Search NASA⌕ Search

SEARCH · Search NASA

Results for “Bayesian Analysis”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8

OGLE-2018-BLG-1185b: A Low-mass Microlensing Planet Orbiting a Low-mass Dwarf

We report an analysis of the planetary microlensing event OGLE-2018-BLG-1185, which was observed by a large number of ground-based telescopes and by the Spitzer Space Telescope. The ground-based light curve indicates a low planet–host star mass ratio of q = (6.9 ± 0.2) × 10{sup −5}, which is near the peak of the wide-orbit exoplanet mass-ratio distribution. We estimate the host star and planet masses with a Bayesian analysis using the measured angular Einstein radius under the assumption that stars of all masses have an equal probability of hosting the planet. The flux variation observed by Spitzer is marginal, but still places a constraint on the microlens parallax. Imposing a conservative constraint that this flux variation should be Δf {sub Spz} < 4 instrumental flux units yields a host mass of M{sub host}=0.37{sub −0.21}{sup +0.35} M{sub ⊙} and a planet mass of m{sub p}=8.4{sub −4.7}{sup +7.9} M{sub ⊕}. A Bayesian analysis including the full parallax constraint from Spitzer suggests smaller host star and planet masses of M{sub host}=0.091{sub −0.018}{sup +0.064} M{sub ⊙} and m{sub p}=2.1{sub −0.4}{sup +1.5} M{sub ⊕}, respectively. Future high-resolution imaging observations with the Hubble Space Telescope or Extremely Large Telescope could distinguish between these two scenarios and help reveal the planetary system properties in more detail.

47 OTHER INSTRUMENTATION↗

Kβ X-ray Emission Spectra Analysis Using Bayesian Optimization

The Kβ X-ray emission spectrum of 3 d transition metals is rich with electronic and structural information due to strong exchange interactions with the valence shell of the metal, and has become crucial for understanding their spin and oxidation states. The spectrum is commonly treated using crystal-field multiplet theory, a semi-empirical theory that uses tunable parameters to control the strength of the effects present in X-ray emission spectroscopy (XES). However, determining the experimental values of these parameters remains a challenge. We present a methodology that applies Bayesian optimization to crystal-field multiplet theory to determine parameter values. The algorithm is tested on the X-ray emission spectra of a collection of Mn, Co, and Ni oxides. We are able to find optimal values for the four most impactful parameters: Slater−Condon reduction factors F dd , F pd , and G pd , and crystal field splitting 10 Dq . The algorithm produces significantly improved accuracy compared to current analysis methods, and probes interparameter dependencies by modeling the error landscape. This advancement enhances XES analysis by offering an approach of obtaining quantitative electronic structural information on 3 d transition metal valence shells, facilitating applications across various scientific fields.

Bayesian optimization↗

OGLE-2013-BLG-1761Lb: A Massive Planet around an M/K Dwarf

We report the discovery and the analysis of the planetary microlensing event, OGLE-2013-BLG-1761. There are some degenerate solutions in this event because the planetary anomaly is only sparsely sampled. However, the detailed light-curve analysis ruled out all stellar binary models and shows the lens to be a planetary system. There is the so-called close/wide degeneracy in the solutions with the planet/host mass ratio of q ∼ (7.0 ± 2.0) × 10{sup −3} and q ∼ (8.1 ± 2.6) × 10{sup −3} with the projected separation in Einstein radius units of s = 0.95 (close) and s = 1.18 (wide), respectively. The microlens parallax effect is not detected, but the finite source effect is detected. Our Bayesian analysis indicates that the lens system is located D{sub L}=6.9{sub −1.2}{sup +1.0} kpc away from us and the host star is an M/K dwarf with a mass of M{sub L}=0.33{sub −0.19}{sup +0.32} M{sub ⊙} orbited by a super-Jupiter mass planet with a mass of m{sub P}=2.7{sub −1.5}{sup +2.5} M{sub Jup} at the projected separation of a{sub ⊥}=1.8{sub −0.5}{sup +0.5} au. The preference of the large lens distance in the Bayesian analysis is due to the relatively large observed source star radius. The distance and other physical parameters may be constrained by the future high-resolution imaging by large ground telescopes or HST. If the estimated lens distance is correct, then this planet provides another sample for testing the claimed deficit of planets in the Galactic bulge.

79 ASTRONOMY AND ASTROPHYSICS↗

Advanced data analysis in inertial confinement fusion and high energy density physics

Bayesian analysis enables flexible and rigorous definition of statistical model assumptions with well-characterized propagation of uncertainties and resulting inferences for single-shot, repeated, or even cross-platform data. This approach has a strong history of application to a variety of problems in physical sciences ranging from inference of particle mass from multi-source high-energy particle data to analysis of black-hole characteristics from gravitational wave observations. The recent adoption of Bayesian statistics for analysis and design of high-energy density physics (HEDP) and inertial confinement fusion (ICF) experiments has provided invaluable gains in expert understanding and experiment performance. In this Review, we discuss the basic theory and practical application of the Bayesian statistics framework. We highlight a variety of studies from the HEDP and ICF literature, demonstrating the power of this technique. Due to the computational complexity of multi-physics models needed to analyze HEDP and ICF experiments, Bayesian inference is often not computationally tractable. Two sections are devoted to a review of statistical approximations, efficient inference algorithms, and data-driven methods, such as deep-learning and dimensionality reduction, which play a significant role in enabling use of the Bayesian framework. We provide additional discussion of various applications of Bayesian and machine learning methods that appear to be sparse in the HEDP and ICF literature constituting possible next steps for the community. We conclude by highlighting community needs, the resolution of which will improve trust in data-driven methods that have proven critical for accelerating the design and discovery cycle in many application areas.

47 OTHER INSTRUMENTATION↗

OGLE-2013-BLG-1761Lb: A Massive Planet around an MK Dwarf

We report the discovery and the analysis of the planetary microlensing event, OGLE-2013-BLG-1761. There are some degenerate solutions in this event because the planetary anomaly is only sparsely sampled. However, the detailed light curve analysis ruled out all stellar binary models and shows the lens to be a planetary system. There is the so-called close wide degeneracy in the solutions with the planet host mass ratio of q approx.(7.0+/-2.0) x 10(exp -3) and q approx.(8.1+/-2.6) x 10(exp -3) with the projected separation in Einstein radius units of s = 0.95 (close) and s = 1.18(wide), respectively. The microlens parallax effect is not detected, but the finite source effect is detected. Our Bayesian analysis indicates that the lens system is located -D(sub L) = 6.9(+ 1.0 -1.2)kpc away from us and the host star is an M/K dwarf with amass of M(sub L) = 0.33(+ 0.32- 1.9)Stellar Mass orbited by a super-Jupiter mass planet with a mass of m(sub p) = 2.7(+ 2.5 - 1.5) M(sub Jup) at the projected separation of a(sub l) = 1.8(+ 0.5 -0.5)au. The preference of the large lens distance in the Bayesian analysis is due to the relatively large observed source star radius. The distance and other physical parameters may be constrained by the future high-resolution imaging by large ground telescopes or HST. If the estimated lens distance is correct, then this planet provides another sample for testing the claimed deficit of planets in the Galactic bulge.

Hirao, Y.↗

Uncertainty quantification for nuclear density functional theory and information content of new measurements

Statistical tools of uncertainty quantification can be used to assess the information content of measured observables with respect to present-day theoretical models, to estimate model errors and thereby improve predictive capability, to extrapolate beyond the regions reached by experiment, and to provide meaningful input to applications and planned measurements. To showcase new opportunities offered by such tools, we make a rigorous analysis of theoretical statistical uncertainties in nuclear density functional theory using Bayesian inference methods. By considering the recent mass measurements from the Canadian Penning Trap at Argonne National Laboratory, we demonstrate how the Bayesian analysis and a direct least-squares optimization, combined with high-performance computing, can be used to assess the information content of the new data with respect to a model based on the Skyrme energy density functional approach. Employing the posterior probability distribution computed with a Gaussian process emulator, we apply the Bayesian framework to propagate theoretical statistical uncertainties in predictions of nuclear masses, two-neutron dripline, and fission barriers. Overall, we find that the new mass measurements do not impose a constraint that is strong enough to lead to significant changes in the model parameters. In addition, the example discussed in this study sets the stage for quantifying and maximizing the impact of new measurements with respect to current modeling and guiding future experimental efforts, thus enhancing the experiment-theory cycle in the scientific method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Variability Timescale and Spectral Index of Sgr A* in the Near Infrared: Approximate Bayesian Computation Analysis of the Variability of the Closest Supermassive Black Hole

Sagittarius A* (Sgr A* ) is the variable radio, near-infrared (NIR), and X-ray source associated with accretion onto the Galactic center black hole. We present an analysis of the most comprehensive NIR variability data set of Sgr A* to date: eight 24 hr epochs of continuous monitoring of Sgr A* at 4.5 μm with the IRAC instrument on the Spitzer Space Telescope, 93 epochs of 2.18 μm data from Naos Conica at the Very Large Telescope, and 30 epochs of 2.12 μm data from the NIRC2 camera at the Keck Observatory, in total 94,929 measurements. A new approximate Bayesian computation method for fitting the first-order structure function extracts information beyond current fast Fourier transformation (FFT) methods of power spectral density (PSD) estimation. With a combined fit of the data of all three observatories, the characteristic coherence timescale of Sgr A* is b 243 57 82 t = - + minutes (90% credible interval). The PSD has no detectable features on timescales down to 8.5 minutes (95% credible level), which is the ISCO orbital frequency for a dimensionless spin parameter a = 0.92. One light curve measured simultaneously at 2.12 and 4.5 μm during a low flux-density phase gave a spectral index αs = 1.6 ± 0.1 (F µ n s n -a ). This value implies that the Sgr A* NIR color becomes bluer during higher flux-density phases. The probability densities of flux densities of the combined data sets are best fit by log-normal distributions. Based on these distributions, the Sgr A* spectral energy distribution is consistent with synchrotron radiation from a nonthermal electron population from below 20 GHz through the NIR.

accretion↗

STUDIES IN ASTRONOMICAL TIME SERIES ANALYSIS. VI. BAYESIAN BLOCK REPRESENTATIONS

This paper addresses the problem of detecting and characterizing local variability in time series and other forms of sequential data. The goal is to identify and characterize statistically significant variations, at the same time suppressing the inevitable corrupting observational errors. We present a simple nonparametric modeling technique and an algorithm implementing it-an improved and generalized version of Bayesian Blocks-that finds the optimal segmentation of the data in the observation interval. The structure of the algorithm allows it to be used in either a real-time trigger mode, or a retrospective mode. Maximum likelihood or marginal posterior functions to measure model fitness are presented for events, binned counts, and measurements at arbitrary times with known error distributions. Problems addressed include those connected with data gaps, variable exposure, extension to piecewise linear and piecewise exponential representations, multivariate time series data, analysis of variance, data on the circle, other data modes, and dispersed data. Simulations provide evidence that the detection efficiency for weak signals is close to a theoretical asymptotic limit derived by Arias-Castro et al. In the spirit of Reproducible Research all of the code and data necessary to reproduce all of the figures in this paper are included as supplementary material.

79 ASTRONOMY AND ASTROPHYSICS↗

Constraints on the sum of the neutrino masses in dynamical dark energy models with w ( z ) ≥ - 1 are tighter than those obtained in Λ CDM

In this work, we explore cosmological constraints on the sum of the three active neutrino masses M ν in the context of dynamical dark energy (DDE) models with equation of state (EoS) parametrized as a function of redshift z by w(z) = w 0 + w a z/(1 + z), and satisfying w(z) ≥ -1 for all z. We make use of cosmic microwave background data from the Planck satellite, baryon acoustic oscillation measurements, and supernovae Ia luminosity distance measurements, and perform a Bayesian analysis. We show that, within these models, the bounds on M ν do not degrade with respect to those obtained in the Λ CDM case; in fact, the bounds are slightly tighter, despite the enlarged parameter space. We explain our results based on the observation that, for fixed choices of w 0 , w a such that w(z) ≥ - 1 (but not w = -1 for all z), the upper limit on M ν is tighter than the Λ CDM limit because of the well-known degeneracy between w and M ν . The Bayesian analysis we have carried out then integrates over the possible values of w 0 - w a such that w (z) ≥ -1, all of which correspond to tighter limits on M ν than the Λ CDM limit. We find a 95% credible interval (C.I.) upper bound of M ν < 0.13 eV . This bound can be compared with the 95% C.I. upper bounds of M ν < 0.16 eV , obtained within the Λ CDM model, and M ν < 0.41 eV, obtained in a DDE model with arbitrary EoS (which allows values of w < -1). Contrary to the results derived for DDE models with arbitrary EoS, we find that a dark energy component with w(z) ≥ -1 is unable to alleviate the tension between high-redshift observables and direct measurements of the Hubble constant H 0 . Lastly, in light of the results of this analysis, we also discuss the implications for DDE models of a possible determination of the neutrino mass ordering by laboratory searches.

79 ASTRONOMY AND ASTROPHYSICS↗

Measurement of the CP-violating phase β s J/ψΦ in B s 0 →J/ψΦ decays with the CDF II detector

We present a measurement of the CP-violating parameter β s J/ψΦ using approximately 6500 B 0 s →J/ψΦ decays reconstructed with the CDF II detector in a sample of pp̄ collisions at √s=1.96 TeV corresponding to 5.2 fb⁻¹ integrated luminosity produced by the Tevatron collider at Fermilab. We find the CP-violating phase to be within the range β s J/ψΦ ϵ [0.02,0.52]∪[1.08,1.55] at 68% confidence level where the coverage property of the quoted interval is guaranteed using a frequentist statistical analysis. This result is in agreement with the standard model expectation at the level of about one Gaussian standard deviation. We consider the inclusion of a potential S-wave contribution to the B 0 s →J/ψK⁺K⁻ final state which is found to be negligible over the mass interval 1.009 s J/ψΦ , we find the B 0 s decay width difference to be ΔΓ s =0.075±0.035(stat)±0.006(syst) ps⁻¹. We also present the most precise measurements of the B 0 s mean lifetime τ (B 0 s )=1.529±0.025(stat)±0.012(syst) ps, the polarization fractions |A0(0)|²=0.524±0.013(stat)±0.015(syst) and |A II (0)|²=0.231±0.014(stat)±0.015(syst), as well as the strong phase δ ⊥ =2.95±0.64(stat)±0.07(syst) rad. In addition, we report an alternative Bayesian analysis that gives results consistent with the frequentist approach.

Aaltonen, T.↗

BASS: An R Package for Fitting and Performing Sensitivity Analysis of Bayesian Adaptive Spline Surfaces

In this work, we present the R package BASS as a tool for nonparametric regression. The primary focus of the package is fitting fully Bayesian adaptive spline surface (BASS) models and performing global sensitivity analyses of these models. The BASS framework is similar to that of Bayesian multivariate adaptive regression splines (BMARS) from Denison, Mallick, and Smith (1998), but with many added features. The software is built to efficiently handle significant amounts of data with many continuous or categorical predictors and with functional response. Under our Bayesian framework, most priors are automatic but these can be modified by the user to focus on parsimony and the avoidance of overfitting. If directed to do so, the software uses parallel tempering to improve the reversible jump Markov chain Monte Carlo (RJMCMC) methods used to perform inference. We discuss the implementation of these features and present the performance of BASS in a number of analyses of simulated and real data.

97 MATHEMATICS AND COMPUTING↗

Daily Monitoring of TeV Gamma-Ray Emission from Mrk 421, Mrk 501, and the Crab Nebula with HAWC

We present results from daily monitoring of gamma-rays in the energy range from ∼0.5 to ∼100 TeV with the first 17 months of data from the High Altitude Water Cherenkov (HAWC) Observatory. Its wide field of view of 2 steradians and duty cycle of >95% are unique features compared to other TeV observatories that allow us to observe every source that transits over HAWC for up to ∼6 hr each sidereal day. This regular sampling yields unprecedented light curves from unbiased measurements that are independent of seasons or weather conditions. For the Crab Nebula as a reference source, we find no variability in the TeV band. Our main focus is the study of the TeV blazars Markarian (Mrk) 421 and Mrk 501. A spectral fit for Mrk 421 yields a power-law index Γ=2.21±0.14{sub stat}±0.20{sub sys} and an exponential cut-off E{sub 0}=5.4±1.1{sub stat}±1.0{sub sys} TeV. For Mrk 501, we find an index Γ=1.60±0.30{sub stat}±0.20{sub sys} and exponential cut-off E{sub 0}=5.7±1.6{sub stat}±1.0{sub sys} TeV. The light curves for both sources show clear variability and a Bayesian analysis is applied to identify changes between flux states. The highest per-transit fluxes observed from Mrk 421 exceed the Crab Nebula flux by a factor of approximately five. For Mrk 501, several transits show fluxes in excess of three times the Crab Nebula flux. In a comparison to lower energy gamma-ray and X-ray monitoring data with comparable sampling, we cannot identify clear counterparts for the most significant flaring features observed by HAWC.

79 ASTRONOMY AND ASTROPHYSICS↗

Cosmic ray propagation and dark matter in light of the latest AMS-02 data

The AMS-02 experiment is measuring the high energy cosmic rays with unprecedented accuracy. We explore the possibility of determining the cosmic-ray propagation models using the AMS-02 data alone. A global Bayesian analysis of the constraints on the cosmic-ray propagation models from the preliminary AMS-02 data on the Boron to Carbon nuclei flux ratio and proton flux is performed, with the assumption that the primary nucleon source is a broken power law in rigidity. The ratio of the diffusion coefficient D{sub 0} to the diffusive halo height Z{sub h} is determined with high accuracy D{sub 0}/Z{sub h}≃2.00±0.07 cm{sup 2}s{sup −1}kpc{sup −1}, and the value of the halo width is found to be Z{sub h}≃3.3 kpc with uncertainty less than 50%. As a consequence, the typical uncertainties in the positron fraction predicted from dark matter (DM) annihilation is reduced to a factor of two, and that in the antiproton flux is about an order of magnitude. Both of them are significantly smaller than that from the analyses prior to AMS-02. Taking into account the uncertainties and correlations in the propagation parameters, we derive conservative upper limits on the cross sections for DM annihilating into various standard model final states from the current PAMELA antiproton data. We also investigate the reconstruction capability of the future high precision AMS-02 antiproton data on the DM properties. The results show that for DM particles lighter than ∼100 GeV and with typical thermal annihilation cross section, the cross section can be well reconstructed with uncertainties about a factor of two for the AMS-02 three-year data taking.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

MODELING THE NON-RECYCLED FERMI GAMMA-RAY PULSAR POPULATION

We use Fermi Gamma-ray Space Telescope detections and upper limits on non-recycled pulsars obtained from the Large Area Telescope (LAT) to constrain how the gamma-ray luminosity L{sub γ} depends on the period P and the period derivative P-dot . We use a Bayesian analysis to calculate a best-fit luminosity law, or dependence of L{sub γ} on P and P-dot , including different methods for modeling the beaming factor. An outer gap (OG) magnetosphere geometry provides the best-fit model, which is L{sub γ}∝P{sup -a} P-dot {sup b} where a = 1.36 ± 0.03 and b = 0.44 ± 0.02, similar to but not identical to the commonly assumed L{sub γ}∝√( E-dot )∝P{sup -1.5} P-dot {sup 0.5}. Given upper limits on gamma-ray fluxes of currently known radio pulsars and using the OG model, we find that about 92% of the radio-detected pulsars have gamma-ray beams that intersect our line of sight. By modeling the misalignment of radio and gamma-ray beams of these pulsars, we find an average gamma-ray beaming solid angle of about 3.7π for the OG model, assuming a uniform beam. Using LAT-measured diffuse fluxes, we place a 2σ upper limit on the average braking index and a 2σ lower limit on the average surface magnetic field strength of the pulsar population of 3.8 and 3.2 × 10{sup 10} G, respectively. We then predict the number of non-recycled pulsars detectable by the LAT based on our population model. Using the 2 yr sensitivity, we find that the LAT is capable of detecting emission from about 380 non-recycled pulsars, including 150 currently identified radio pulsars. Using the expected 5 yr sensitivity, about 620 non-recycled pulsars are detectable, including about 220 currently identified radio pulsars. We note that these predictions significantly depend on our model assumptions.

79 ASTRONOMY AND ASTROPHYSICS↗

An analysis of Bayesian estimates for missing higher orders in perturbative calculations

With current high precision collider data, the reliable estimation of theoretical uncertainties due to missing higher orders (MHOs) in perturbation theory has become a pressing issue for collider phenomenology. Traditionally, the size of the MHOs is estimated through scale variation, a simple but ad hoc method without probabilistic interpretation. Bayesian approaches provide a compelling alternative to estimate the size of the MHOs, but it is not clear how to interpret the perturbative scales, like the factorisation and renormalisation scales, in a Bayesian framework. Recently, it was proposed that the scales can be incorporated as hidden parameters into a Bayesian model. In this paper, we thoroughly scrutinise Bayesian approaches to MHO estimation and systematically study the performance of different models on an extensive set of high-order calculations. We extend the framework in two significant ways. First, we define a new model that allows for asymmetric probability distributions. Second, we introduce a prescription to incorporate information on perturbative scales without interpreting them as hidden model parameters. We clarify how the two scale prescriptions bias the result towards specific scale choice, and we discuss and compare different Bayesian MHO estimates among themselves and to the traditional scale variation approach. Finally, we provide a practical prescription of how existing perturbative results at the standard scale variation points can be converted to 68%/95% credibility intervals in the Bayesian approach using the new public code MiHO.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗