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DOE OSTI2023

Modified Eigen-Decomposition-based Interval Analysis (MEDIA) for Power System Dynamic State Estimation

The Bayesian approach has been used for the dynamic state estimation (DSE) of a power system. However, due to the complexity of noise resources, it is difficult to quantify measurement and process noise using probability density functions (PDFs). To overcome the difficulty, the authors of this paper propose a modified eigen-decomposition-based interval analysis (MEDIA) method, which employs bounds instead of PDFs to quantify the noise, and uses the eigen decomposition method to reduce the negative impact of the overestimation problem. Using the simulation data generated from IEEE 16-machine and IEEE 10-machine systems, it is shown that the proposed MEDIA method can estimate the hard boundaries of dynamic states in real time. Furthermore, comparison with the forward-backward propagation method and the extended set-membership filter also shows that the proposed MEDIA method performs better by providing narrower boundaries in the DSE.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Securing Grid-interactive Efficient Buildings (GEB) through Cyber Defense and Resilient System (CYDRES)

The DOE CYDRES project is driven by the urgent need to address critical research gaps in the domain of cyber-physical security of smart buildings, including Grid-interactive Efficient Buildings (GEBs). CYDRES, a real-time advanced building resilient platform, aims to enhance the cyber-attack-immune capabilities of buildings through multi-layered prevention, detection, and adaptation mechanisms. CYDRES consists of five key modules: a multi-layer network analyzer, an Automatic Fault Detection, Diagnosis, and Prognosis (AFDDP) framework, an intelligent mode selector, a cyber-resilient control framework, and a situation awareness platform. The Network Analyzer employs a data-driven framework that includes a protocol state learning tool and a CRF (Conditional Random Field) command validator. In Hardware-In-the-Loop (HIL) testbeds, it achieved 100% detection accuracy with a false alarm rate of 3%, validating its efficacy in identifying selected cyber-attacks. The AFDDP framework leverages pattern matching, PCA (Principal Component Analysis)-based strategies, and a DBN (Dynamic Bayesian Network)-based fault diagnosis approach to pinpoint the causes of physical system abnormalities using Building Automation System (BAS) data. In HIL experiments, the AFDDP module attained a detection accuracy of over 95% with a false alarm rate below 7%. Additionally, the fault detector utilized machine learning (Random Forest) and deep learning (Multi-Layer Perceptron) methods with acoustic sensor data to achieve a 100% fault detection accuracy in Heating, Ventilation, and Air-Conditioning (HVAC) equipment. The Mode Selector offered real-time impact analysis, allowing immediate actions to protect BASs in the face of emerging threats. The cyber-resilient control framework included an adaptive Model Predictive Control (MPC) and a measurement compensator, reducing temperature violations by up to 94% and improving the total demand flexibility by up to 70% in HIL experiments. Such HIL experiments covered a cyber-attack case and a physical fault case, showcasing CYDRES’ efficiency in maintaining operational continuity during threats. The situation awareness platform in Grafana enhanced real-time threat detection and response visualization, augmenting the operational awareness for building operators. CYDRES demonstrated high technical effectiveness in various test scenarios, particularly in HIL environments. The project's phased development approach ensured efficient use of resources, highlighting its practical feasibility and readiness for commercialization. By enhancing the security and resilience of building operations, CYDRES represents a significant advance in mitigating risks associated with cyber-physical systems, thereby enhancing public confidence in the safety of modern building infrastructure. Future directions for the project include expanding testing protocols, refining AFDDP methodologies, exploring more comprehensive resilient control strategies, and testing in real commercial buildings.

42 ENGINEERING↗
DOE OSTI2023

Bayesian optimization with active learning of design constraints using an entropy-based approach

Abstract The design of alloys for use in gas turbine engine blades is a complex task that involves balancing multiple objectives and constraints. Candidate alloys must be ductile at room temperature and retain their yield strength at high temperatures, as well as possess low density, high thermal conductivity, narrow solidification range, high solidus temperature, and a small linear thermal expansion coefficient. Traditional Integrated Computational Materials Engineering (ICME) methods are not sufficient for exploring combinatorially-vast alloy design spaces, optimizing for multiple objectives, nor ensuring that multiple constraints are met. In this work, we propose an approach for solving a constrained multi-objective materials design problem over a large composition space, specifically focusing on the Mo-Nb-Ti-V-W system as a representative Multi-Principal Element Alloy (MPEA) for potential use in next-generation gas turbine blades. Our approach is able to learn and adapt to unknown constraints in the design space, making decisions about the best course of action at each stage of the process. As a result, we identify 21 Pareto-optimal alloys that satisfy all constraints. Our proposed framework is significantly more efficient and faster than a brute force approach.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Bayes_Opt-SWMM: A Gaussian process-based Bayesian optimization tool for real-time flood modeling with SWMM

Real-time flood model plays a pivotal role in averting urban flood damage, particularly when there is minimal lead time for preparatory measures. However, urban flood modeling in real-time often contends with inherent uncertainties arising from input data uncertainty and parameter ambiguities. Here this study introduces a real-time calibration (RTC) tool called Bayes_Opt-SWMM, specifically tailored for real-time urban flood modeling and uncertainty optimization. This tool leverages the Gaussian process-based Bayesian optimization algorithm and interfaces seamlessly with the Stormwater Management Model (SWMM). It integrates real-time model forcing data and flood monitoring collected through sensors and gauges which are strategically placed within critical locations of urban drainage systems. Our approach hinges on the Surrogate Model based Uncertainty Optimization (SMUO) concept, providing an avenue for enhancing real-time flood modeling. Bayes_Opt-SWMM runs the optimization process using a surrogate model called Gaussian Process emulator with two inference methods: (1) the Gaussian Process (GP) model and (2) Markov Chain Monte Carlo (MCMC) algorithm in GP model (GP_MCMC). Furthermore, three acquisition functions, namely Expected Improvement (EI), Maximum Probability of Improvement (MPI), and Lower Confidence Bound (LCB), facilitate optimal parameter fitting within the surrogate models. The efficiency of GP-based surrogate models in learning SWMM model parameters, leads to an improved uncertainty quantification and accelerated real-time flood modeling in urban areas. Overall, Bayes_Opt-SWMM emerges as a cost-effective and valuable tool for real-time flood modeling and monitoring, with significant potential for managing intelligent storm water systems in urban environments.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

MultiPEM Toolbox: User Manual [Rev. 2]

This document explains use of the Multi-Phenomenology Explosion Monitoring (Multi PEM) Toolbox, a collection of R scripts for estimating the unknown device parameters of a new event with uncertainty quantification. The methodology and application used for illustration in this user manual are fully documented in a Los Alamos National Laboratory technical report hereafter designated “WPA” for reference. Additional details on the application are found in a recent journal article. Two assessment types are available: rapid and complete. Rapid assessments are conducted in two stages, as described in Section 2. In the first stage, calibration data are used to estimate forward and error model parameters (WPA, §5.1) and (if relevant) errors-in-variables yield values for calibration sources (WPA, §3, Equation (3)). In the second stage, new event data are used to estimate the unknown new event device parameters (WPA, §5.2) with uncertainty quantification. Two options for treating the inferred first stage parameters in second stage Bayesian analysis are available: fixing them at their maximum likelihood estimate (default), or multiple imputation. Multiple imputation involves utilizing several posterior samples (imputations) of the first stage parameters as fixed values in the second stage posterior sampling of the new event device parameters. Second stage sampling is conducted across imputations in parallel to improve computational efficiency. This method produces improved uncertainty quantification of the new event device parameters compared with the default treatment of the first stage parameters, at the expense of additional computation. Complete assessments are conducted in a single stage, as described in Section 3. Calibration and (if relevant) new event data are used simultaneously to estimate all forward model, error model, and (if relevant) new event device parameters with uncertainty quantification on the latter. As the name suggests, rapid assessments generally run substantially faster than complete assessments (even with multiple imputation), because the results of first stage analysis can be stored and incorporated into estimating a relatively low-dimensional space of new event device parameters whenever relevant new event data becomes available. On the other hand, complete assessments must be run on the full set of model and device parameters with calibration and new event data every time the latter becomes available.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2020

A Second Look at 12 Candidate Dual AGNs Using BAYMAX

We present an analysis of 12 optically selected dual active galactic nucleus (AGN) candidates at z < 0.34. Each candidate was originally identified via double-peaked [O III] λ5007 emission lines and received follow-up Chandra and Hubble Space Telescope (HST) observations. Because the X-ray data are low-count (<100 counts) with small separations (<1''), a robust analysis is necessary for classifying each source. Pairing long-slit [O III] observations with existing Chandra observations, we re-analyze the X-ray observations with Bayesian AnalYsis of AGNs in X-rays to determine whether the X-ray emission from each system is more likely a single or dual point source. We find that 4 of the 12 sources are likely dual X-ray point-source systems. We examine each point source's spectra via a Monte Carlo method that probabilistically identifies the likely origin of each photon. When doing so, we find that (i) the secondary X-ray point sources in two of the systems have L(X)< 10(exp 40) erg/s, such that we cannot rule out a non-AGN origin, (ii) one source has a secondary with L(X)> 10(exp 40) erg/s but a spectrum that is too soft to definitively preclude being X-ray emitting diffuse gas that was photoionized by the primary AGN, and (iii) one system (SDSS J1126+2944) is a dual AGN. Additionally, using complementary HST observations, we analyze a subsample of systems that are visually identified as merging. Our results suggest that dual AGNs may preferentially reside in mergers with small separations, consistent with both simulations and observations.

Adi Foord↗
DOE OSTI2024

Targeted materials discovery using Bayesian algorithm execution

Rapid discovery and synthesis of future materials requires intelligent data acquisition strategies to navigate large design spaces. A popular strategy is Bayesian optimization, which aims to find candidates that maximize material properties; however, materials design often requires finding specific subsets of the design space which meet more complex or specialized goals. We present a framework that captures experimental goals through straightforward user-defined filtering algorithms. These algorithms are automatically translated into one of three intelligent, parameter-free, sequential data collection strategies (SwitchBAX, InfoBAX, and MeanBAX), bypassing the time-consuming and difficult process of task-specific acquisition function design. Our framework is tailored for typical discrete search spaces involving multiple measured physical properties and short time-horizon decision making. We demonstrate this approach on datasets for TiO 2 nanoparticle synthesis and magnetic materials characterization, and show that our methods are significantly more efficient than state-of-the-art approaches. Overall, our framework provides a practical solution for navigating the complexities of materials design, and helps lay groundwork for the accelerated development of advanced materials.

42 ENGINEERING↗
DOE OSTI2025

Explainable multi-fidelity Bayesian neural network for distribution system state estimation

Distribution System State Estimation (DSSE) is frequently constrained by limited real-time measurements, the uncertainties introduced by distributed energy resources, and the presence of bad data. To address them, this paper proposes an enhanced Multi-Fidelity Bayesian Neural Network (MFBNN) DSSE approach. A low-fidelity layer based on a Deep Neural Network (DNN) is first pre-trained on pseudo-measurement data to learn fundamental state features. Subsequently, a high-fidelity Bayesian Neural Network (BNN) layer leverages limited but high-quality real-time measurements to refine these features, thereby achieving accurate DSSE. Additionally, the deep SHapley Additive exPlanation (SHAP) is developed to quantify the influence of measurement data on DSSE through dual perspectives of global feature importance and local nodal contributions, establishing a hierarchical explainability framework for machine learning-based DSSE. Comparative studies conducted on the IEEE 13-bus system and a real-world 2135-node system from Dominion Energy demonstrate that the proposed method excels in estimation accuracy, even under situations of high noise levels, bad data, and missing data. Further comparisons with Weighted Least Squares (WLS) and other machine learning-based DSSE approaches verify that the proposed framework offers higher accuracy, improved interpretability, and enhanced robustness.

Bad data↗
DOE OSTI2026

A score-based diffusion model approach for adaptive learning of stochastic partial differential equation solutions

In this paper, we propose a novel framework for adaptively learning the time-evolving solutions of stochastic partial differential equations (SPDEs) using score-based diffusion models within a recursive Bayesian inference setting. SPDEs play a central role in modeling complex physical systems under uncertainty, but their numerical solutions often suffer from model errors and reduced accuracy due to incomplete physical knowledge and environmental variability. To address these challenges, we encode the governing physics into the score function of a diffusion model using simulation data and incorporate observational information via a likelihood-based correction in a reverse-time stochastic differential equation. This enables adaptive learning through iterative refinement of the solution as new data becomes available. To improve computational efficiency in high-dimensional settings, we introduce the ensemble score filter, a training-free approximation of the score function designed for real-time inference. Numerical experiments on benchmark SPDEs demonstrate the accuracy and robustness of the proposed method under sparse and noisy observations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Applying Bayesian inference and deterministic anisotropy to retrieve the molecular structure ∣Ψ(R)∣2 distribution from gas-phase diffraction experiments

Abstract Currently, our general approach to retrieving molecular structures from ultrafast gas-phase diffraction heavily relies on complex ab initio electronic or vibrational excited state simulations to make conclusive interpretations. Without such simulations, inverting this measurement for the structural probability distribution is typically intractable. This creates a so-called inverse problem. Here we address this inverse problem by developing a broadly applicable method that approximates the molecular frame structure ∣Ψ( R , t )∣ 2 distribution independent of these complex simulations. We retrieve the vibronic ground state ∣Ψ( R )∣ 2 for both simulated stretched NO 2 and measured N 2 O. From measured N 2 O, we observe 40 mÅ coordinate-space resolution from 3.75 Å −1 reciprocal space range and poor signal-to-noise, a 50X improvement over traditional Fourier transform methods. In simulated NO 2 diffraction experiments, typical to high signal-to-noise levels predict 100–1000X resolution improvements, down to 0.1 mÅ. By directly measuring the width of ∣Ψ( R )∣ 2 , we open ultrafast gas-phase diffraction capabilities to measurements beyond current analysis approaches. This method has the potential to effectively turn gas-phase ultrafast diffraction into a discovery-oriented technique to probe systems that are prohibitively difficult to simulate.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Identifying microbial drivers in biological phenotypes with a Bayesian network regression model

Abstract In Bayesian Network Regression models, networks are considered the predictors of continuous responses. These models have been successfully used in brain research to identify regions in the brain that are associated with specific human traits, yet their potential to elucidate microbial drivers in biological phenotypes for microbiome research remains unknown. In particular, microbial networks are challenging due to their high dimension and high sparsity compared to brain networks. Furthermore, unlike in brain connectome research, in microbiome research, it is usually expected that the presence of microbes has an effect on the response (main effects), not just the interactions. Here, we develop the first thorough investigation of whether Bayesian Network Regression models are suitable for microbial datasets on a variety of synthetic and real data under diverse biological scenarios. We test whether the Bayesian Network Regression model that accounts only for interaction effects (edges in the network) is able to identify key drivers (microbes) in phenotypic variability. We show that this model is indeed able to identify influential nodes and edges in the microbial networks that drive changes in the phenotype for most biological settings, but we also identify scenarios where this method performs poorly which allows us to provide practical advice for domain scientists aiming to apply these tools to their datasets. BNR models provide a framework for microbiome researchers to identify connections between microbes and measured phenotypes. We allow the use of this statistical model by providing an easy‐to‐use implementation which is publicly available Julia package at https://github.com/solislemuslab/BayesianNetworkRegression.jl .

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Decision-Making Under Uncertainty for a Digital Thread-Enabled Design Process

Abstract Digital thread is a data-driven architecture that links together information from all stages of the product lifecycle. Despite increasing application in manufacturing, maintenance/operations, and design related tasks, a principled formulation of analyzing the decision-making problem under uncertainty for the digital thread remains absent. The contribution of this article is to present a formulation using Bayesian statistics and decision theory. First, we address how uncertainty propagates in the product lifecycle and how the digital thread evolves based on the decisions we make and the data we collect. By using these mechanics, we explore designing over multiple product generations or iterations and provide an algorithm to solve the underlying multistage decision problem. We illustrate our method on an example structural design problem where our method can quantify and optimize different types and sequences of decisions, ranging from experimentation, manufacturing, and sensor placement/selection, to minimize total accrued costs.

Engineering↗
DOE OSTI2022

Development of an open-source regional data assimilation system in PEcAn v. 1.7.2: application to carbon cycle reanalysis across the contiguous US using SIPNET

Abstract. The ability to monitor, understand, and predict the dynamics of the terrestrial carbon cycle requires the capacity to robustly and coherently synthesize multiple streams of information that each provide partial information about different pools and fluxes. In this study, we introduce a new terrestrial carbon cycle data assimilation system, built on the PEcAn model–data eco-informatics system, and its application for the development of a proof-of-concept carbon “reanalysis” product that harmonizes carbon pools (leaf, wood, soil) and fluxes (GPP, Ra, Rh, NEE) across the contiguous United States from 1986–2019. We first calibrated this system against plant trait and flux tower net ecosystem exchange (NEE) using a novel emulated hierarchical Bayesian approach. Next, we extended the Tobit–Wishart ensemble filter (TWEnF) state data assimilation (SDA) framework, a generalization of the common ensemble Kalman filter which accounts for censored data and provides a fully Bayesian estimate of model process error, to a regional-scale system with a calibrated localization. Combined with additional workflows for propagating parameter, initial condition, and driver uncertainty, this represents the most complete and robust uncertainty accounting available for terrestrial carbon models. Our initial reanalysis was run on an irregular grid of ∼ 500 points selected using a stratified sampling method to efficiently capture environmental heterogeneity. Remotely sensed observations of aboveground biomass (Landsat LandTrendr) and leaf area index (LAI) (MODIS MOD15) were sequentially assimilated into the SIPNET model. Reanalysis soil carbon, which was indirectly constrained based on modeled covariances, showed general agreement with SoilGrids, an independent soil carbon data product. Reanalysis NEE, which was constrained based on posterior ensemble weights, also showed good agreement with eddy flux tower NEE and reduced root mean square error (RMSE) compared to the calibrated forecast. Ultimately, PEcAn's new open-source regional data assimilation framework provides a scalable workflow for harmonizing multiple data constraints and providing a uniform synthetic platform for carbon monitoring, reporting, and verification (MRV) as well as accelerating terrestrial carbon cycle research.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2008

Sensor Selection and Data Validation for Reliable Integrated System Health Management

For new access to space systems with challenging mission requirements, effective implementation of integrated system health management (ISHM) must be available early in the program to support the design of systems that are safe, reliable, highly autonomous. Early ISHM availability is also needed to promote design for affordable operations; increased knowledge of functional health provided by ISHM supports construction of more efficient operations infrastructure. Lack of early ISHM inclusion in the system design process could result in retrofitting health management systems to augment and expand operational and safety requirements; thereby increasing program cost and risk due to increased instrumentation and computational complexity. Having the right sensors generating the required data to perform condition assessment, such as fault detection and isolation, with a high degree of confidence is critical to reliable operation of ISHM. Also, the data being generated by the sensors needs to be qualified to ensure that the assessments made by the ISHM is not based on faulty data. NASA Glenn Research Center has been developing technologies for sensor selection and data validation as part of the FDDR (Fault Detection, Diagnosis, and Response) element of the Upper Stage project of the Ares 1 launch vehicle development. This presentation will provide an overview of the GRC approach to sensor selection and data quality validation and will present recent results from applications that are representative of the complexity of propulsion systems for access to space vehicles. A brief overview of the sensor selection and data quality validation approaches is provided below. The NASA GRC developed Systematic Sensor Selection Strategy (S4) is a model-based procedure for systematically and quantitatively selecting an optimal sensor suite to provide overall health assessment of a host system. S4 can be logically partitioned into three major subdivisions: the knowledge base, the down-select iteration, and the final selection analysis. The knowledge base required for productive use of S4 consists of system design information and heritage experience together with a focus on components with health implications. The sensor suite down-selection is an iterative process for identifying a group of sensors that provide good fault detection and isolation for targeted fault scenarios. In the final selection analysis, a statistical evaluation algorithm provides the final robustness test for each down-selected sensor suite. NASA GRC has developed an approach to sensor data qualification that applies empirical relationships, threshold detection techniques, and Bayesian belief theory to a network of sensors related by physics (i.e., analytical redundancy) in order to identify the failure of a given sensor within the network. This data quality validation approach extends the state-of-the-art, from red-lines and reasonableness checks that flag a sensor after it fails, to include analytical redundancy-based methods that can identify a sensor in the process of failing. The focus of this effort is on understanding the proper application of analytical redundancy-based data qualification methods for onboard use in monitoring Upper Stage sensors.

Garg, Sanjay↗
NASA NTRS2021

Systematic KMTNet Planetary Anomaly Search. I. OGLE-2019-BLG-1053Lb, a BuriedTerrestrial Planet

In order to exhume the buried signatures of “missing planetary caustics” in Korea Microlensing Telescope Network (KMTNet) data, we conducted a systematic anomaly search of the residuals from point-source point-lens fits, based on a modified version of the KMTNet Event Finder algorithm. This search revealed the lowest-mass-ratio planetary caustic to date in the microlensing event OGLE-2019-BLG-1053, for which the planetary signal had not been noticed before. The planetary system has a planet–host mass ratio ofq= (1.25±0.13) × 10−5. A Bayesian analysis yielded estimates of the mass of the host star, Mhost =-0.61+0.29 -0.24 Mo, the mass of its planet, Mplanet =-2.48 +1.19 -0.98 Mo, the projected planet – host separation, a^= 3.4 +0.5/-0.5 au, and the lens distance, DL =-6.8 +0.6 -0.90kpc.The discovery of this very-low-mass-ratio planet illustrates the utility of our method and opens a new window for a large and homogeneous sample to study the microlensing planet–host mass ratio function down to q∼ 10−5.

Exoplanet detection methods↗
DOE OSTI2022

Optimal Experimental Design for Inverse Problems in the Presence of Observation Correlations

Optimal experimental design (OED) is the general formalism of sensor placement and decisions on the data collection strategy for engineered or natural experiments. This problem is prevalent in many critical fields such as battery design, numerical weather prediction, geosciences, environmental and urban studies. State-of-the-art computational methods for experimental design do not accommodate correlation structure in observational errors produced by many expensive-to-operate devices such as X-ray machines, radars, and satellites. Discarding evident data correlations leads to biased results, higher expenses, and waste of valuable resources. We present a general formulation of the OED formalism for model-constrained large-scale Bayesian linear inverse problems, where measurement errors are generally correlated. The proposed approach utilizes the Hadamard product of matrices to formulate the weighted-likelihood, and is valid for both finite as well as infinite-dimensional Bayesian inverse problems. Extensive numerical experiments are carried out for empirical verification of the proposed approach using an advection-diffusion model, where the objective is to optimally place a small set of sensors, under a limited budget, to predict the concentration of a contaminant in a closed and bounded domain.

Correlated observations↗
NASA NTRS2005

Bayesian Inference in Satellite Gravity Inversion

To solve a geophysical inverse problem means applying measurements to determine the parameters of the selected model. The inverse problem is formulated as the Bayesian inference. The Gaussian probability density functions are applied in the Bayes's equation. The CHAMP satellite gravity data are determined at the altitude of 400 kilometer altitude over the South part of the Pannonian basin. The model of interpretation is the right vertical cylinder. The parameters of the model are obtained from the minimum problem solved by the Simplex method.

Kis, K. I.↗
NASA NTRS2005

Influence of Coronal Abundance Variations

The PI of this project was Jeff Scargle of NASA/Ames. Co-I's were Alma Connors of Eureka Scientific/Wellesley, and myself. Part of the work was subcontracted to Eureka Scientific via SAO, with Vinay Kashyap as PI. This project was originally assigned grant number NCC2-1206, and was later changed to NCC2-1350 for administrative reasons. The goal of the project was to obtain, derive, and develop statistical and data analysis tools that would be of use in the analyses of high-resolution, high-sensitivity data that are becoming available with new instruments. This is envisioned as a cross-disciplinary effort with a number of "collaborators" including some at SA0 (Aneta Siemiginowska, Peter Freeman) and at the Harvard Statistics department (David van Dyk, Rostislav Protassov, Xiao-li Meng, Epaminondas Sourlas, et al). We have developed a new tool to reliably measure the metallicities of thermal plasma. It is unfeasible to obtain high-resolution grating spectra for most stars, and one must make the best possible determination based on lower-resolution, CCD-type spectra. It has been noticed that most analyses of such spectra have resulted in measured metallicities that were significantly lower than when compared with analyses of high- resolution grating data where available (see, e.g., Brickhouse et al., 2000, ApJ 530,387). Such results have led to the proposal of the existence of so-called Metal Abundance Deficient, or "MAD" stars (e.g., Drake, J.J., 1996, Cool Stars 9, ASP Conf.Ser. 109, 203). We however find that much of these analyses may be systematically underestimating the metallicities, and using a newly developed method to correctly treat the low-counts regime at the high-energy tail of the stellar spectra (van Dyk et al. 2001, ApJ 548,224), have found that the metallicities of these stars are generally comparable to their photospheric values. The results were reported at the AAS (Sourlas, Yu, van Dyk, Kashyap, and Drake, 2000, BAAS 196, v32, #54.02), and at the conference on Statistical Challenges in Modem Astronomy (Sourlas, van Dyk, Kashyap, Drake, and Pease, 2003, SCMA 111, Eds. E.D.Feigelson, G.J.Babu, New York:Springer, p489-490). We also described the limitations of one of the most egregiously misused and misapplied statistical tests in astrophysical literature, the F-test for verifying model components (Protassov, van Dyk, Connors, Kashyap, and Siemiginowska, 2002, ApJ, 571,545). Indeed, a search through the ApJ archives turned up 170 papers in the 5 previous years that used the F-test explicitly in some form or the other, and with the vast majority of them not using it correctly! Indeed, looking at just 4 issues of the ApJ in 2001, we found 13 instances of its use, of which nine were demonstrably incorrect. Clearly, it is difficult to understate the importance of this issue. We also worked on speeding up Bayes Blocks and Sparse Bayes Blocks algorithms to make them more tractable for large searches. We also supported staistics students and postdocs in both explicit physics- model-based (spectra with tens of thousands of atomic lines) and "model-free" -- i.e. non-parametric or semi-parametric -- algorithms. Work on using more of the latter is just beginning; while using multi-scale methods for Poisson imaging has come to hition. In fact, "An Image Restoration Technique with Error Estimates", by D. Esch, A. Connors, M. Karovska, and D. van Dyk, was published by ApJ (Esch et a1.2004, ApJ, 610, 1213). The code has been delivered to M. Karovska for CXC; and is available for beta-testing upon request. The other large project we worked on was on the self-consistent modeling of logN-logs curves in the Poisson limit. logN-logs curves are a fundamental tool in the study of source populations, luminosity functions, and cosmological parameters. However, their determination is hampered by statistical effects such as the Eddington bias, incompleteness due to detection efficiency, faint source flux fluctuations, etc. We have develed a new and powerful method using the full Poisson machinery that allows us to model the logN-logs distribution of X-ray sources in a self-consistent manner. Because we properly account for all the above statistical effects, our modeling is valid over the full range of the data, and not just for strong sources, as is normally done. Using a Bayesian approach and modeling the fluxes with known functional forms such as simple or broken power-laws, and conditioning the expected photon counts on the fluxes, the background contamination, effective area, detector vignetting, and detection probability, we can delve deeply into the low counts regime and extend the usefulness of medium sensitivity surveys such as ChAMP by orders of magnitude. The built-in flexibility of the algorithm also allows a simultaneous analysis of multiple datasets. We have applied this analysis to a set a Chandra observations (Sourlas, Kashyap, Zezas, van Dyk, 2004, HEAD #8, #16.32)

Scargle, Jeffrey D.↗