Bayesian Multiscale Models for Poisson Processes

@article{Kolaczyk1999BayesianMM,
  title={Bayesian Multiscale Models for Poisson Processes},
  author={E. Kolaczyk},
  journal={Journal of the American Statistical Association},
  year={1999},
  volume={94},
  pages={920-933}
}
  • E. Kolaczyk
  • Published 1999
  • Mathematics
  • Journal of the American Statistical Association
  • Abstract I introduce a class of Bayesian multiscale models (BMSM's) for one-dimensional inhomogeneous Poisson processes. The focus is on estimating the (discretized) intensity function underlying the process. Unlike the usual transform-based approach at the heart of most wavelet-based methods for Gaussian data, these BMSM's are constructed using recursive dyadic partitions (RDP's) within an entirely likelihood-based framework. Each RDP may be associated with a binary tree, and a new multiscale… CONTINUE READING
    129 Citations
    Bayesian Inference on Multiscale Models for Poisson Intensity Estimation: Applications to Photon-Limited Image Denoising
    • 75
    • PDF
    A Bayesian multiscale framework for Poisson inverse problems
    • R. Nowak, E. Kolaczyk
    • Mathematics, Computer Science
    • 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258)
    • 1999
    • 20
    Multiscale Poisson data smoothing
    • 53
    • PDF
    A Class of Multi-Scale Time Series Models
    • 6
    • PDF
    Multi-scale Random Field Models
    • 6
    • PDF
    Photon-limited image denoising by inference on multiscale models
    • 6
    • PDF
    Reconstruction in emission tomography via a Bayesian multiscale statistical framework
    Bayesian Methods and Extensions for the Two State Markov Modulated Poisson Process
    • 14
    Bayesian Multiscale Smoothing of Gaussian Noised Images
    • 8
    • PDF

    References

    SHOWING 1-10 OF 29 REFERENCES
    Multiscale representations of Markov random fields
    • 153
    • PDF
    Wavelet thresholding via a Bayesian approach
    • 601
    • PDF
    Multiscale Modeling and Estimation of Poisson Processes with Application to Photon-Limited Imaging
    • 178
    • PDF
    Adaptive Bayesian Wavelet Shrinkage
    • 592
    • PDF
    Wavelet analysis and synthesis of fractional Brownian motion
    • P. Flandrin
    • Mathematics, Computer Science
    • IEEE Trans. Inf. Theory
    • 1992
    • 912
    Multiple shrinkage and subset selection in wavelets
    • 291
    • PDF