Bayesian Paradigm

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M R Wachter - One of the best experts on this subject based on the ideXlab platform.

  • implementing the Bayesian Paradigm reporting research results over the world wide web
    Conference of American Medical Informatics Association, 1996
    Co-Authors: Harold P Lehmann, M R Wachter
    Abstract:

    Abstract For decades, statisticians, philosophers, medical investigators and others interested in data analysis have argued that the Bayesian Paradigm is the proper approach for reporting the results of scientific analyses for use by clients and readers. To date, the methods have been too complicated for non-statisticians to use. In this paper we argue that the World-Wide Web provides the perfect environment to put the Bayesian Paradigm into practice: the likelihood function of the data is parsimoniously represented on the server side, the reader uses the client to represent her prior belief, and a downloaded program (a Java applet) performs the combination. In our approach, a different applet can be used for each likelihood function, prior belief can be assessed graphically, and calculation results can be reported in a variety of ways. We present a prototype implementation, BayesApplet, for two-arm clinical trials with normally-distributed outcomes, a prominent model for clinical trials. The primary implication of this work is that publishing medical research results on the Web can take a form beyond or different from that currently used on paper, and can have a profound impact on the publication and use of research results.

Harold P Lehmann - One of the best experts on this subject based on the ideXlab platform.

  • Bayesian Communication of Research Results over the World Wide Web
    M.D. computing : computers in medical practice, 1997
    Co-Authors: Harold P Lehmann, Bach Nguyen
    Abstract:

    : The World Wide Web provides a unique opportunity to reconsider how the results of scientific studies can best be presented to clinicians. For decades statisticians, philosophers, medical investigators, and others interested in data analysis have assumed that the Bayesian Paradigm is the proper approach for reporting the findings of scientific analyses for use by client computers and readers. At the heart of that approach is the inclusion of the reader's preexisting knowledge and beliefs. Yet, to date, the methods for inclusion have been too complicated for non-statisticians to use. We believe that the World Wide Web provides an ideal environment for putting the Bayesian Paradigm into practice: the author publishes the data from the server side, the reader uses the client to represent her or his prior belief, a downloaded program (a Java applet) combines the two. This article describes a prototype implementation for two-arm clinical trials with normally distributed outcomes.

  • implementing the Bayesian Paradigm reporting research results over the world wide web
    Conference of American Medical Informatics Association, 1996
    Co-Authors: Harold P Lehmann, M R Wachter
    Abstract:

    Abstract For decades, statisticians, philosophers, medical investigators and others interested in data analysis have argued that the Bayesian Paradigm is the proper approach for reporting the results of scientific analyses for use by clients and readers. To date, the methods have been too complicated for non-statisticians to use. In this paper we argue that the World-Wide Web provides the perfect environment to put the Bayesian Paradigm into practice: the likelihood function of the data is parsimoniously represented on the server side, the reader uses the client to represent her prior belief, and a downloaded program (a Java applet) performs the combination. In our approach, a different applet can be used for each likelihood function, prior belief can be assessed graphically, and calculation results can be reported in a variety of ways. We present a prototype implementation, BayesApplet, for two-arm clinical trials with normally-distributed outcomes, a prominent model for clinical trials. The primary implication of this work is that publishing medical research results on the Web can take a form beyond or different from that currently used on paper, and can have a profound impact on the publication and use of research results.

Aggelos. K. Katsaggelos - One of the best experts on this subject based on the ideXlab platform.

  • IbPRIA (1) - Bayesian reconstruction of color images acquired with a single CCD
    Pattern Recognition and Image Analysis, 2005
    Co-Authors: Miguel Vega, Rafael Molina, Aggelos. K. Katsaggelos
    Abstract:

    Most of the available digital color cameras use a single Coupled Charge Device (CCD) with a Color Filter Array (CFA) in acquiring an image. In order to produce a visible color image a demosaicing process must be applied, which produces undesirable artifacts. This paper addresses the demosaicing problem from a superresolution point of view. Utilizing the Bayesian Paradigm, an estimate of the reconstructed images and the model parameters is generated.

  • IbPRIA (2) - Bayesian reconstruction for transmission tomography with scale hyperparameter estimation
    Pattern Recognition and Image Analysis, 2005
    Co-Authors: Antonio Martínez López, Rafael Molina, Aggelos. K. Katsaggelos
    Abstract:

    In this work we propose a new method to estimate the scale hyperparameter for transmission tomography in Nuclear Medicine image reconstruction problems. Within the Bayesian Paradigm, Evidence Analysis and circulant preconditioners are used to obtain the scale hyperparameter. For the prior distribution, we use Generalized Gaussian Markov Random Fields (GGMRF), a nonquadratic function that preserves the edges in the reconstructed image. The experimental results indicate that the proposed method produces satisfactory reconstructions.

  • IbPRIA - Bayesian SPECT Image Reconstruction with Scale Hyperparameter Estimation for Scalable Prior
    Pattern Recognition and Image Analysis, 2003
    Co-Authors: Antonio Martínez López, Rafael Molina, Aggelos. K. Katsaggelos
    Abstract:

    In this work we propose a new method to estimate the scale hyperparameter for convex priors with scalable energy functions in Single Photon Emission Computed Tomography (SPECT) image reconstruction problems. Within the Bayesian Paradigm, Evidence Analysis and circulant preconditioners are used to obtain the scale hyperparameter. The proposed method is tested on synthetic SPECT images using Generalized Gaussian Markov Random Fields (GGMRF) as scalable prior distributions.

  • A Bayesian approach for the estimation and transmission of regularization parameters for reducing blocking artifacts
    IEEE Transactions on Image Processing, 2000
    Co-Authors: Javier Mateos, Aggelos. K. Katsaggelos, Rafael Molina
    Abstract:

    With block-based compression approaches for both still images and sequences of images annoying blocking artifacts are exhibited, primarily at high compression ratios. They are due to the independent processing (quantization) of the block transformed values of the intensity or the displaced frame difference. We propose the application of the hierarchical Bayesian Paradigm to the reconstruction of block discrete cosine transform (BDCT) compressed images and the estimation of the required parameters. We derive expressions for the iterative evaluation of these parameters applying the evidence analysis within the hierarchical Bayesian Paradigm. The proposed method allows for the combination of parameters estimated at the coder and decoder. The performance of the proposed algorithms is demonstrated experimentally.

  • Bayesian and regularization methods for hyperparameter estimation in image restoration
    IEEE Transactions on Image Processing, 1999
    Co-Authors: Rafael Molina, Aggelos. K. Katsaggelos, Javier Mateos
    Abstract:

    In this paper, we propose the application of the hierarchical Bayesian Paradigm to the image restoration problem. We derive expressions for the iterative evaluation of the two hyperparameters applying the evidence and maximum a posteriori (MAP) analysis within the hierarchical Bayesian Paradigm. We show analytically that the analysis provided by the evidence approach is more realistic and appropriate than the MAP approach for the image restoration problem. We furthermore study the relationship between the evidence and an iterative approach resulting from the set theoretic regularization approach for estimating the two hyperparameters, or their ratio, defined as the regularization parameter. Finally the proposed algorithms are tested experimentally.

Shishir K Shah - One of the best experts on this subject based on the ideXlab platform.

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

  • IbPRIA (1) - Bayesian reconstruction of color images acquired with a single CCD
    Pattern Recognition and Image Analysis, 2005
    Co-Authors: Miguel Vega, Rafael Molina, Aggelos. K. Katsaggelos
    Abstract:

    Most of the available digital color cameras use a single Coupled Charge Device (CCD) with a Color Filter Array (CFA) in acquiring an image. In order to produce a visible color image a demosaicing process must be applied, which produces undesirable artifacts. This paper addresses the demosaicing problem from a superresolution point of view. Utilizing the Bayesian Paradigm, an estimate of the reconstructed images and the model parameters is generated.

  • IbPRIA (2) - Bayesian reconstruction for transmission tomography with scale hyperparameter estimation
    Pattern Recognition and Image Analysis, 2005
    Co-Authors: Antonio Martínez López, Rafael Molina, Aggelos. K. Katsaggelos
    Abstract:

    In this work we propose a new method to estimate the scale hyperparameter for transmission tomography in Nuclear Medicine image reconstruction problems. Within the Bayesian Paradigm, Evidence Analysis and circulant preconditioners are used to obtain the scale hyperparameter. For the prior distribution, we use Generalized Gaussian Markov Random Fields (GGMRF), a nonquadratic function that preserves the edges in the reconstructed image. The experimental results indicate that the proposed method produces satisfactory reconstructions.

  • IbPRIA - Bayesian SPECT Image Reconstruction with Scale Hyperparameter Estimation for Scalable Prior
    Pattern Recognition and Image Analysis, 2003
    Co-Authors: Antonio Martínez López, Rafael Molina, Aggelos. K. Katsaggelos
    Abstract:

    In this work we propose a new method to estimate the scale hyperparameter for convex priors with scalable energy functions in Single Photon Emission Computed Tomography (SPECT) image reconstruction problems. Within the Bayesian Paradigm, Evidence Analysis and circulant preconditioners are used to obtain the scale hyperparameter. The proposed method is tested on synthetic SPECT images using Generalized Gaussian Markov Random Fields (GGMRF) as scalable prior distributions.

  • A Bayesian approach for the estimation and transmission of regularization parameters for reducing blocking artifacts
    IEEE Transactions on Image Processing, 2000
    Co-Authors: Javier Mateos, Aggelos. K. Katsaggelos, Rafael Molina
    Abstract:

    With block-based compression approaches for both still images and sequences of images annoying blocking artifacts are exhibited, primarily at high compression ratios. They are due to the independent processing (quantization) of the block transformed values of the intensity or the displaced frame difference. We propose the application of the hierarchical Bayesian Paradigm to the reconstruction of block discrete cosine transform (BDCT) compressed images and the estimation of the required parameters. We derive expressions for the iterative evaluation of these parameters applying the evidence analysis within the hierarchical Bayesian Paradigm. The proposed method allows for the combination of parameters estimated at the coder and decoder. The performance of the proposed algorithms is demonstrated experimentally.

  • Bayesian and regularization methods for hyperparameter estimation in image restoration
    IEEE Transactions on Image Processing, 1999
    Co-Authors: Rafael Molina, Aggelos. K. Katsaggelos, Javier Mateos
    Abstract:

    In this paper, we propose the application of the hierarchical Bayesian Paradigm to the image restoration problem. We derive expressions for the iterative evaluation of the two hyperparameters applying the evidence and maximum a posteriori (MAP) analysis within the hierarchical Bayesian Paradigm. We show analytically that the analysis provided by the evidence approach is more realistic and appropriate than the MAP approach for the image restoration problem. We furthermore study the relationship between the evidence and an iterative approach resulting from the set theoretic regularization approach for estimating the two hyperparameters, or their ratio, defined as the regularization parameter. Finally the proposed algorithms are tested experimentally.