. Statements in LBC can be thought of as expressing computational experiments which can be performed automatically by means of the model checker. Indeed, many of these computational experiments can be higher-order meaning that one succinct and precise specification in LBC can represent a number of experiments which can be automatically executed by the model checker.

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In the recent trends, automated systems are increasingly seen to be embedded in human life with the increase of human dependence on software to perform safetycritical tasks like airbag deployment in automobiles to real-time mission planning in UAVs (Unmanned Aircraft Vehicles). The safety-critical nature of the aerospace domain demands for a software without any errors to perform these tasks. Therefore the field of computer science needs to address these challenges by providing necessary formalisms, techniques, and tools that will ensure the correctness of systems despite their complexity. DO-178C/EC-12C is a standard that governs the certification of software for airborne systems in commercial aircraft. The additional supplement DO- 333 enables us to use the formal methods in our technique of verifying the autonomous behaviour of UAV’s. The Mission Manager system is primarily responsible for the execution of behaviour sequence in online and offline mission planning of UAV. This work presents the process of software verification by making use of formal modelling using model checking of the Mission Manager component of ARTIS (Autonomous Rotorcraft Testbed for Intelligent Systems) UAV by gaining advantages from a generic modelling approach. The main idea is to make use of the designed generic models into specific cases like ARTIS in our case. The generic models are designed using the ALFU(R)S (Autonomy Levels For Unmanned Rotorcraft System) framework that delineates the commonalities of several UAVs considered around the world which also includes the ARTIS UAV. Furthermore this work walks through every process involved in model checking like requirements extraction and documentation using a template based method, requirements specification using the temporal logics like LTL and CTL, developing a formal model using NuSMV as a model checking tool to analyze the requirements against the model for the Mission Manager component of MiPlEx (Mission Planning and Execution). Additionally as a validation approach, test sequences are generated by using trap properties or negation properties. This aids for a test generation approach by harnessing counterexample generating capabilities of the NuSMV Model Checker.