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Directed Acyclic Graphs: A Tool for Understanding the NASA Human Spaceflight System Risks - Human System Risk Board

For over a decade, the National Aeronautics and Space Administration (NASA) has tracked and configuration-managed approximately 30 risks to astronaut health and performance that occur before, during and after spaceflight. The Human System Risk Board (HSRB), a Health and Medical Technical Authority (HMTA) Board at NASA Johnson Space Center, is the entity responsible for identifying, assessing, analyzing, and monitoring the official understanding of the risk or risk posture for each of the Human System Risks and determining – based on evaluation of the available evidence – when that risk posture changes. The ultimate purpose of tracking and researching these risks is to find ways to reduce the risk that astronaut crews face during spaceflight. Historically, research, development and operations relevant to one risk have been conducted in isolation from other risks; these individual risk ‘silos’ enabled initial characterization of each specific risk. In spaceflight however, the impact of exposure to risk for astronaut crews is cumulative, and not independent of exposures or other risks, as all the adverse effects of the spaceflight environment begin at launch, continue throughout the duration of the mission and in some cases across the lifetime of the crews. In January of 2020, the HSRB at NASA embarked on a pilot project designed to assess the potential value of causal diagramming as a tool to facilitate understanding of these cumulative and interdependent effects as applied within Human System Risk management. This process uses directed acyclic graphs as a means of formalizing a shared mental model of the causal flow of risk among Risk Board stakeholders. Initially this model was to improve communication among those stakeholders, but the potential value exceeds communication alone. The causal diagrams are formulated as directed acyclic graphs (DAGs) to function as a type of knowledge graph for reference for the board and its stakeholders. This document is a sister document to NASA/TM 20220006812 Directed Acyclic Graph Guidance Documentation (1). In that document, the basic guidance for creating and standardizing directed acyclic graphs as tools for cross-risk analysis is provided. This document contains the initial configuration managed DAGs that were created as a result of applying those principles. These initial versions were accepted by the HSRB in January of 2022. Each of the Human System Risks are represented by a DAG that has been reviewed by the larger Human Health and Performance community at NASA including life scientists, physical scientists, physicians, nurses, pharmacists, exercise specialists and more. These results show the starting point for Human System Risk DAGs as shared mental models and communication aids across the boundaries of the various expertise needed to understand and mitigate the human risks in spaceflight. Because they are a starting point, each of these DAGs can be expected to change over time as new or refined evidence becomes available. The process for updating these DAGs can be found in the JSC-66705 Human System Risk Management Plan (2) that is publicly available on the NASA Technical Reports Server.

Erik L. Antonsen↗

TDAG: Tree-based Directed Acyclic Graph Partitioning for Quantum Circuits

We propose the Tree-based Directed Acyclic Graph (TDAG) partitioning for quantum circuits, a novel quantum circuit partitioning method which partitions circuits by viewing them as a series of binary trees and selecting the tree containing the most gates. TDAG produces results of comparable quality (number of partitions) to an existing method called ScanPartitioner (an exhaustive search algorithm) with an 95% average reduction in execution time. Furthermore, TDAG improves compared to a faster partitioning method called QuickPartitioner by 38% in terms of quality of the results with minimal overhead in execution time.

Clark, Joseph↗

Directed Acyclic Graph Guidance Documentation

For over a decade, the National Aeronautics and Space Administration (NASA) has tracked and configuration-managed approximately 30 risks to astronaut health and performance that occur before, during and after spaceflight. The Human System Risk Board (HSRB), a Health and Medical Technical Authority (HMTA) Board at NASA Johnson Space Center, is the entity responsible for identifying, assessing, analyzing, and monitoring the official understanding of the risk or risk posture for each of the Human System Risks and determining – based on evaluation of the available evidence – when that risk posture changes. The ultimate purpose of tracking and researching these risks is to find ways to reduce the risk that astronaut crews face during spaceflight. Historically, research, development and operations relevant to one risk have been conducted in isolation from other risks; these individual risk ‘silos’ enabled initial characterization of each specific risk. In spaceflight however, the impact of exposure to risk for astronaut crews is cumulative, and not independent of exposures or other risks, as all the adverse effects of the spaceflight environment begin at launch, continue throughout the duration of the mission and in some cases across the lifetime of the crews. In January of 2020, the HSRB at NASA embarked on a pilot project designed to assess the potential value of causal diagramming as a tool to facilitate understanding these cumulative and interdependent effects as applied within Human System Risk management. This process uses directed acyclic graphs as a means of formalizing a shared mental model of the causal flow of risk among Risk Board stakeholders. Initially this model was to improve communication among those stakeholders, but the potential value exceeds communication alone. Formalization of the process for creating these causal diagrams will enable the creation of a composite risk network that is vetted by members of the NASA community and configuration managed. The causal diagrams are formulated as directed acyclic graphs (DAGs) to function as a type of knowledge graph for reference for the board and its stakeholders. This document outlines the pilot process, the standardized approaches, and guidance for risk custodian teams when creating and updating DAGs as a part of the NASA Human System Risk Management process.

Risk↗

Human System Risk Communication: Directed Acyclic Graphs

- The Human System Risk Board (HSRB) is responsible for the management of a portfolio of 30 human system risks that NASA tracks and configuration manages to mitigate for future crewed exploration missions. - The HSRB has been exploring the concept of causal diagrams (in the form of Directed Acyclic Graphs or DAGs) as an approach to creating knowledge graphs for each risk to enable shared mental models of causal flow from spaceflight hazards to mission outcomes among HSRB Stakeholders. - These diagrams are intended to improve insight and communication of risk across the myriad subject matter experts and management interested in human system risk reduction. This includes program managers, systems engineers, and operators in addition to the Human Health and Performance Directorate. - The DAG project was intended to create the foundation for composition of the 30 baselined DAGs into a single risk network and software is being developed in parallel to enable this forward work.

directed acrylic graph↗

Incorporation of Human Risk Directed Acyclic Graphs (DAG) With Mishap Investigations to Un-Silo Knowledge

NASA’s Human System Risk Board (HSRB) has been a central driver in efforts to understand, mitigate, and communicate the 29 human systems risks monitored by the board. As a result of the collaboration between research, operations, and technical authorities, large bodies of knowledge have been collected and digested to represent the current understanding of the risks. As a part of these bodies of knowledge, directed acyclic graphs (DAGs) have been developed to communicate the current understanding of the causal relationship of the hazards, contributing factors, countermeasures, other risks, and outcomes that contribute to the overall risk. This risk knowledge is applied in a theoretical sense for potential incidents during exploration even while informed by surveillance data. However, there have been mishaps and close calls during past space exploration that intersect with one or more of the Human System Risks DAGs and knowledge bases. The purpose of this exercise was to un-silo this risk knowledge and connect it to the close call of EVA 23 through the development of a DAG representing the intersection of the HSRB Risks and the events of the close call. The development of the DAG occurred through an iterative process, with each iteration expanding and/or refining the nodes and connections described by the source materials. In addition to the risk documentation developed by the HSRB, lessons learned and other mishap investigation documents were utilized to understand the events that led to water entering the helmet of a crewmember on the EVA. New nodes specific to the events of EVA 23 were interconnected with existing HSRB DAG nodes and edges. Nodes within the DAG were defined within a “DAG-tionary” with any updates to a definition that may have previously existed from the HSRB DAGs, and edges were recorded in a matrix. Both the DAG-tionary and matrix describe where nodes and edges are present across the Risk and Mishap DAG. This DAG will then be reviewed by experts outside of HSRB and HRP to confirm that interpretations of the non-health related events (such as the engineering nodes) are represented accurately. DISCUSSION This process highlighted a method by which the knowledge generated among the contributing members of the HSRB Risks can be effectively adapted and utilized through the tools employed by the Risk Custodian teams. By leveraging these tools, new context and insights to the information at hand can be brought forward to address current spaceflight challenges. Moreover, un-siloing this knowledge through future DAGs and other efforts can drive interprofessional collaboration and foster communication. This will enable teams to work together more effectively, leveraging their diverse expertise to tackle the complex challenges of space exploration and human research. Ultimately, this collaboration will bring NASA closer to achieve agency goals and contribute to the overall shared mission and vision.

Samuel Jacobs↗

Development of A Directed Acyclic Graph for Venous Thromboembolism During Spaceflight

Introduction: Recent studies have reported the development of venous blood flow stasis in astronauts and an occlusive venous thrombosis during spaceflight. Subsequent investigations revealed approximately one quarter of surveilled crew members had some degree of blood flow stasis in the left internal jugular vein. Therefore, NASA’s Human System Risk Board now formally tracks venous thromboembolism (VTE) as a “concern” for human spaceflight. To investigate potential mechanisms by which exposures concomitant with spaceflight (e.g., microgravity, radiation) may contribute to VTE, we developed a causal diagram in the form of a directed acyclic graph (DAG). Methods: The mechanisms by which spaceflight exposures may elevate the risk of VTE and the downstream effects on mission outcomes were critically analyzed, taking into account scientific literature and subject matter expertise consultation, and a DAG was generated. A Level-of-Evidence score for each causal relationship was assigned based on assessing the literature against a set of criteria derived from the A. Bradford Hill Causal Guidelines. Results: The set of three main factors that predispose people to VTE (hypercoagulability, endothelial damage, and blood stasis) is known as Virchow’s Triad. In constructing the DAG for VTE we articulated various mechanisms by which the principal spaceflight hazards (microgravity, radiation, closed hostile environment, isolation and confinement, distance from Earth) are thought to interact with or cause the components in Virchow’s triad. We found sufficient evidence to at least speculate that fluid shifts from microgravity, compensatory alterations in hematologic indices, spaceflight atmospheric conditions, and oxidative stress/inflammation from radiation may be potential contributors to VTE development. Discussion: Developing the DAG entailed a systematic and repeatable approach for visualizing relationships between contributing factors that may lead to VTE in spaceflight. Articulating pathways linking spaceflight exposures to VTE risk factors and possible VTE development enables subject matter experts from different domains to construct a shared mental model. Assignment of levels of evidence scores to the relationships helps identify knowledge and capability gaps that should be considered for further investigation. Furthermore, the DAG highlights modifiable variables and may therefore facilitate the development of new VTE risk mitigation strategies.

Alexander Svoronos↗

DG2DAG: Learning Directed Acyclic Graphs from Functional Priors

Physics-based systems-of-systems models are computationally expensive. Reduced graphical models can decrease computational complexity, but may not proffer an end-to-end model from upstream inputs to downstream outputs. We consequently are interested in reducing models on directed graphs to models on a directed acyclic subgraph such that preserves accurate reconstruction of nodes. The consequence is a model with a topological ordering, providing a one-way flow of computation, and a causal interpr

Voronin, Alexey [Sandia National Laboratories (SNL↗

Evidence Report: Risk of Renal Stone Formation

Kidney stone formation and passage has the potential to greatly impact mission success and crewmember health, especially for long-duration missions. Alterations in hydration state (relative dehydration), spaceflight-induced changes in urine biochemistry (urine super-saturation), and bone metabolism (increased calcium excretion) during exposure to microgravity may increase the risk of kidney stone formation. There are possible countermeasures and treatments available that are used terrestrially that may then be applied to spaceflight. Directed Acyclic Graphs (DAGs) are used throughout this document to communicate spaceflight conditions that may lead to renal stone formation, the countermeasures that may be used to prevent their formation, and possible treatment modalities. The DAGs are sorted by strength of evidence, according to Table 6. Additionally, for the full Renal Stone Evidence Report Content: Directed Acyclic Graphs and Evidence Report, please see Appendix A, Expanded Directed Acyclic Graphs (DAGs) and Evidence. Additionally, a proposed Concept of Operations for the Prevention, Diagnosis, and Treatment of Renal Stones for a Mars Mission was created in conjunction with and to complement this Evidence Report update. Please see Appendix B, Proposed Expanded Concept of Operations for the Prevention, Diagnosis and Treatment of Renal Stones for Mars Missions, for the full report. Areas in the following Evidence Report will be cross-linked to scenarios from the Concept of Operations.

Emily Stratton↗

A Method for Validating Causal Diagrams of Human Health Risk in Space Flight

The complexity of cause-and-effect relationships between spaceflight hazards and resulting health conditions clouds understanding of the totality of human system risk in space. In response, NASA has introduced Directed Acyclic Graphs (causal diagrams) into the human systems risk management process. These diagrams allow for a common understanding of the mechanisms that lead from unique hazards of spaceflight to the health outcomes important to agencies and astronauts. However, the paucity of available biomedical data from spaceflight creates a need for methods of validating causal models that can accommodate data from spaceflight model analogs. Here we outline one approach utilizing open-access rodent bone datasets from the Ames Life Sciences Data Archive. The properties of directed acyclic graphs themselves can provide an epistemological and statistical framework for validation of a priori causal representations of human system risk in space flight. The assumed causal connections on the graph creates sets of logical implications: variables that – if the causal diagram is correct – should be correlated, as well as sets that should be conditionally independent. By testing these implied correlations and conditional independencies both statistically and heuristically, we can provide evidence for or against specific causal pathways on the causal diagram. In addition to validation of expert-generated causal diagrams, machine learning techniques can learn the most likely structure of a causal diagram from a given dataset. Comparison with and reconciliation between machine-learned causal diagrams and expert-generated diagrams is another technique for challenging assumptions and improving our understanding of causal mechanisms. Accurately representing complex causation is essential to systemic understanding of human health risks in space travel. Having a robust system of validating causal diagrams helps us arrive at more accurate representations of causal systems. This process will be integral to developing the countermeasures necessary for extended exploration of the moon and Mars.

Robert Reynolds↗

Integrating the PanDA Workload Management System with the Vera C. Rubin Observatory

The Vera C. Rubin Observatory will produce an unprecedented astronomical data set for studies of the deep and dynamic universe. Its Legacy Survey of Space and Time (LSST) will image the entire southern sky every three to four days and produce tens of petabytes of raw image data and associated calibration data over the course of the experiment’s run. More than 20 terabytes of data must be stored every night, and annual campaigns to reprocess the entire dataset since the beginning of the survey will be conducted over ten years. The Production and Distributed Analysis (PanDA) system was evaluated by the Rubin Observatory Data Management team and selected to serve the Observatory’s needs due to its demonstrated scalability and flexibility over the years, for its Directed Acyclic Graph (DAG) support, its support for multi-site processing, and its highly scalable complex workflows via the intelligent Data Delivery Service (iDDS). PanDA is also being evaluated for prompt processing where data must be processed within 60 seconds after image capture. This paper will briefly describe the Rubin Data Management system and its Data Facilities (DFs). Finally, it will describe in depth the work performed in order to integrate the PanDA system with the Rubin Observatory to be able to run the Rubin Science Pipelines using PanDA.

79 ASTRONOMY AND ASTROPHYSICS↗

Verification, Validation, and Calibration Through a Causal Lens

While typical validation and verification approaches focus on identifying the associations between data elements using statistical and machine learning methods, the novel methods in this paper focus instead on identifying causal relationships between data elements. Statistical and machine-learning-based approaches are strictly data-driven, meaning that they provide quantitative comparison measures between data sets without explicitly considering the hypotheses behind them. This can lead to the erroneous conclusion that, if two data sets are close enough, the models that generated them are similar. In addition, when experimental and simulated data differ to an extent that fails to meet the acceptance criteria, calibration techniques are used to tweak simulation model parameters to reduce the gap between the two types of data. This produces the false expectation that a simulation model will match reality. The methods presented in this paper move away from these strictly data-driven methods for validation and calibration toward more robust, model-driven methods based on causal inference. Causal inference aims to identify the possible mechanisms that might have generated data. Thus, this analysis targets the prediction of the effects when one (or more) of the identified mechanisms are altered. There are many approaches to identify, quantify, and illustrate causal relationships. For the scope of this paper, directed graphs are employed as causal models. If the directed graph lacks cycles, it is known as a directed acyclic graph. A node in such a graph represents an observed data element while a directed edge connecting two nodes represents a causal relationship between two variables. The developed causal methods are designed to extract causal models from simulation models and experimental data. Causal models capture the causal relationships between data elements (e.g., simulated and experimental data). In this context, validation and verification are performed by comparing causal models. The proposed approach does not only inform system analysts on how a simulation model matches real-world data, but also identifies elements of the simulation model that should be revised when discrepancies between simulation and experimental data are observed. Through these causal methods, analysts can identify the portion of the model equation(s) that are behind an edge connecting two variables. Hence, once the structural differences between causal models have been determined, model calibration can occur by changing only those model parameters that impact the identified causal relationships.

97 MATHEMATICS AND COMPUTING↗

VALIDATION, VERIFICATION, AND CALIBRATION THROUGH A CAUSAL LENS

This paper presents an alternative method based on causal inference to perform validation, verification, and calibration of simulation models. While classical validation and verification approaches focus on the identification of the associations between data elements using statistical and machine learning methods, the novel methods in this paper focus instead on the identification of causal relationships between data elements. Statistical and machine learning-based approaches are strictly data-driven, meaning that they provide quantitative comparison measures between datasets without explicitly considering the hypotheses behind them. This can lead to the erroneous conclusion that, if two data sets are close enough, then the models that generated them are similar. In addition, when experimental and simulated data differ to an extent that fails to meet the acceptance criteria, calibration techniques are used to tweak simulation model parameters to reduce the gap between the two types of data. This produces the false expectation that a simulation model will match reality. The methods presented in this paper move away from these strictly data-driven methods for validation and calibration toward more robust, model-driven methods based on causal inference. Causal inference aims to identify the possible mechanisms that might have generated data. Thus, this analysis targets the prediction of the effects when one (or more) of the identified mechanisms are altered. There are many approaches to identify, quantify and illustrate causal relationships. For the scope of this paper, directed graphs are employed as causal models. If the directed graph lacks cycles it is known as a directed acyclic graph (DAG). A node in such a graph represents an observed data element while a directed edge connecting two nodes represents a causal relationship between two variables. The developed causal methods are designed to extract causal models from simulation models and from experimental data. Causal models capture the causal relationships between data elements (e.g., simulated and experimental data). In this context, validation and verification are performed by comparing causal models. The proposed approach does not only inform system analysts on how a simulation model matches real-world data, but also identifies elements of the simulation model that should be revised when discrepancies between simulation and experimental data are observed. Through these causal methods, analysts have a means to identify the portion of the model equation(s) that are behind an edge connecting two variables. Hence, once the structural differences between causal models have been determined, model calibration can occur by changing only those model parameters that impact the identified causal relationships.

97 MATHEMATICS AND COMPUTING↗

Machine Learning for the Validation of Expert-Elicited Causal Risk Diagrams

Exposure to spaceflight poses risk to human health in complex ways. To help manage this risk, the Human Systems Risk Board (HSRB) at the National Aeronautics and Space Administration (NASA) maintains a set of causal diagrams that attempt to explain how spaceflight hazards generate health risks and lead to adverse outcomes both in-mission, immediately post-mission, and over the long term. These causal risk diagrams are formulated as directed acyclic graphs (DAGs) and can function as knowledge graphs of connected risks and outcomes. These DAGs have proven useful for communication, and, through network analysis, have allowed for the identification of structurally important factors in the risk network. However, the utility these DAGs provide is directly proportional to their verisimilitude, making assessment of this trait using empirical data – whether from actual human spaceflight or various spaceflight analogue exposures and model organisms – a high priority. In this research we explore the use of machine learning algorithms to learn DAG structure from empirical data as a means of evaluating human-elicited DAG structures. To do so, we test several different graph structure-learning algorithms on data concerning changes in the bones of rats and mice after exposure to either spaceflight or a spaceflight analogue. We explore potential methods for indexing the similarity between each algorithm’s output DAG with all the others and with that of the expert-elicited DAG. We discuss next steps in this ongoing line of research and open science initiatives underway to complete them.

directed acyclic graphs↗

Human Systems Risk Network - A Ranking Analysis of Risks

INTRODUCTION The Human Systems Risk Board (HSRB) is responsible for understanding, managing, and mitigating the risks associated with spaceflight. For a particular mission, the HSRB assigns each human system risk a rating on a 5x5 grid assessing its likelihood and consequence, which is ultimately used to compare and rank the risks. The HSRB approaches risk management by primarily establishing the context of each human system risk individually with the understanding that mitigating one risk might affect the likelihood, consequence, and mitigation approaches of another. To support this effort the HSRB, subject matter experts, and risk custodian teams created directed acyclic graphs (DAG), often called a causal graph, for the twenty-nine risks. In this presentation, we propose a new ranking algorithm for the risks which includes the downstream influence of each risk according to the information in the DAGs and provide an application of graph theoretic tools. METHODS In 2014, Mindock and Klaus proposed a taxonomy for human system risk influences which we have adopted to categorize the nodes in each DAG. Analyzing the nodes that correspond to the risks in this taxonomy allows us to analyze and understand how each risk influences the others. We construct an auxiliary network, which we call the Primary Risk Network (PRN), where the nodes are the twenty-nine space flight risks and, a directed edge connects Risk A to Risk B if Risk A has some influence on the likelihood or consequence of Risk B as described in the DAGS. We perform a variety of graph theoretic ranking methods on the nodes (or risks) in the PRN, including Katz centrality. RESULTS We rank the nodes in the PRN using the Katz centrality score. The ten risks with the highest score are pictured in Figure 1, colored (light to dark) according to their score. We analyze other centrality measures like betweenness centrality, eigenvector centrality, and the Estrada index, and provide the meaning of the corresponding rankings in terms of the risks. Future work includes analyzing the other categories in the taxonomy defined by Mindock and Klaus [1]. For example, we are interested in analyzing the nodes that are labeled as countermeasures or capabilities and perform similar analysis to measure their effect on certain medical conditions.

dag↗

Strategies for Quantifying Human Space Flight Performance in the Crew Health and Performance System

The Crew Health and Performance-Probabilistic Risk Assessment (CHP-PRA) team at NASA Glenn Research Center is planning a customized approach to quantify human spaceflight performance changes with respect to changes to the CHP system functions and capabilities. Using the Directed Acyclic Graphs (DAG) initiated by NASA’s Human Systems Risk Board (HSRB) [1], the team is surveying potential candidate models and novel strategies that generate metrics suitable for supporting decision making related to how the CHP system may influence human system performance risk. One such investigation includes classic Human Reliability Analysis (HRA) models. Traditionally, HRA methods estimate the occurrence of human errors and their impact on the success of an activity when designing and operating a system. While humans perceive, interpret, decide on, and carry out a course of action, the factors affecting performance and error likelihood are commonly referred to as performance shaping factors (PSFs). Originally developed to alleviate safety concerns related to nuclear power plant operations, HRA methods such as THERP [2] and CREAM [3] dismantle an activity into tasks, requiring elemental steps to be executed, and assess their failure due to predefined PSFs. In this study, we compare generic HRA methods and those that incorporate some human spaceflight aspects, such as sleep conditions (SCREAM [4]), with respect to how they may be adopted to capture performance with an intention to mitigate detrimental outcomes elucidated by the HSRB DAGs. We suggest strategies to quantify astronaut performance specific to spaceflight activities and illustrate how such concepts may help in optimizing the CHP system capabilities with respect to Artemis missions.

dag↗

Potential Use of a Bayesian Network for Discriminating Flash Type from Future GOES-R Geostationary Lightning Mapper (GLM) data

Continuous monitoring of the ratio of cloud flashes to ground flashes may provide a better understanding of thunderstorm dynamics, intensification, and evolution, and it may be useful in severe weather warning. The National Lighting Detection Network TM (NLDN) senses ground flashes with exceptional detection efficiency and accuracy over most of the continental United States. A proposed Geostationary Lightning Mapper (GLM) aboard the Geostationary Operational Environmental Satellite (GOES-R) will look at the western hemisphere, and among the lightning data products to be made available will be the fundamental optical flash parameters for both cloud and ground flashes: radiance, area, duration, number of optical groups, and number of optical events. Previous studies have demonstrated that the optical flash parameter statistics of ground and cloud lightning, which are observable from space, are significantly different. This study investigates a Bayesian network methodology for discriminating lightning flash type (ground or cloud) using the lightning optical data and ancillary GOES-R data. A Directed Acyclic Graph (DAG) is set up with lightning as a "root" and data observed by GLM as the "leaves." This allows for a direct calculation of the joint probability distribution function for the lighting type and radiance, area, etc. Initially, the conditional probabilities that will be required can be estimated from the Lightning Imaging Sensor (LIS) and the Optical Transient Detector (OTD) together with NLDN data. Directly manipulating the joint distribution will yield the conditional probability that a lightning flash is a ground flash given the evidence, which consists of the observed lightning optical data [and possibly cloud data retrieved from the GOES-R Advanced Baseline Imager (ABI) in a more mature Bayesian network configuration]. Later, actual GLM and NLDN data can be used to refine the estimates of the conditional probabilities used in the model; i.e., the Bayesian network is a learning network. Methods for efficient calculation of the conditional probabilities (e.g., an algorithm using junction trees), finding data conflicts, goodness of fit, and dealing with missing data will also be addressed.

Solakiewiz, Richard↗