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Pearl (2000), Spirtes et al (1993) and Lauritzen (2001) set up a new framework to encode the causal relationships between the random variables by a causal Bayesian network. The estimation of the conditional probabilities in a Bayesian network has received considerable attention by several investigators (e. g., Jordan (1998), Geiger and Heckerman (1997), Ileckerman et al (1995)), but, this issue has not been studied in a causal Bayesian network. In this thesis, we define the multicausal essential graph on the equivalence class of Bayesian networks in which each member of this class manifests a sort of strong type of invariance under (causal) manipulation called hypercausality. We then characterise the families of prior distributions on the parameters of the Bayesian networks which are consistent with hypercausality and show that their unmanipulated uncertain Bayesian networks must demonstrate the independence assumptions. As a result, such prior distributions satisfy a generalisation of the Geiger and lieckerman condition. In particular, when the corresponding essential graph is undirected, the mentioned class of prior distributions will reduce to the Hyper-Dirichlet family (see Chapter 6). In tile second part of this thesis, we will calculate certain local sensitivity measures and through them we are able to provide the solutions for the following questions: Is the network structure that is learned from data robust with respect to changes of the directionality of some specific arrows? Is the local conditional distributions associated with the specified node robust with respect to the changes to its prior distribution or with respect to the changes to the local conditional distribution of another node? Most importantly, is the posterior distribution associated with the parameters of any node robust with respect to the changes to the prior distribution associated with the parameters of one specific node? Finally, are the quantities mentioned above robust with respect to the changes in the independence assumptions described in Chapter 3? Most of the local sensitivity measures (particularly, local measures of the overall posteriors sensitivity), developed in the last decade, tend to diverge to infinity as the sample size becomes very large (Gustafson (1994) and Gustafson et al (1996)). This is in contrast to our knowledge that, starting from different priors, posteriors tend to agree as the data accumulate. Here we define a now class of metrics with more satisfactory asymptotic behaviour. The advantage of the corresponding local sensitivity measures is boundedness for large sample size.

Diabetes is a chronic disease which affects the glucose homeostasis system and its prevalence is rapidly increasing around the globe. Presently, the coronavirus disease 2019 (COVID-19) pandemic is a major issue for those with diabetes as the disease leads to more severe symptoms of the novel severe acute respiratory syndrome coronavirus 2 infection. In this study, mathematical models were developed and analysed to understand diabetes pathways. Dynamical systems theory were used to determine mathematical properties of the models and establish threshold quantities. Numerical simulations were performed to confirm the results of traditional mathematical analysis along with machine learning based sensitivity analysis to ascertain robustness of results. Sensitivity analysis was used to determine parameters influencing the dynamics of the glucose homeostasis system for the models. Analytical results of the first model showed three equilibrium points, a stable physio-logical, stable pathological (Type 1 diabetes state) and an unstable Type 2diabetes state, thus confirming known biological characteristics of the glucose homeostasis system. The model exhibits a backward bifurcation phenomenon when the model threshold quantity is less than unity, where an individual transit from unstable Type 2 diabetes state to a stable physiological state. This result demonstrates that Type 2 diabetes is reversible when acting on risk factors, and this is also true for biological findings. Sensitivity analysis identified all parameters that make up the threshold quantity as influential in determining model dynamics. The second model was developed to focus on Type 1 diabetes dynamics. The results showed two stable states, a physiological and pathological state, in line with known biological findings. Sensitivity analysis highlighted key parameters that determine the dynamics of the glucose homeostasis system and confirmed mathematical analysis findings. The two glucose homeostasis models developed were then fitted to published data on experimental mice with Type 1 diabetes using a Bayesian approach in order to determine a suitable model framework for Type 1 diabetes. The results from model selection suggest that the model with noβ-cells is more suitable in predicting Type 1 diabetes dynamics. Overall, the research highlights the importance of both traditional mathematical modelling and parameter based sensitivity analysis approaches in understanding important model parameter sand establishing diabetes pathways. Further, the study provided insights on a suitable model framework for understanding Type 1 diabetes.

The reuse of building components can decrease the embodied energy and greenhouse gases of the construction activities and help get closer to a circular economy using fewer virgin materials. Part of the recent efforts to promote the reuse rates includes estimating the reusability of the load-bearing building components to assist the stakeholders in making sound judgements of the reuse potentials at the end-of-life of a building and alleviate the uncertainties and perceived risks. This study develops probabilistic models using advanced supervised machine learning techniques to predict the reuse potential of structural elements at the end-of-life of a building, from technical, economic, and social perspectives. After performing a thorough literature search and identifying, analysing, and categorising the independent variables affecting the reusability of building structural elements, these factors were used to develop an online questionnaire. This questionnaire was then shared with a representative sample of practitioners in the construction industry, including managers, CEOs, architects, engineers, consultants, and deconstruction experts with previous experience in reusing recovered building structural components. The received questionnaires were reviewed, and the initial dataset was split into three separate datasets to address the technical, economic, and social aspects of the study. Then, the missing values were estimated, and the class imbalances were addressed using advanced techniques. In the next stage, and for each dataset, a total number of thirteen predictive models were developed in the R software using 13 advanced supervised machine learning methods. The performance and transparency of these models were compared to choose the best-practice Building Structural Elements Reusability Predictive Models (BSE-RPMs), which provide reliable predictions. Random Forest (RF) models were selected as the best practice BSE-RPMs for all three datasets, with a considerable overall accuracy of 96%, 89%, and 94% for the technical, economic, and social models, respectively. Since RF models are known as black-box models, advanced supervised machine learning methods such as sensitivity analysis and visualisation techniques were employed to open the selected RF BSE-RPMs. Eventually, using advanced rule extraction methods, three easy-to-understand predictive models (learners) were developed for assessing the technical, economic, and social reusability of the load-bearing building components, with an overall accuracy of 85%, 82%, and 91%, respectively. This research has contributed to promoting the reuse of building structural elements in two ways. First, using advanced supervised machine learning techniques such as the Boruta method and recursive feature elimination technique, this research identifies and ranks the main reusability factors based on the experience of the stakeholders with the recovered building structural elements in the building sector. Second, for the first time, it develops three sets of easy-to-understand learners (predictive rules) that can be used by practitioners to have an initial assessment of the technical, economic, and social reusability of the load-bearing components. The developed learners can be easily used by various stakeholders and have the potential to promote the reuse rate of the structural elements of the existing buildings, which were not designed for deconstruction. These sets of rules can also encourage more deconstruction projects since the developers would have a better judgment about the reusability of the structure of an existing building at its end-of-life, which, in turn, can accelerate the growth of reuse markets.