Markov Influence Diagrams.

Markov influence diagrams (MIDs) are a new type of probabilistic graphical model that extends influence diagrams in the same way that Markov decision trees extend decision trees. They have been designed to build state-transition models, mainly in medicine, and perform cost-effectiveness analyses. Using a causal graph that may contain several variables per cycle, MIDs can model various patient characteristics without multiplying the number of states; in particular, they can represent the history of the patient without using tunnel states. OpenMarkov, an open-source tool, allows the decision analyst to build and evaluate MIDs-including cost-effectiveness analysis and several types of deterministic and probabilistic sensitivity analysis-with a graphical user interface, without writing any code. This way, MIDs can be used to easily build and evaluate complex models whose implementation as spreadsheets or decision trees would be cumbersome or unfeasible in practice. Furthermore, many problems that previously required discrete event simulation can be solved with MIDs; i.e., within the paradigm of state-transition models, in which many health economists feel more comfortable

Computational Solutions Based on Bayesian Networks to Hierarchize and to Predict Factors Influencing Gender Fairness in the Transport System: Four Use Cases

: Previous studies have highlighted inequalities and gender differences in the transport system. Some factors or fairness characteristics (FCs) strongly influence gender fairness in the transport system. The difference with previous studies, which focus on general concepts, is the incorporation of level 3 FCs, which are more detailed aspects or measures that can be implemented by companies or infrastructure managers and operators in order to increase fairness and inclusion in each use case. The aim of this paper is to find computational solutions, Bayesian networks, and analytic hierarchy processes capable of hierarchizing level 3 FCs and to predict by simulation their values in the case of applying some improvements. This methodology was applied to data from women in four use cases: railway transport, autonomous vehicles, bicycle sharing stations, and transport employment. The results showed that fairer railway transport requires increased personal space, hospitality rooms, help points, and helpline numbers. For autonomous vehicles, the perception of safety, security, and sustainability should be increased. The priorities for bicycle sharing stations are safer cycling paths avoiding hilly terrains and introducing electric bicycles, child seats, or trailers to carry cargo. In transport employment, the priorities are fair recruitment and promotion processes and the development of family-friendly policies

Systems Mapping

This open access book explores a range of new and older systems mapping methods focused on representing causal relationships in systems. In a practical manner, it describes the methods and considers the differences between them; describes how to use them yourself; describes how to choose between and combine them; considers the role of data, evidence, and stakeholder opinion; and describes how they can be useful in a range of policy and research settings. This book provides a key starting point and general-purpose resource for understanding complex adaptive systems in practical, actionable, and participatory ways. The book successfully meets the growing need in a range of social, environmental, and policy challenges for a richer more nuanced, yet actionable and participatory understanding of the world. The authors provide a clear framework to alleviate any confusion about the use of appropriate terms and methods, enhance the appreciation of the value they can bring, and clearly explain the differences between approaches and the resulting outputs of mapping processes and analysis

Open Markov Processes and Reaction Networks

We define the concept of an `open' Markov process, a continuous-time Markov chain equipped with specified boundary states through which probability can flow in and out of the system. External couplings which fix the probabilities of boundary states induce non-equilibrium steady states characterized by non-zero probability currents flowing through the system. We show that these non-equilibrium steady states minimize a quadratic form which we call `dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.Comment: 140 pages, University of California Riverside PhD Dissertatio

Teaching Probabilistic Graphical Models with OpenMarkov

OpenMarkov is an open-source software tool for probabilistic graphical models. It has been developed especially for medicine, but has also been used to build applications in other fields and for tuition, in more than 30 countries. In this paper we explain how to use it as a pedagogical tool to teach the main concepts of Bayesian networks and influence diagrams, such as conditional dependence and independence, d-separation, Markov blankets, explaining away, optimal policies, expected utilities, etc., and some inference algorithms: logic sampling, likelihood weighting, and arc reversal. The facilities for learning Bayesian networks interactively can be used to illustrate step by step the performance of the two basic algorithms: search-and-score and PC