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Hanswalter Rix - One of the best experts on this subject based on the ideXlab platform.

  • the joker a custom monte carlo sampler for binary star and exoplanet radial velocity data
    The Astrophysical Journal, 2017
    Co-Authors: Adrian M Pricewhelan, David W Hogg, Daniel Foremanmackey, Hanswalter Rix
    Abstract:

    Given sparse or low-quality radial velocity measurements of a star, there are often many qualitatively different stellar or exoplanet companion orbit models that are consistent with the data. The consequent multimodality of the likelihood function leads to extremely challenging search, optimization, and Markov chain Monte Carlo (MCMC) Posterior sampling over the orbital parameters. Here we create a custom Monte Carlo sampler for sparse or noisy radial velocity measurements of two-body systems that can produce Posterior samples for orbital parameters even when the likelihood function is poorly behaved. The six standard orbital parameters for a binary system can be split into four nonlinear parameters (period, eccentricity, argument of pericenter, phase) and two linear parameters (velocity amplitude, barycenter velocity). We capitalize on this by building a sampling method in which we densely sample the prior probability density function (Pdf) in the nonlinear parameters and perform rejection sampling using a likelihood function marginalized over the linear parameters. With sparse or uninformative data, the sampling obtained by this rejection sampling is generally multimodal and dense. With informative data, the sampling becomes effectively unimodal but too sparse: in these cases we follow the rejection sampling with standard MCMC. The method produces correct samplings in orbital parameters for data that include as few as three epochs. The Joker can therefore be used to produce proper samplings of multimodal Pdfs, which are still informative and can be used in hierarchical (population) modeling. We give some examples that show how the Posterior Pdf depends sensitively on the number and time coverage of the observations and their uncertainties.

  • the joker a custom monte carlo sampler for binary star and exoplanet radial velocity data
    arXiv: Solar and Stellar Astrophysics, 2016
    Co-Authors: Adrian M Pricewhelan, David W Hogg, Daniel Foremanmackey, Hanswalter Rix
    Abstract:

    Given sparse or low-quality radial-velocity measurements of a star, there are often many qualitatively different stellar or exoplanet companion orbit models that are consistent with the data. The consequent multimodality of the likelihood function leads to extremely challenging search, optimization, and MCMC Posterior sampling over the orbital parameters. Here we create a custom Monte Carlo sampler for sparse or noisy radial-velocity measurements of two-body systems that can produce Posterior samples for orbital parameters even when the likelihood function is poorly behaved. The six standard orbital parameters for a binary system can be split into four non-linear parameters (period, eccentricity, argument of pericenter, phase) and two linear parameters (velocity amplitude, barycenter velocity). We capitalize on this by building a sampling method in which we densely sample the prior Pdf in the non-linear parameters and perform rejection sampling using a likelihood function marginalized over the linear parameters. With sparse or uninformative data, the sampling obtained by this rejection sampling is generally multimodal and dense. With informative data, the sampling becomes effectively unimodal but too sparse: in these cases we follow the rejection sampling with standard MCMC. The method produces correct samplings in orbital parameters for data that include as few as three epochs. The Joker can therefore be used to produce proper samplings of multimodal Pdfs, which are still informative and can be used in hierarchical (population) modeling. We give some examples that show how the Posterior Pdf depends sensitively on the number and time coverage of the observations and their uncertainties.

Jean-yves Tourneret - One of the best experts on this subject based on the ideXlab platform.

  • An EM-based multipath interference mitigation in GNSS receivers
    Signal Processing, 2019
    Co-Authors: Cheng Cheng, Jean-yves Tourneret
    Abstract:

    In multipath (MP) environments, the received signals depend on several factors related to the global navigation satellite systems (GNSS) receiver environment and motion. Thus it is difficult to use a spe- cific propagation model to accurately capture the dynamics of the MP signal when the GNSS receiver is moving in urban canyons. This paper formulates the problem of MP interference mitigation in the GNSS receiver as a joint state (containing the direct signal parameters) and time-varying model parameter (con- taining the MP signal parameters) estimation. Accordingly, we propose to exploit the EM algorithm for achieving the joint state and time-varying parameter estimation in the context of MP interference mit- igation in GNSS receivers. More precisely, the proposed EM-based MP mitigation approach is decom- posed into two iterative steps: (a) the Posterior Pdf of the direct signal parameters and the expected log-likelihood function necessary in the expectation step of the EM algorithm are approximated by using an appropriate particle filter; (b) the maximum likelihood solution for MP signal parameters is then ob- tained using Newton’s method in the maximization step. The convergence of the proposed approach is analyzed based on the existing convergence theorem associated with the EM algorithm. Finally, a com- prehensive simulation study is conducted to compare the performance of the proposed EM-based MP mitigation approach with other state-of-the-art MP mitigation approaches in static and realistic scenar- ios.

Cheng Cheng - One of the best experts on this subject based on the ideXlab platform.

  • An EM-based multipath interference mitigation in GNSS receivers
    'Elsevier BV', 2019
    Co-Authors: Cheng Cheng, Tourneret Jean-yves
    Abstract:

    International audienceIn multipath (MP) environments, the received signals depend on several factors related to the global navigation satellite systems (GNSS) receiver environment and motion. Thus it is difficult to use a spe- cific propagation model to accurately capture the dynamics of the MP signal when the GNSS receiver is moving in urban canyons. This paper formulates the problem of MP interference mitigation in the GNSS receiver as a joint state (containing the direct signal parameters) and time-varying model parameter (con- taining the MP signal parameters) estimation. Accordingly, we propose to exploit the EM algorithm for achieving the joint state and time-varying parameter estimation in the context of MP interference mit- igation in GNSS receivers. More precisely, the proposed EM-based MP mitigation approach is decom- posed into two iterative steps: (a) the Posterior Pdf of the direct signal parameters and the expected log-likelihood function necessary in the expectation step of the EM algorithm are approximated by using an appropriate particle filter; (b) the maximum likelihood solution for MP signal parameters is then ob- tained using Newton’s method in the maximization step. The convergence of the proposed approach is analyzed based on the existing convergence theorem associated with the EM algorithm. Finally, a com- prehensive simulation study is conducted to compare the performance of the proposed EM-based MP mitigation approach with other state-of-the-art MP mitigation approaches in static and realistic scenar- ios

  • An EM-based multipath interference mitigation in GNSS receivers
    Signal Processing, 2019
    Co-Authors: Cheng Cheng, Jean-yves Tourneret
    Abstract:

    In multipath (MP) environments, the received signals depend on several factors related to the global navigation satellite systems (GNSS) receiver environment and motion. Thus it is difficult to use a spe- cific propagation model to accurately capture the dynamics of the MP signal when the GNSS receiver is moving in urban canyons. This paper formulates the problem of MP interference mitigation in the GNSS receiver as a joint state (containing the direct signal parameters) and time-varying model parameter (con- taining the MP signal parameters) estimation. Accordingly, we propose to exploit the EM algorithm for achieving the joint state and time-varying parameter estimation in the context of MP interference mit- igation in GNSS receivers. More precisely, the proposed EM-based MP mitigation approach is decom- posed into two iterative steps: (a) the Posterior Pdf of the direct signal parameters and the expected log-likelihood function necessary in the expectation step of the EM algorithm are approximated by using an appropriate particle filter; (b) the maximum likelihood solution for MP signal parameters is then ob- tained using Newton’s method in the maximization step. The convergence of the proposed approach is analyzed based on the existing convergence theorem associated with the EM algorithm. Finally, a com- prehensive simulation study is conducted to compare the performance of the proposed EM-based MP mitigation approach with other state-of-the-art MP mitigation approaches in static and realistic scenar- ios.

Linwei Wang - One of the best experts on this subject based on the ideXlab platform.

  • quantifying the uncertainty in model parameters using gaussian process based markov chain monte carlo in cardiac electrophysiology
    Medical Image Analysis, 2018
    Co-Authors: Jwala Dhamala, Hermenegild Arevalo, John L Sapp, Milan B Horacek, Natalia A Trayanova, Linwei Wang
    Abstract:

    Abstract Model personalization requires the estimation of patient-specific tissue properties in the form of model parameters from indirect and sparse measurement data. Moreover, a low-dimensional representation of the parameter space is needed, which often has a limited ability to reveal the underlying tissue heterogeneity. As a result, significant uncertainty can be associated with the estimated values of the model parameters which, if left unquantified, will lead to unknown variability in model outputs that will hinder their reliable clinical adoption. Probabilistic estimation of model parameters, however, remains an unresolved challenge. Direct Markov Chain Monte Carlo (MCMC) sampling of the Posterior distribution function (Pdf) of the parameters is infeasible because it involves repeated evaluations of the computationally expensive simulation model. To accelerate this inference, one popular approach is to construct a computationally efficient surrogate and sample from this approximation. However, by sampling from an approximation, efficiency is gained at the expense of sampling accuracy. In this paper, we address this issue by integrating surrogate modeling of the Posterior Pdf into accelerating the Metropolis-Hastings (MH) sampling of the exact Posterior Pdf. It is achieved by two main components: (1) construction of a Gaussian process (GP) surrogate of the exact Posterior Pdf by actively selecting training points that allow for a good global approximation accuracy with a focus on the regions of high Posterior probability; and (2) use of the GP surrogate to improve the proposal distribution in MH sampling, in order to improve the acceptance rate. The presented framework is evaluated in its estimation of the local tissue excitability of a cardiac electrophysiological model in both synthetic data experiments and real data experiments. In addition, the obtained Posterior distributions of model parameters are interpreted in relation to the factors contributing to parameter uncertainty, including different low-dimensional representations of the parameter space, parameter non-identifiability, and parameter correlations.

Adrian M Pricewhelan - One of the best experts on this subject based on the ideXlab platform.

  • the joker a custom monte carlo sampler for binary star and exoplanet radial velocity data
    The Astrophysical Journal, 2017
    Co-Authors: Adrian M Pricewhelan, David W Hogg, Daniel Foremanmackey, Hanswalter Rix
    Abstract:

    Given sparse or low-quality radial velocity measurements of a star, there are often many qualitatively different stellar or exoplanet companion orbit models that are consistent with the data. The consequent multimodality of the likelihood function leads to extremely challenging search, optimization, and Markov chain Monte Carlo (MCMC) Posterior sampling over the orbital parameters. Here we create a custom Monte Carlo sampler for sparse or noisy radial velocity measurements of two-body systems that can produce Posterior samples for orbital parameters even when the likelihood function is poorly behaved. The six standard orbital parameters for a binary system can be split into four nonlinear parameters (period, eccentricity, argument of pericenter, phase) and two linear parameters (velocity amplitude, barycenter velocity). We capitalize on this by building a sampling method in which we densely sample the prior probability density function (Pdf) in the nonlinear parameters and perform rejection sampling using a likelihood function marginalized over the linear parameters. With sparse or uninformative data, the sampling obtained by this rejection sampling is generally multimodal and dense. With informative data, the sampling becomes effectively unimodal but too sparse: in these cases we follow the rejection sampling with standard MCMC. The method produces correct samplings in orbital parameters for data that include as few as three epochs. The Joker can therefore be used to produce proper samplings of multimodal Pdfs, which are still informative and can be used in hierarchical (population) modeling. We give some examples that show how the Posterior Pdf depends sensitively on the number and time coverage of the observations and their uncertainties.

  • the joker a custom monte carlo sampler for binary star and exoplanet radial velocity data
    arXiv: Solar and Stellar Astrophysics, 2016
    Co-Authors: Adrian M Pricewhelan, David W Hogg, Daniel Foremanmackey, Hanswalter Rix
    Abstract:

    Given sparse or low-quality radial-velocity measurements of a star, there are often many qualitatively different stellar or exoplanet companion orbit models that are consistent with the data. The consequent multimodality of the likelihood function leads to extremely challenging search, optimization, and MCMC Posterior sampling over the orbital parameters. Here we create a custom Monte Carlo sampler for sparse or noisy radial-velocity measurements of two-body systems that can produce Posterior samples for orbital parameters even when the likelihood function is poorly behaved. The six standard orbital parameters for a binary system can be split into four non-linear parameters (period, eccentricity, argument of pericenter, phase) and two linear parameters (velocity amplitude, barycenter velocity). We capitalize on this by building a sampling method in which we densely sample the prior Pdf in the non-linear parameters and perform rejection sampling using a likelihood function marginalized over the linear parameters. With sparse or uninformative data, the sampling obtained by this rejection sampling is generally multimodal and dense. With informative data, the sampling becomes effectively unimodal but too sparse: in these cases we follow the rejection sampling with standard MCMC. The method produces correct samplings in orbital parameters for data that include as few as three epochs. The Joker can therefore be used to produce proper samplings of multimodal Pdfs, which are still informative and can be used in hierarchical (population) modeling. We give some examples that show how the Posterior Pdf depends sensitively on the number and time coverage of the observations and their uncertainties.