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NASA NTRS2011

Tests of the Grobner Basis Solution for Lightning Ground Flash Fraction Retrieval

Satellite lightning imagers such as the NASA Tropical Rainfall Measuring Mission Lightning Imaging Sensor (TRMM/LIS) and the future GOES-R Geostationary Lightning Mapper (GLM) are designed to detect total lightning (ground flashes + cloud flashes). However, there is a desire to discriminate ground flashes from cloud flashes from the vantage point of space since this would enhance the overall information content of the satellite lightning data and likely improve its operational and scientific applications (e.g., in severe weather warning, lightning nitrogen oxides studies, and global electric circuit analyses). A Bayesian inversion method was previously introduced for retrieving the fraction of ground flashes in a set of flashes observed from a satellite lightning imager. The method employed a constrained mixed exponential distribution model to describe the lightning optical measurements. To obtain the optimum model parameters (one of which is the ground flash fraction), a scalar function was minimized by a numerical method. In order to improve this optimization, a Grobner basis solution was introduced to obtain analytic representations of the model parameters that serve as a refined initialization scheme to the numerical optimization. In this study, we test the efficacy of the Grobner basis initialization using actual lightning imager measurements and ground flash truth derived from the national lightning network.

Koshak, William↗
NASA NTRS2004

Putting Priors in Mixture Density Mercer Kernels

This paper presents a new methodology for automatic knowledge driven data mining based on the theory of Mercer Kernels, which are highly nonlinear symmetric positive definite mappings from the original image space to a very high, possibly infinite dimensional feature space. We describe a new method called Mixture Density Mercer Kernels to learn kernel function directly from data, rather than using predefined kernels. These data adaptive kernels can en- code prior knowledge in the kernel using a Bayesian formulation, thus allowing for physical information to be encoded in the model. We compare the results with existing algorithms on data from the Sloan Digital Sky Survey (SDSS). The code for these experiments has been generated with the AUTOBAYES tool, which automatically generates efficient and documented C/C++ code from abstract statistical model specifications. The core of the system is a schema library which contains template for learning and knowledge discovery algorithms like different versions of EM, or numeric optimization methods like conjugate gradient methods. The template instantiation is supported by symbolic- algebraic computations, which allows AUTOBAYES to find closed-form solutions and, where possible, to integrate them into the code. The results show that the Mixture Density Mercer-Kernel described here outperforms tree-based classification in distinguishing high-redshift galaxies from low- redshift galaxies by approximately 16% on test data, bagged trees by approximately 7%, and bagged trees built on a much larger sample of data by approximately 2%.

Srivastava, Ashok N.↗
NASA NTRS2012

Analysis of Fine-Mode Aerosol Retrieval Capabilities by Different Passive Remote Sensing Instrument Designs

Remote sensing of aerosol optical properties is difficult, but multi-angle, multi-spectral, polarimetric instruments have the potential to retrieve sufficient information about aerosols that they can be used to improve global climate models. However, the complexity of these instruments means that it is difficult to intuitively understand the relationship between instrument design and retrieval success. We apply a Bayesian statistical technique that relates instrument characteristics to the information contained in an observation. Using realistic simulations of fine size mode dominated spherical aerosols, we investigate three instrument designs. Two of these represent instruments currently in orbit: the Multiangle Imaging SpectroRadiometer (MISR) and the POLarization and Directionality of the Earths Reflectances (POLDER). The third is the Aerosol Polarimetry Sensor (APS), which failed to reach orbit during recent launch, but represents a viable design for future instruments. The results show fundamental differences between the three, and offer suggestions for future instrument design and the optimal retrieval strategy for current instruments. Generally, our results agree with previous validation efforts of POLDER and airborne prototypes of APS, but show that the MISR aerosol optical thickness uncertainty characterization is possibly underestimated.

Knobelspiesse, Kirk↗
NASA NTRS2020

KMT-2019-BLG-0842Lb: A Cold Planet below the Uranus/Sun Mass Ratio

We report the discovery of a cold planet with a very low planet/host mass ratio of q = (4.09 ± 0.27) × 10^−5, which is similar to the ratio of Uranus/Sun (q = 4.37 × 10^−5) in the solar system. The Bayesian estimates for the host mass, planet mass, system distance, and planet–host projected separation are M(host) = 0.76 ± 0.40Mꙩ, M(planet) = 10.3 ± 5.5Mꚛ, D(L) = 3.3 ± 1.3 kpc, and a(⊥) = 3.3 ± 1.4 au, respectively. The consistency of the color and brightness expected from the estimated lens mass and distance with those of the blend suggests the possibility that the most blended light comes from the planet host, and this hypothesis can be established if high-resolution images are taken during the next (2020) bulge season. We discuss the importance of conducting optimized photometry and aggressive follow-up observations for moderately or very high magnification events to maximize the detection rate of planets with very low mass ratios.

Youn Kil Jung↗
NASA NTRS2005

An Ensemble Approach to Building Mercer Kernels with Prior Information

This paper presents a new methodology for automatic knowledge driven data mining based on the theory of Mercer Kernels, which are highly nonlinear symmetric positive definite mappings from the original image space to a very high, possibly dimensional feature space. we describe a new method called Mixture Density Mercer Kernels to learn kernel function directly from data, rather than using pre-defined kernels. These data adaptive kernels can encode prior knowledge in the kernel using a Bayesian formulation, thus allowing for physical information to be encoded in the model. Specifically, we demonstrate the use of the algorithm in situations with extremely small samples of data. We compare the results with existing algorithms on data from the Sloan Digital Sky Survey (SDSS) and demonstrate the method's superior performance against standard methods. The code for these experiments has been generated with the AUTOBAYES tool, which automatically generates efficient and documented C/C++ code from abstract statistical model specifications. The core of the system is a schema library which contains templates for learning and knowledge discovery algorithms like different versions of EM, or numeric optimization methods like conjugate gradient methods. The template instantiation is supported by symbolic-algebraic computations, which allows AUTOBAYES to find closed-form solutions and, where possible, to integrate them into the code.

Srivastava, Ashok N.↗
NASA NTRS2025

Shock-Stationary Application of Pseudoshock Models During High-Amplitude Combustion-Driven Unsteadiness

The isolator pseudo-shock provides necessary compression within a dual-mode scramjet engine and buffers the engine system against unstart. Quasi-1D flux-conserved models are the state-of-the-art reduced-order model for optimization and online control of dual-mode scramjet engines. The stability and efficacy of this modeling approach is evaluated against data from a combustor-driven direct-connect experiment. The experiment exhibited strong combustor-driven unsteadiness that produced upstream propagating weak shocks into the isolator, interacting with the pseudo-shock. While this configuration resulted in unsteadiness that is atypical of standard operation, the experiment provided an opportunity to evaluate the modeling techniques in highly transient states. Such transients could occur during maneuvering or result from unexpected combustor events. A flexible quasi-1D formulation, the Fievet flux-conserved model is fit using Bayesian inference in the laboratory and shock-stationary reference frames. Model performance is analyzed using the Bayesian posteriors and model evaluations over the measured shock train speed range. It is concluded that to produce consistent isolator pressure profile estimates in this unsteady environment, the model must be implemented in a shock-stationary reference frame. Implementing this conclusion in model-based engine controllers may reduce needed unstart safety margins and increase maximum performance.

Bayesian↗
NASA NTRS1995

On the uncertainty in single molecule fluorescent lifetime and energy emission measurements

Time-correlated single photon counting has recently been combined with mode-locked picosecond pulsed excitation to measure the fluorescent lifetimes and energy emissions of single molecules in a flow stream. Maximum likelihood (ML) and least square methods agree and are optimal when the number of detected photons is large however, in single molecule fluorescence experiments the number of detected photons can be less than 20, 67% of those can be noise and the detection time is restricted to 10 nanoseconds. Under the assumption that the photon signal and background noise are two independent inhomogeneous poisson processes, we derive the exact joint arrival time probably density of the photons collected in a single counting experiment performed in the presence of background noise. The model obviates the need to bin experimental data for analysis, and makes it possible to analyze formally the effect of background noise on the photon detection experiment using both ML or Bayesian methods. For both methods we derive the joint and marginal probability densities of the fluorescent lifetime and fluorescent emission. the ML and Bayesian methods are compared in an analysis of simulated single molecule fluorescence experiments of Rhodamine 110 using different combinations of expected background nose and expected fluorescence emission. While both the ML or Bayesian procedures perform well for analyzing fluorescence emissions, the Bayesian methods provide more realistic measures of uncertainty in the fluorescent lifetimes. The Bayesian methods would be especially useful for measuring uncertainty in fluorescent lifetime estimates in current single molecule flow stream experiments where the expected fluorescence emission is low. Both the ML and Bayesian algorithms can be automated for applications in molecular biology.

Brown, Emery N.↗
NASA NTRS1996

On the Uncertainty in Single Molecule Fluorescent Lifetime and Energy Emission Measurements

Time-correlated single photon counting has recently been combined with mode-locked picosecond pulsed excitation to measure the fluorescent lifetimes and energy emissions of single molecules in a flow stream. Maximum likelihood (ML) and least squares methods agree and are optimal when the number of detected photons is large, however, in single molecule fluorescence experiments the number of detected photons can be less than 20, 67 percent of those can be noise, and the detection time is restricted to 10 nanoseconds. Under the assumption that the photon signal and background noise are two independent inhomogeneous Poisson processes, we derive the exact joint arrival time probability density of the photons collected in a single counting experiment performed in the presence of background noise. The model obviates the need to bin experimental data for analysis, and makes it possible to analyze formally the effect of background noise on the photon detection experiment using both ML or Bayesian methods. For both methods we derive the joint and marginal probability densities of the fluorescent lifetime and fluorescent emission. The ML and Bayesian methods are compared in an analysis of simulated single molecule fluorescence experiments of Rhodamine 110 using different combinations of expected background noise and expected fluorescence emission. While both the ML or Bayesian procedures perform well for analyzing fluorescence emissions, the Bayesian methods provide more realistic measures of uncertainty in the fluorescent lifetimes. The Bayesian methods would be especially useful for measuring uncertainty in fluorescent lifetime estimates in current single molecule flow stream experiments where the expected fluorescence emission is low. Both the ML and Bayesian algorithms can be automated for applications in molecular biology.

Brown, Emery N.↗
NASA NTRS2008

A Physical Model to Estimate Snowfall over Land using AMSU-B Observations

In this study, we present an improved physical model to retrieve snowfall rate over land using brightness temperature observations from the National Oceanic and Atmospheric Administration's (NOAA) Advanced Microwave Sounder Unit-B (AMSU-B) at 89 GHz, 150 GHz, 183.3 +/- 1 GHz, 183.3 +/- 3 GHz, and 183.3 +/- 7 GHz. The retrieval model is applied to the New England blizzard of March 5, 2001 which deposited about 75 cm of snow over much of Vermont, New Hampshire, and northern New York. In this improved physical model, prior retrieval assumptions about snowflake shape, particle size distributions, environmental conditions, and optimization methodology have been updated. Here, single scattering parameters for snow particles are calculated with the Discrete-Dipole Approximation (DDA) method instead of assuming spherical shapes. Five different snow particle models (hexagonal columns, hexagonal plates, and three different kinds of aggregates) are considered. Snow particle size distributions are assumed to vary with air temperature and to follow aircraft measurements described by previous studies. Brightness temperatures at AMSU-B frequencies for the New England blizzard are calculated using these DDA calculated single scattering parameters and particle size distributions. The vertical profiles of pressure, temperature, relative humidity and hydrometeors are provided by MM5 model simulations. These profiles are treated as the a priori data base in the Bayesian retrieval algorithm. In algorithm applications to the blizzard data, calculated brightness temperatures associated with selected database profiles agree with AMSU-B observations to within about +/- 5 K at all five frequencies. Retrieved snowfall rates compare favorably with the near-concurrent National Weather Service (NWS) radar reflectivity measurements. The relationships between the NWS radar measured reflectivities Z(sub e) and retrieved snowfall rate R for a given snow particle model are derived by a histogram matching technique. All of these Z(sub e)-R relationships fall in the range of previously established Z(sub e)-R relationships for snowfall. This suggests that the current physical model developed in this study can reliably estimate the snowfall rate over land using the AMSU-B measured brightness temperatures.

Kim, Min-Jeong↗
NASA NTRS2014

Reconstructing the Sky Location of Gravitational-Wave Detected Compact Binary Systems: Methodology for Testing and Comparison

The problem of reconstructing the sky position of compact binary coalescences detected via gravitational waves is a central one for future observations with the ground-based network of gravitational-wave laser interferometers, such as Advanced LIGO and Advanced Virgo. Different techniques for sky localization have been independently developed. They can be divided in two broad categories: fully coherent Bayesian techniques, which are high latency and aimed at in-depth studies of all the parameters of a source, including sky position, and "triangulation-based" techniques, which exploit the data products from the search stage of the analysis to provide an almost real-time approximation of the posterior probability density function of the sky location of a detection candidate. These techniques have previously been applied to data collected during the last science runs of gravitational-wave detectors operating in the so-called initial configuration. Here, we develop and analyze methods for assessing the self consistency of parameter estimation methods and carrying out fair comparisons between different algorithms, addressing issues of efficiency and optimality. These methods are general, and can be applied to parameter estimation problems other than sky localization. We apply these methods to two existing sky localization techniques representing the two above-mentioned categories, using a set of simulated inspiralonly signals from compact binary systems with a total mass of equal to or less than 20M solar mass and nonspinning components. We compare the relative advantages and costs of the two techniques and show that sky location uncertainties are on average a factor approx. equals 20 smaller for fully coherent techniques than for the specific variant of the triangulation-based technique used during the last science runs, at the expense of a factor approx. equals 1000 longer processing time.

technique used↗
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 NTRS2022

On the Effects of Cloud Water Content on Passive Microwave Snowfall Retrievals

The Bayesian passive microwave retrievals of snowfall often rely on mathematical matching of the observed vectors of brightness temperature with an a priori database of precipitation profiles and their corresponding brightness temperatures. Mathematical proximity does not necessarily lead to consistent retrievals due to limited information content of passive microwave observations. This paper defines imposter (genuine) vectors of brightness temperature as those that are mathematically close but physically inconsistent (consistent) and characterizes them through the Silhouette Coefficient (SC) analysis. The Neyman–Pearson (NP) hypothesis testing is used to separate the imposter and genuine brightness temperatures based on their associated values of cloud ice (IWP) and liquid water path (LWP), given by coincidences of CloudSat Profiling Radar (CPR) and the Global Precipitation Measurement (GPM) Microwave Imager (GMI). The study determines thresholds for IWP and LWP that allow optimal identification of imposter brightness temperatures of non-snowing and snowing clouds, which can mislead the passive microwave retrieval algorithms to falsely detect or miss the snowfall events. It is demonstrated that emission signal of supercooled liquid water in snowing clouds can lead to improved passive microwave retrieval of snowfall and conditioning the retrievals to the cloud IWP and LWP can result in marginal correction of the snowfall detection probability; however, reduce the probability of false alarm by 6%–8% over sea ice and open oceans.

Snowfall↗
NASA NTRS2004

Bayesian Vision for Shape Recovery

We present a new Bayesian vision technique that aims at recovering a shape from two or more noisy observations taken under similar lighting conditions. The shape is parametrized by a piecewise linear height field, textured by a piecewise linear irradiance field, and we assume Gaussian Markovian priors for both shape vertices and irradiance variables. The observation process. also known as rendering, is modeled by a non-affine projection (e.g. perspective projection) followed by a convolution with a piecewise linear point spread function. and contamination by additive Gaussian noise. We assume that the observation parameters are calibrated beforehand. The major novelty of the proposed method consists of marginalizing out the irradiances considered as nuisance parameters, which is achieved by Laplace approximations. This reduces the inference to minimizing an energy that only depends on the shape vertices, and therefore allows an efficient Iterated Conditional Mode (ICM) optimization scheme to be implemented. A Gaussian approximation of the posterior shape density is computed, thus providing estimates both the geometry and its uncertainty. We illustrate the effectiveness of the new method by shape reconstruction results in a 2D case. A 3D version is currently under development and aims at recovering a surface from multiple images, reconstructing the topography by marginalizing out both albedo and shading.

Jalobeanu, Andre↗
NASA NTRS2013

Downscaling Satellite Precipitation with Emphasis on Extremes: A Variational 1-Norm Regularization in the Derivative Domain

The increasing availability of precipitation observations from space, e.g., from the Tropical Rainfall Measuring Mission (TRMM) and the forthcoming Global Precipitation Measuring (GPM) Mission, has fueled renewed interest in developing frameworks for downscaling and multi-sensor data fusion that can handle large data sets in computationally efficient ways while optimally reproducing desired properties of the underlying rainfall fields. Of special interest is the reproduction of extreme precipitation intensities and gradients, as these are directly relevant to hazard prediction. In this paper, we present a new formalism for downscaling satellite precipitation observations, which explicitly allows for the preservation of some key geometrical and statistical properties of spatial precipitation. These include sharp intensity gradients (due to high-intensity regions embedded within lower-intensity areas), coherent spatial structures (due to regions of slowly varying rainfall),and thicker-than-Gaussian tails of precipitation gradients and intensities. Specifically, we pose the downscaling problem as a discrete inverse problem and solve it via a regularized variational approach (variational downscaling) where the regularization term is selected to impose the desired smoothness in the solution while allowing for some steep gradients(called 1-norm or total variation regularization). We demonstrate the duality between this geometrically inspired solution and its Bayesian statistical interpretation, which is equivalent to assuming a Laplace prior distribution for the precipitation intensities in the derivative (wavelet) space. When the observation operator is not known, we discuss the effect of its misspecification and explore a previously proposed dictionary-based sparse inverse downscaling methodology to indirectly learn the observation operator from a database of coincidental high- and low-resolution observations. The proposed method and ideas are illustrated in case studies featuring the downscaling of a hurricane precipitation field.

Hurricanes↗
NASA NTRS2012

The Ground Flash Fraction Retrieval Algorithm Employing Differential Evolution: Simulations and Applications

The ability to estimate the fraction of ground flashes in a set of flashes observed by a satellite lightning imager, such as the future GOES-R Geostationary Lightning Mapper (GLM), would likely improve operational and scientific applications (e.g., severe weather warnings, lightning nitrogen oxides studies, and global electric circuit analyses). A Bayesian inversion method, called the Ground Flash Fraction Retrieval Algorithm (GoFFRA), was recently developed for estimating the ground flash fraction. The method uses a constrained mixed exponential distribution model to describe a particular lightning optical measurement called the Maximum Group Area (MGA). To obtain the optimum model parameters (one of which is the desired ground flash fraction), a scalar function must be minimized. This minimization is difficult because of two problems: (1) Label Switching (LS), and (2) Parameter Identity Theft (PIT). The LS problem is well known in the literature on mixed exponential distributions, and the PIT problem was discovered in this study. Each problem occurs when one allows the numerical minimizer to freely roam through the parameter search space; this allows certain solution parameters to interchange roles which leads to fundamental ambiguities, and solution error. A major accomplishment of this study is that we have employed a state-of-the-art genetic-based global optimization algorithm called Differential Evolution (DE) that constrains the parameter search in such a way as to remove both the LS and PIT problems. To test the performance of the GoFFRA when DE is employed, we applied it to analyze simulated MGA datasets that we generated from known mixed exponential distributions. Moreover, we evaluated the GoFFRA/DE method by applying it to analyze actual MGAs derived from low-Earth orbiting lightning imaging sensor data; the actual MGA data were classified as either ground or cloud flash MGAs using National Lightning Detection Network[TM] (NLDN) data. Solution error plots are provided for both the simulations and actual data analyses.

Koshak, William↗
NASA NTRS2011

Reducing the Risk and Improving Mission Success for NASA's Human Mission to a Near-Earth Asteroid: How Many Robotic Surveyors?

NASA's recent attention and interest in sending a human mission to land on a Near-Earth asteroid raises the question of need for a robotic surveyor. This paper describes a Bayesian approach for comparing the productivity and cost-risk tradeoffs of sending (versus not sending) one or more robotic surveyor missions prior to a human mission to land on an asteroid. The probability of finding an asteroid suitable for landing was derived from an analysis of more than 1200 asteroids in order to define a quantitative estimate of suitability. The low cost of the surveyors relative to the human mission underlined the multi-surveyor strategy as relatively inexpensive insurance against the risks of encountering an unsuitable asteroid for landing on arrival by a human mission.

decision analysis↗
NASA NTRS2013

Uncertainty Quantification of GEOS-5 L-band Radiative Transfer Model Parameters Using Bayesian Inference and SMOS Observations

Uncertainties in L-band (1.4 GHz) radiative transfer modeling (RTM) affect the simulation of brightness temperatures (Tb) over land and the inversion of satellite-observed Tb into soil moisture retrievals. In particular, accurate estimates of the microwave soil roughness, vegetation opacity and scattering albedo for large-scale applications are difficult to obtain from field studies and often lack an uncertainty estimate. Here, a Markov Chain Monte Carlo (MCMC) simulation method is used to determine satellite-scale estimates of RTM parameters and their posterior uncertainty by minimizing the misfit between long-term averages and standard deviations of simulated and observed Tb at a range of incidence angles, at horizontal and vertical polarization, and for morning and evening overpasses. Tb simulations are generated with the Goddard Earth Observing System (GEOS-5) and confronted with Tb observations from the Soil Moisture Ocean Salinity (SMOS) mission. The MCMC algorithm suggests that the relative uncertainty of the RTM parameter estimates is typically less than 25 of the maximum a posteriori density (MAP) parameter value. Furthermore, the actual root-mean-square-differences in long-term Tb averages and standard deviations are found consistent with the respective estimated total simulation and observation error standard deviations of m3.1K and s2.4K. It is also shown that the MAP parameter values estimated through MCMC simulation are in close agreement with those obtained with Particle Swarm Optimization (PSO).

MCMC↗
NASA NTRS2010

Non-Targeted Effects and the Dose Response for Heavy Ion Tumorigenesis

BACKGROUND: There is no human epidemiology data available to estimate the heavy ion cancer risks experienced by astronauts in space. Studies of tumor induction in mice are a necessary step to estimate risks to astronauts. Previous experimental data can be better utilized to model dose response for heavy ion tumorigenesis and plan future low dose studies. DOSE RESPONSE MODELS: The Harderian Gland data of Alpen et al.[1-3] was re-analyzed [4] using non-linear least square regression. The data set measured the induction of Harderian gland tumors in mice by high-energy protons, helium, neon, iron, niobium and lanthanum with LET s ranging from 0.4 to 950 keV/micron. We were able to strengthen the individual ion models by combining data for all ions into a model that relates both radiation dose and LET for the ion to tumor prevalence. We compared models based on Targeted Effects (TE) to one motivated by Non-targeted Effects (NTE) that included a bystander term that increased tumor induction at low doses non-linearly. When comparing fitted models to the experimental data, we considered the adjusted R2, the Akaike Information Criteria (AIC), and the Bayesian Information Criteria (BIC) to test for Goodness of fit.In the adjusted R2test, the model with the highest R2values provides a better fit to the available data. In the AIC and BIC tests, the model with the smaller values of the summary value provides the better fit. The non-linear NTE models fit the combined data better than the TE models that are linear at low doses. We evaluated the differences in the relative biological effectiveness (RBE) and found the NTE model provides a higher RBE at low dose compared to the TE model. POWER ANALYSIS: The final NTE model estimates were used to simulate example data to consider the design of new experiments to detect NTE at low dose for validation. Power and sample sizes were calculated for a variety of radiation qualities including some not considered in the Harderian Gland data set and with different background tumor incidences. We considered different experimental designs with varying number of doses and varying low doses dependant on the LET of the radiation. The optimal design to detect a NTE for an individual ion had 4 doses equally spaced below a maximal dose where bending due to cell sterilization was < 2%. For example at 100 keV/micron we would irradiate at 0.03 Gy, 0.065 Gy, 0.13 Gy, and 0.26 Gy and require 850 mice including a control dose for a sensitivity to detect NTE with 80% power. Sample sizes could be improved by combining ions similar to the methods used with the Harderian Gland data.

Chappelli, Lori J.↗