The Experts below are selected from a list of 8901 Experts worldwide ranked by ideXlab platform

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

  • a metropolis hastings based method for sampling from the g wishart distribution in gaussian graphical models
    Electronic Journal of Statistics, 2011
    Co-Authors: Nicholas Mitsakakis, Helene Massam, Michael Escobar
    Abstract:

    Abstract: In Gaussian graphical models, the Conjugate Prior for the precision matrix K is called G-Wishart distribution, WG(δ,D). In this paper we propose a new sampling method for the WG(δ,D) based on the Metropolis Hastings algorithm and we show its validity through a number of numerical experiments. We show that this method can be easily used to estimate the Deviance Information Criterion, providing with a computationally inexpensive approach for model selection.

  • a Conjugate Prior for discrete hierarchical log linear models
    Annals of Statistics, 2009
    Co-Authors: Helene Massam, Jinnan Liu, Adrian Dobra
    Abstract:

    In the Bayesian analysis of contingency table data, the selection of a Prior distribution for either the log-linear parameters or the cell probabilities parameter is a major challenge. Though the Conjugate Prior on cell probabilities has been defined by Dawid and Lauritzen (1993) for decomposable graphical models, it has not been identified for the larger class of graphical models Markov with respect to an arbitrary undirected graph or for the even wider class of hierarchical log-linear models. In this paper, working with the log-linear parameters used by GLIM, we first define the Conjugate Prior for these parameters and then derive the induced Prior for the cell probabilities: this is done for the general class of hierarchical log-linear models. We show that the Conjugate Prior has all the properties that one expects from a Prior: notational simplicity, ability to reflect either no Prior knowledge or a Priori expert knowledge, a moderate number of hyperparameters and mathematical convenience. It also has the strong hyper Markov property which allows for local updates within prime components for graphical models.

  • a Conjugate Prior for discrete hierarchical log linear models
    arXiv: Statistics Theory, 2007
    Co-Authors: Helene Massam, Jinnan Liu, Adrian Dobra
    Abstract:

    In Bayesian analysis of multi-way contingency tables, the selection of a Prior distribution for either the log-linear parameters or the cell probabilities parameters is a major challenge. In this paper, we define a flexible family of Conjugate Priors for the wide class of discrete hierarchical log-linear models, which includes the class of graphical models. These Priors are defined as the Diaconis--Ylvisaker Conjugate Priors on the log-linear parameters subject to "baseline constraints" under multinomial sampling. We also derive the induced Prior on the cell probabilities and show that the induced Prior is a generalization of the hyper Dirichlet Prior. We show that this Prior has several desirable properties and illustrate its usefulness by identifying the most probable decomposable, graphical and hierarchical log-linear models for a six-way contingency table.

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

  • a Conjugate Prior for discrete hierarchical log linear models
    Annals of Statistics, 2009
    Co-Authors: Helene Massam, Jinnan Liu, Adrian Dobra
    Abstract:

    In the Bayesian analysis of contingency table data, the selection of a Prior distribution for either the log-linear parameters or the cell probabilities parameter is a major challenge. Though the Conjugate Prior on cell probabilities has been defined by Dawid and Lauritzen (1993) for decomposable graphical models, it has not been identified for the larger class of graphical models Markov with respect to an arbitrary undirected graph or for the even wider class of hierarchical log-linear models. In this paper, working with the log-linear parameters used by GLIM, we first define the Conjugate Prior for these parameters and then derive the induced Prior for the cell probabilities: this is done for the general class of hierarchical log-linear models. We show that the Conjugate Prior has all the properties that one expects from a Prior: notational simplicity, ability to reflect either no Prior knowledge or a Priori expert knowledge, a moderate number of hyperparameters and mathematical convenience. It also has the strong hyper Markov property which allows for local updates within prime components for graphical models.

  • a Conjugate Prior for discrete hierarchical log linear models
    arXiv: Statistics Theory, 2007
    Co-Authors: Helene Massam, Jinnan Liu, Adrian Dobra
    Abstract:

    In Bayesian analysis of multi-way contingency tables, the selection of a Prior distribution for either the log-linear parameters or the cell probabilities parameters is a major challenge. In this paper, we define a flexible family of Conjugate Priors for the wide class of discrete hierarchical log-linear models, which includes the class of graphical models. These Priors are defined as the Diaconis--Ylvisaker Conjugate Priors on the log-linear parameters subject to "baseline constraints" under multinomial sampling. We also derive the induced Prior on the cell probabilities and show that the induced Prior is a generalization of the hyper Dirichlet Prior. We show that this Prior has several desirable properties and illustrate its usefulness by identifying the most probable decomposable, graphical and hierarchical log-linear models for a six-way contingency table.

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

  • poisson multi bernoulli mapping using gibbs sampling
    IEEE Transactions on Signal Processing, 2017
    Co-Authors: Maryam Fatemi, Karl Granstrom, Lennart Svensson, Francisco J R Ruiz, Lars Hammarstrand
    Abstract:

    This paper addresses the mapping problem. Using a Conjugate Prior form, we derive the exact theoretical batch multiobject posterior density of the map given a set of measurements. The landmarks in the map are modeled as extended objects, and the measurements are described as a Poisson process, conditioned on the map. We use a Poisson process Prior on the map and prove that the posterior distribution is a hybrid Poisson, multi-Bernoulli mixture distribution. We devise a Gibbs sampling algorithm to sample from the batch multiobject posterior. The proposed method can handle uncertainties in the data associations and the cardinality of the set of landmarks, and is parallelizable, making it suitable for large-scale problems. The performance of the proposed method is evaluated on synthetic data and is shown to outperform a state-of-the-art method.

  • poisson multi bernoulli Conjugate Prior for multiple extended object estimation
    arXiv: Computation, 2016
    Co-Authors: Karl Granstrom, Maryam Fatemi, Lennart Svensson
    Abstract:

    This paper presents a Poisson multi-Bernoulli mixture (PMBM) Conjugate Prior for multiple extended object estimation. A Poisson point process is used to describe the existence of yet undetected targets, while a multi-Bernoulli mixture describes the distribution of the targets that have been detected. The prediction and update equations are presented for the standard transition density and measurement likelihood. Both the prediction and the update preserve the PMBM form of the density, and in this sense the PMBM density is a Conjugate Prior. However, the unknown data associations lead to an intractably large number of terms in the PMBM density, and approximations are necessary for tractability. A gamma Gaussian inverse Wishart implementation is presented, along with methods to handle the data association problem. A simulation study shows that the extended target PMBM filter outperforms the extended target PHD, CPHD and LMB filters. An experiment with Lidar data illustrates the benefit of tracking both detected and undetected targets.

  • poisson multi bernoulli Conjugate Prior for estimation of both detected and undetected extended objects
    2016
    Co-Authors: Karl Granstrom, Maryam Fatemi, Lennart Svensson
    Abstract:

    This paper presents a Poisson multi-Bernoulli mixture (PMBM) Conjugate Prior for multiple extended object estimation. A Poisson point process is used to describe the existence of yet undetected targets, while a multi-Bernoulli mixture describes the distribution of the targets that have been detected. The prediction and update equations are presented for the standard transition density and measurement likelihood. Both the prediction and the update preserve the PMBM form of the density, and in this sense the PMBM density is a Conjugate Prior. However, the unknown data associations lead to an intractably large number of terms in the PMBM density, and approximations are necessary for tractability. A gamma Gaussian inverse Wishart implementation is presented, along with methods to handle the data association problem. A simulation study shows that the extended target PMBM filter outperforms the extended target PHD, CPHD and LMB filters.

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

  • poisson multi bernoulli mapping using gibbs sampling
    IEEE Transactions on Signal Processing, 2017
    Co-Authors: Maryam Fatemi, Karl Granstrom, Lennart Svensson, Francisco J R Ruiz, Lars Hammarstrand
    Abstract:

    This paper addresses the mapping problem. Using a Conjugate Prior form, we derive the exact theoretical batch multiobject posterior density of the map given a set of measurements. The landmarks in the map are modeled as extended objects, and the measurements are described as a Poisson process, conditioned on the map. We use a Poisson process Prior on the map and prove that the posterior distribution is a hybrid Poisson, multi-Bernoulli mixture distribution. We devise a Gibbs sampling algorithm to sample from the batch multiobject posterior. The proposed method can handle uncertainties in the data associations and the cardinality of the set of landmarks, and is parallelizable, making it suitable for large-scale problems. The performance of the proposed method is evaluated on synthetic data and is shown to outperform a state-of-the-art method.

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

  • poisson multi bernoulli mapping using gibbs sampling
    IEEE Transactions on Signal Processing, 2017
    Co-Authors: Maryam Fatemi, Karl Granstrom, Lennart Svensson, Francisco J R Ruiz, Lars Hammarstrand
    Abstract:

    This paper addresses the mapping problem. Using a Conjugate Prior form, we derive the exact theoretical batch multiobject posterior density of the map given a set of measurements. The landmarks in the map are modeled as extended objects, and the measurements are described as a Poisson process, conditioned on the map. We use a Poisson process Prior on the map and prove that the posterior distribution is a hybrid Poisson, multi-Bernoulli mixture distribution. We devise a Gibbs sampling algorithm to sample from the batch multiobject posterior. The proposed method can handle uncertainties in the data associations and the cardinality of the set of landmarks, and is parallelizable, making it suitable for large-scale problems. The performance of the proposed method is evaluated on synthetic data and is shown to outperform a state-of-the-art method.

  • poisson multi bernoulli Conjugate Prior for multiple extended object estimation
    arXiv: Computation, 2016
    Co-Authors: Karl Granstrom, Maryam Fatemi, Lennart Svensson
    Abstract:

    This paper presents a Poisson multi-Bernoulli mixture (PMBM) Conjugate Prior for multiple extended object estimation. A Poisson point process is used to describe the existence of yet undetected targets, while a multi-Bernoulli mixture describes the distribution of the targets that have been detected. The prediction and update equations are presented for the standard transition density and measurement likelihood. Both the prediction and the update preserve the PMBM form of the density, and in this sense the PMBM density is a Conjugate Prior. However, the unknown data associations lead to an intractably large number of terms in the PMBM density, and approximations are necessary for tractability. A gamma Gaussian inverse Wishart implementation is presented, along with methods to handle the data association problem. A simulation study shows that the extended target PMBM filter outperforms the extended target PHD, CPHD and LMB filters. An experiment with Lidar data illustrates the benefit of tracking both detected and undetected targets.

  • poisson multi bernoulli Conjugate Prior for estimation of both detected and undetected extended objects
    2016
    Co-Authors: Karl Granstrom, Maryam Fatemi, Lennart Svensson
    Abstract:

    This paper presents a Poisson multi-Bernoulli mixture (PMBM) Conjugate Prior for multiple extended object estimation. A Poisson point process is used to describe the existence of yet undetected targets, while a multi-Bernoulli mixture describes the distribution of the targets that have been detected. The prediction and update equations are presented for the standard transition density and measurement likelihood. Both the prediction and the update preserve the PMBM form of the density, and in this sense the PMBM density is a Conjugate Prior. However, the unknown data associations lead to an intractably large number of terms in the PMBM density, and approximations are necessary for tractability. A gamma Gaussian inverse Wishart implementation is presented, along with methods to handle the data association problem. A simulation study shows that the extended target PMBM filter outperforms the extended target PHD, CPHD and LMB filters.