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At least 1,315 records · Page 73

The HUNTER Dynamic Human Reliability Analysis Tool: Coupling an External Plant Code

The Human Unimodel for Nuclear Technology to Enhance Reliability (HUNTER) is a framework to support dynamic human reliability analysis (HRA) with the aim to develop standalone software to perform the dynamic HRA calculations. Within the HRA, human actions in nuclear power plants (NPPs) are predicated by plant states, and human actions influence the plant. In other words, plant operations are necessarily recursive, and it becomes challenging to model complex human-plant interactions. Consequently, we have linked two software simulations that complement those shortcomings. RELAP5-3D—the Reactor Excursion and Leak Analysis Program (RELAP; Aumiller, Tomlinson, and Bauer 2001) is the foundational thermal-hydraulic software used to model nuclear systems. Using RELAP5-3D, we have simulated the plant operations proceeding according to procedures developed to address emergent situations in NPPs. Plant operations include various actions such as the operator checking plant parameters, as well as actions that are continuously performed over time until a specific parameter reaches certain criteria. That means that HUNTER and RELAP5-3D exchange information with each other and should be carried out simultaneously over time. To simulate plant operations, which represent the actual operator checks of plant parameters and corresponding manual control actions, changes in plant status are identified through simulation and performed according to the criteria and order of the procedure. Thus, the goal of coupling HUNTER with RELAP5-3D is to facilitate synchronous coupling, where human and plant models provide iterative feedback loops that drive the course of actions. The advantage of coupling with RELAP5-3D to serve as the external environment module in HUNTER is the ability to customize the plant model and streamline for particular model applications. In this paper, we will address the key features of the coupling and the coupling structure built to perform the feedback loops.

99 GENERAL AND MISCELLANEOUS↗

"Reducing Detailed Vehicle Energy Dynamics to Physics-Like Models"

The energy demand of vehicles, particularly in unsteady drive cycles, is affected by complex dynamics internal to the engine and other powertrain components. Yet, in many applications, particularly macroscopic traffic flow modeling and optimization, structurally simple approximations to the complex vehicle dynamics are needed that nevertheless reproduce the correct effective energy behavior. This work presents a systematic model reduction pipeline that starts from complex vehicle models based on the Autonomie software and derives a hierarchy of simplified models that are fast to evaluate, easy to disseminate in open-source frameworks, and compatible with optimization frameworks. The pipeline, based on a virtual chassis dynamometer and subsequent approximation strategies, is reproducible and is applied to six different vehicle classes to produce concrete explicit energy models that represent an average vehicle in each class and leverage the accuracy and validation work of the Autonomie software.

Khoudari, Nour↗

Annular Flow Simulation Supported by Iterative In-Memory Mesh Adaptation

Various flow regimes exist in a boiling water reactor (BWR) as the steam quality increases in the uprising coolant flow, from bubbly flow, slug/churn flow, to annular flow. The annular flow is characterized by the presence of a fast-moving gas core and the surrounding liquid film flowing on the conduit wall. Additionally, entrained droplets can be observed in the gas core with ingested bubbles in the liquid film. The dynamics occurring on the wavy interface between the liquid film and gas core plays a crucial role in affecting the heat transfer rate and pressure drop within the BWR core. However, a fundamental understanding of annular flow is still lacking, partly due to the difficulty in obtaining detailed local data in annular flow experiments. In the current study, a novel simulation framework is developed for the annular flow by coupling a computational fluid dynamics flow solver with state-of-the-art meshing software. The gas-liquid interface is tracked with the level set method. Based on the computed flow solutions, the computational mesh is dynamically adapted in memory to meet the local mesh resolution requirement. This iterative simulation-adaptation framework can ensure the fine mesh resolution across the interface, which not only helps mitigate the mass conservation degradation known to level set methods but also improves the representation of dramatic interface topological changes such as wave breaking and droplet entrainment. The present investigation will shed light onto the complex interfacial processes involved in annular flow and generate much needed simulation data for annular flow modeling.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

SciDAC-Center for Plasma Edge Simulation Report

The Common Component Architecture (CCA) effort is the embodiment of a long-range program of research and development into the formulation, roles, and use of component technologies in high-performance scientific computing. CCA components can interoperate with other components in a variety of frameworks, including SCIRun2 from the University of Utah. The SCIRun2 framework is also developing the ability to connect components from a variety of different models through a mechanism called meta-components. The meta component model operates by providing a plugin architecture for component models. Abstract components are manipulated and managed by the SCIRun2 framework, while concrete component models perform the actual work and communicate with each other directly. We will leverage the SCIRun2 framework and the Kepler system to orchestrate components in the Fusion Simulation Project (FSP) and to provide a CCA-based interface with Kepler. The groundwork for this functionality is being performed with the Scientific Data Management center. The SDM center is developing CCA-compliant interfaces for expressing and executing workflows and create workflow components based on SCIRun and Ptolemy (Kepler) execution engines, including development of uniform interfaces for selecting, starting, and monitoring scientific workflows. Accomplishments include Introduction to CCA and Simulation Software Systems, Introduction into SCIRun2 and Bridging within SCIRun2, CCALoop: A scalable design for a distributed component framework, and Combining Workflow methodologies with Component Architectures.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

R2U2: Tool Overview

R2U2 (Realizable, Responsive, Unobtrusive Unit) is an extensible framework for runtime System HealthManagement (SHM) of cyber-physical systems. R2U2 can be run in hardware (e.g., FPGAs), or software; can monitorhardware, software, or a combination of the two; and can analyze a range of different types of system requirementsduring runtime. An R2U2 requirement is specified utilizing a hierarchical combination of building blocks: temporal formula runtime observers (in LTL or MTL), Bayesian networks, sensor filters, and Boolean testers. Importantly, the framework is extensible; it is designed to enable definitions of new building blocks in combination with the core structure. Originally deployed on Unmanned Aerial Systems (UAS), R2U2 is designed to run on a wide range of embedded platforms, from autonomous systems like rovers, satellites, and robots, to human-assistive ground systems and cockpits. R2U2 is named after the requirements it satisfies; while the exact requirements vary by platform and mission, the ability to formally reason about realizability, responsiveness, and unobtrusiveness is necessary for flight certifiability, safety-critical system assurance, and achievement of technology readiness levels for target systems. Realizability ensures that R2U2 is suficiently expressive to encapsulate meaningful runtime requirements while maintaining adaptability to run on different platforms, transition between different mission stages, and update quickly between missions. Responsiveness entails continuously monitoring the system under test, real-time reasoning, reporting intermediate status, and as-early-as-possible requirements evaluations. Unobtrusiveness ensures compliance with the crucial properties of the target architecture: functionality, certifiability, timing, tolerances, cost, or other constraints.

Rozier, Kristin Y.↗

A Framework for Error-Bounded Approximate Computing, with an Application to Dot Products

Approximate computing techniques, which trade off the computation accuracy of an algorithm for better performance and energy efficiency, have been successful in reducing computation and power costs in several domains. However, error sensitive applications in high-performance computing are unable to benefit from existing approximate computing strategies that are not developed with guaranteed error bounds. While approximate computing techniques can be developed for individual high-performance computing applications by domain specialists, this often requires additional theoretical analysis and potentially extensive software modification. Hence, the development of low-level error-bounded approximate computing strategies that can be introduced into any high-performance computing application without requiring additional analysis or significant software alterations is desirable. In this paper, we provide a contribution in this direction by proposing a general framework for designing error-bounded approximate computing strategies and apply it to the dot product kernel to develop \bf qdot---an error-bounded approximate dot product kernel. Following the introduction of qdot, here we perform a theoretical analysis that yields a deterministic bound on the relative approximation error introduced by qdot. Empirical tests are performed to illustrate the tightness of the derived error bound and to demonstrate the effectiveness of qdot on a synthetic dataset, as well as two scientific benchmarks---the conjugate gradient (CG) and power methods. In some instances, using qdot for the dot products in CG can result in many components being quantized to half precision without increasing the iteration count required for convergence to the same solution as CG using a double precision dot product.

97 MATHEMATICS AND COMPUTING↗

DASAO: software tool for the management of safeguards, waste and decommissioning

Decommissioning of nuclear facilities is a complex process involving operations such as detailed surveys, decontamination and dismantling of equipment's, demolition of buildings and management of resulting waste and nuclear materials if any. This process takes place in a well-developed legal framework and is controlled and followed-up by stakeholders like the Safety Authority, the Radwaste management Agency and the Safeguards Organism. In the framework of its nuclear waste and decommissioning program and more specifically the decommissioning of the BR3 reactor, SCK-CEN has developed different software tools to secure the waste and material traceability, to support the sound management of the decommissioning project and to facilitate the control and the follow-up by the stakeholders. In the case of Belgium, it concerns the Federal Agency for Nuclear Control, the National Agency for radioactive waste management and fissile material and EURATOM and IAEA. In 2005, Belgonucleaire decided to shutdown her Dessel MOX fuel fabrication plant and the production stopped in 2006. According to the final decommissioning plan ('PDF') approved by NIRAS, the decommissioning works should start in 2008 at the earliest. In 2006, the management of Belgonucleaire identified the need for an integrated database and decided to entrust SCK-CEN with its development, because SCK-CEN relies on previous experience in comparable applications namely already approved by authorities such as NIRAS, FANC and EURATOM. The main objectives of this integrated software tool are: - simplified and updated safeguards; - waste and material traceability; - computerized documentation; - support to project management; - periodic and final reporting to waste and safety authorities. The software called DASAO (Database for Safeguards, Waste and Decommissioning) was successfully commissioned in 2008 and extensively used from 2009 to the satisfaction of Belgonucleaire and the stakeholders. SCK-CEN is now implementing a simplified release of the software for the management of the decommissioning of the Thetis reactor. Its decommissioning will start in March 2013 and will be completed by the end of 2014. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Face Recognition Oak Ridge (FaRO): A Framework for Distributed and Scalable Biometrics Applications

The facial biometrics community has seen a recent abundance of high-accuracy facial analytic models become freely available. Although these models' capabilities in facial detection, landmark detection, attribute analysis, and recognition are ever-increasing, they aren't always straightforward to deploy in a real-world environment. In reality, the use of the field's ever growing collection of models is becoming exceedingly difficult as library dependencies update and deprecate. Researchers often encounter headaches when attempting to utilize multiple models requiring different or conflicting software packages. Face Recognition Oak Ridge (FaRO) is an open-source project designed to provide a highly modular, flexible framework for unifying facial analytic models through a compartmentalized plug-and-play paradigm built on top of the gRPC (Google Remote Procedure Call) protocol. FaRO's server-client architecture and flexible portability allows easy construction of modularized and heterogeneous face analysis pipelines, distributed over many machines with differing hardware and software resources. This paper outlines FaRO's architecture and current capabilities, along with some experiments in model testing and distributed scaling through FaRO.

Bolme, David↗

GenAI4UQ: A software for forward and inverse uncertainty quantification using conditional generative AI

We introduce GenAI4UQ, a software package for forward and inverse uncertainty quantification in model calibration, parameter estimation, and ensemble forecasting. GenAI4UQ leverages a generative AI-based conditional modeling framework to address limitations of traditional inverse modeling techniques, such as Markov Chain Monte Carlo (MCMC) methods. By replacing computationally intensive iterative processes with a direct, learned mapping, GenAI4UQ enables efficient calibration of input parameters and generation of predictions directly from observations. The software supports rapid ensemble forecasting with robust uncertainty quantification while maintaining computational and storage efficiency. Built-in auto-tuning of hyperparameters simplifies model training, ensuring accessibility for users with varying expertise. Its versatile conditional generative framework is applicable across diverse scientific domains. While GenAI4UQ offers significant advantages in flexibility and efficiency, users should interpret its uncertainty estimates with caution in data-sparse scenarios, as the model may overestimate uncertainty—an effect common to all surrogate-based approaches including MCMC with surrogate models. Despite this, GenAI4UQ transforms inverse modeling by providing a fast, reliable, and user-friendly solution. It empowers researchers and practitioners to quickly estimate parameter distributions and generate model predictions for new observations, facilitating efficient decision-making and advancing the state of uncertainty quantification in computational modeling.

97 MATHEMATICS AND COMPUTING↗

An Automated Method for Identifying Inconsistencies within Diagrammatic Software Requirements Specifications

The development of large-scale, composite software in a geographically distributed environment is an evolutionary process. Often, in such evolving systems, striving for consistency is complicated by many factors, because development participants have various locations, skills, responsibilities, roles, opinions, languages, terminology and different degrees of abstraction they employ. This naturally leads to many partial specifications or viewpoints. These multiple views on the system being developed usually overlap. From another aspect, these multiple views give rise to the potential for inconsistency. Existing CASE tools do not efficiently manage inconsistencies in distributed development environment for a large-scale project. Based on the ViewPoints framework the WHERE (Web-Based Hypertext Environment for requirements Evolution) toolkit aims to tackle inconsistency management issues within geographically distributed software development projects. Consequently, WHERE project helps make more robust software and support software assurance process. The long term goal of WHERE tools aims to the inconsistency analysis and management in requirements specifications. A framework based on Graph Grammar theory and TCMJAVA toolkit is proposed to detect inconsistencies among viewpoints. This systematic approach uses three basic operations (UNION, DIFFERENCE, INTERSECTION) to study the static behaviors of graphic and tabular notations. From these operations, subgraphs Query, Selection, Merge, Replacement operations can be derived. This approach uses graph PRODUCTIONS (rewriting rules) to study the dynamic transformations of graphs. We discuss the feasibility of implementation these operations. Also, We present the process of porting original TCM (Toolkit for Conceptual Modeling) project from C++ to Java programming language in this thesis. A scenario based on NASA International Space Station Specification is discussed to show the applicability of our approach. Finally, conclusion and future work about inconsistency management issues in WHERE project will be summarized.

Zhang, Zhong↗

Kinetic Monte Carlo Simulations of Chemical Reactions on Surfaces

Lattice based kinetic Monte Carlo (kMC) simulations are a powerful tool for micro-kinetic modeling. The kinetic Monte Carlo technique stochastically simulates chemical reaction processes (e.g. adsorption, desorption, diffusion), where the probability of a given reaction process being selected is weighted by its rate constant. The open source software package, KMOS1, allows fast construction of kMC simulations by automatically implementing a computationally efficient kMC framework, thus allowing the researcher to focus on accurate parameterization and formulation of the kinetic model. From this, the spatiotemporal evolution (e.g. concentration, surface configuration, turnover frequencies) of crystal surfaces or bulk crystalline structures is obtained. KMOS uses the variable step-size method implementation of kMC. At each step, the VSSM updates available events, calculates the corresponding transition rates and simulation time, and selects one of the available events. The lattice based kMC technique has many potential applications within SRNL where chemical kinetics are of interest. By transitioning through time along a trajectory of configuration space, fundamental insights to a system's dominant reactions and parameters can be gained, leading to improved materials and process design. In this work, we have established capabilities for fast implementation of kMC simulations through the installation and testing of the KMOS software on SRNL high performance computing resources. The parameterization of kMC simulations is often performed from first-principles energetic calculations. For the purposes of this work, the test cases use arbitrary species and thus, have arbitrary parameterization. In order to demonstrate the use of KMOS, two primary test cases are shown. Case 1 involves simple adsorption and desorption. Case 2 involves a slightly more complex mechanism. The evolution of the surface concentration and the final surface configuration for simulation Case 2 is shown. Rate-limiting processes and rate-limiting configurations are not always known or understood, but kMC provides information pertaining to both. The capability to implement efficient micro-kinetic models using the kinetic Monte Carlo technique has been established through the testing and installation of KMOS on SRNL HPC resources.

97 MATHEMATICS AND COMPUTING↗

VIPER: Volatiles Investigating Polar Exploration Rover

We will review the technical components of the NASA lunar rover mission, VIPER, with a focus on software components that rely on ROS 2 and Gazebo. We’ll start with an overview of the hardware and software components. Next, we’ll explore some of the custom Gazebo plugins for simulating the rover and the lunar surface. We’ll describe a fault injection framework that was built on ROS 2 parameters and how it is used to simulate hardware faults. Finally, we’ll see how ROS 2 is used as part of the rover ground software.

Jacob Michael Perron↗

Low SWaP Onboard Satellite Navigation, Guidance, and Control Technology

Onboard autonomy is a necessity for responsive space operations. Autonomous navigation, guidance, and control (NGC) enables space missions to reduce their dependence on high demand ground assets and costly ground personnel. It also allows for in-situ decision making and higher return on mission data. A flight software and hardware system providing this capability, called “autoNGC,” is currently being developed at NASA Goddard Space Flight Center for infusion into multiple future missions. The first build of autoNGC, providing autonomous navigation for lunar orbiting spacecraft, is targeted for completion by Fall 2024. It provides sensor fusion of multiple measurement types including pseudo-range from a weak signal Global Navigation Satellite Service (GNSS) receiver, 1-way and 2-way direct to Earth (DTE) range and Doppler, bearing and range from optical camera sensed images, and an accelerometer. AutoNGC is also being targeted for future missions that involve small body proximity operations, Sun Earth Libration point orbits, and distributed systems missions (DSMs) including those at outer planets. AutoNGC flight software is being built upon the plug-and-play architecture of the core Flight System (cFS) [Ref. 1]. Figure (Slide 7) shows the message-based software bus layout of various software applications (“apps”) consisting of the standard cFS apps and autoNGC interface apps and libraries. Accurate onboard navigation and timing is obtained through the Goddard Enhanced Onboard Navigation System (GEONS) software library [Ref. 2], which fuses different measurement types through an extended Kalman filter (EKF) framework. Optical measurements that are ingested in GEONS are provided by the cFS Goddard Image Analysis and Navigation Tool (cGIANT) app [Ref. 3]. This app processes optical images to extract the bearing angles of the centroid of the imaged body (near or far), the range to the imaged body, and/or of the features on the surface of a body to perform terrain relative navigation (TRN). Measurement of range to the body’s center of mass can also be derived from the detection of the limb. The first build of autoNGC for a lunar orbiting spacecraft is a minimal size, weight, and power (SWaP) hardware design allowing for inclusion into CubeSats and SmallSat-size class buses. Advancements in miniaturized space processors, such as the SpaceCube 3.0 Mini and the SpaceCube Mini-Z [Ref. 4] are utilized for low SWaP while maintaining a high level of performance. Figure (Slide 11) shows the composition of the first autoNGC build. The current enclosure design has dimensions 12 cm x 17 cm x 13.5 cm. The box mass is expected to be less than 2 kg, and the nominal power is 21 W. The hardware interfaces are designed for flexibility with a variety of sensor inputs. The achievable navigation performance depends on the sensors utilized, including the onboard clock for 1-way pseudo-range measurements. Analysis using a configuration that consists of weak signal GPS, TRN, and 1-way DTE has shown position and velocity accuracies of 10 meters and 2 cm/s (3-σ ) RSS, respectively, with onboard time knowledge estimated to better than 13 ns (3-σ ), for a spacecraft in a representative 12-hour eccentric lunar orbit. Other measurement types such as x-rays from known pulsars (called XNAV) and cross-links can also be processed in GEONS. With the plug-and-play architecture of autoNGC, cFS apps can easily be added and replaced, even after launch. Goddard is actively seeking partners to collaborate in the development of additional capabilities for autoNGC, including industry, academia, and others across the US Government. Plans are being formulated to make the autoNGC software platform available for use by any US government organization to leverage the non-recurring engineering associated with the development of onboard autonomous NGC 3 capabilities. As advancements in space qualified sensors, microprocessors, and algorithms are made, the autoNGC platform provides a ready starting point for inclusion of these technologies.

C. J. Gramling↗

Extension of mutation testing for the requirements and design faults - 322

Mutation Testing is a fault-based software testing technique that is considered to be the most efficient in detecting faults. It focuses on the software code level and follows a set of rules which are called mutation operators to systematically seed faults into the source code. Each seeded fault results is a new version of the software, which is called a mutant. Mutation testing promises to be effective in identifying adequate test data which can be used to find faults in the source code. However, traditional mutation testing is not geared towards the detection of requirements and design faults. To cover the full spectrum of possible faults, the mutation framework has been extended from the code level to the requirements and design level. Twenty-nine defects that appear in requirements and design documents were identified to define appropriate mutants. Then corresponding mutation operators that model the defects were developed. For each mutation operator, the strategy to generate a mutant and the evaluation of the number of possible mutants were defined. Existing code level cost reduction techniques were tailored for requirements and design mutation operators that result in a large number of mutants. With the extended mutation testing framework, the full spectrum of possible faults will be tested and identified to ensure the safety and functionality of the software. (authors)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Engineering Overview of a Multidisciplinary HSCT Design Framework Using Medium-Fidelity Analysis Codes

An objective of the HPCC Program at NASA Langley has been to promote the use of advanced computing techniques to more rapidly solve the problem of multidisciplinary optimization of a supersonic transport configuration. As a result, a software system has been designed and is being implemented to integrate a set of existing discipline analysis codes, some of them CPU-intensive, into a distributed computational framework for the design of a High Speed Civil Transport (HSCT) configuration. The proposed paper will describe the engineering aspects of integrating these analysis codes and additional interface codes into an automated design system. The objective of the design problem is to optimize the aircraft weight for given mission conditions, range, and payload requirements, subject to aerodynamic, structural, and performance constraints. The design variables include both thicknesses of structural elements and geometric parameters that define the external aircraft shape. An optimization model has been adopted that uses the multidisciplinary analysis results and the derivatives of the solution with respect to the design variables to formulate a linearized model that provides input to the CONMIN optimization code, which outputs new values for the design variables. The analysis process begins by deriving the updated geometries and grids from the baseline geometries and grids using the new values for the design variables. This free-form deformation approach provides internal FEM (finite element method) grids that are consistent with aerodynamic surface grids. The next step involves using the derived FEM and section properties in a weights process to calculate detailed weights and the center of gravity location for specified flight conditions. The weights process computes the as-built weight, weight distribution, and weight sensitivities for given aircraft configurations at various mass cases. Currently, two mass cases are considered: cruise and gross take-off weight (GTOW). Weights information is obtained from correlations of data from three sources: 1) as-built initial structural and non-structural weights from an existing database, 2) theoretical FEM structural weights and sensitivities from Genesis, and 3) empirical as-built weight increments, non-structural weights, and weight sensitivities from FLOPS. For the aeroelastic analysis, a variable-fidelity aerodynamic analysis has been adopted. This approach uses infrequent CPU-intensive non-linear CFD to calculate a non-linear correction relative to a linear aero calculation for the same aerodynamic surface at an angle of attack that results in the same configuration lift. For efficiency, this nonlinear correction is applied after each subsequent linear aero solution during the iterations between the aerodynamic and structural analyses. Convergence is achieved when the vehicle shape being used for the aerodynamic calculations is consistent with the structural deformations caused by the aerodynamic loads. To make the structural analyses more efficient, a linearized structural deformation model has been adopted, in which a single stiffness matrix can be used to solve for the deformations under all the load conditions. Using the converged aerodynamic loads, a final set of structural analyses are performed to determine the stress distributions and the buckling conditions for constraint calculation. Performance constraints are obtained by running FLOPS using drag polars that are computed using results from non-linear corrections to the linear aero code plus several codes to provide drag increments due to skin friction, wave drag, and other miscellaneous drag contributions. The status of the integration effort will be presented in the proposed paper, and results will be provided that illustrate the degree of accuracy in the linearizations that have been employed.

Weston, R. P.↗

Mathematical framework for the analysis of dynamic stochastic systems with the RAVEN code

RAVEN (Reactor Analysis and Virtual control Environment) is a software code under development at Idaho National Laboratory aimed at performing probabilistic risk assessment and uncertainty quantification using RELAP-7, for which it acts also as a simulation controller. In this paper we will present the equations characterizing a dynamic stochastic system and we will then discuss the behavior of each stochastic term and how it is accounted for in the RAVEN software design. Moreover we will present preliminary results of the implementation. (authors)

97 MATHEMATICS AND COMPUTING↗

Data Analysis with Graphical Models: Software Tools

Probabilistic graphical models (directed and undirected Markov fields, and combined in chain graphs) are used widely in expert systems, image processing and other areas as a framework for representing and reasoning with probabilities. They come with corresponding algorithms for performing probabilistic inference. This paper discusses an extension to these models by Spiegelhalter and Gilks, plates, used to graphically model the notion of a sample. This offers a graphical specification language for representing data analysis problems. When combined with general methods for statistical inference, this also offers a unifying framework for prototyping and/or generating data analysis algorithms from graphical specifications. This paper outlines the framework and then presents some basic tools for the task: a graphical version of the Pitman-Koopman Theorem for the exponential family, problem decomposition, and the calculation of exact Bayes factors. Other tools already developed, such as automatic differentiation, Gibbs sampling, and use of the EM algorithm, make this a broad basis for the generation of data analysis software.

Buntine, Wray L.↗