IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v55y2011i3p1180-1195.html
   My bibliography  Save this article

Indirect density estimation using the iterative Bayes algorithm

Author

Listed:
  • Ma, Jun

Abstract

Many practical problems involve density estimation from indirect observations and they are classified as indirect density estimation problems. For example, image deblurring and image reconstruction in emission tomography belong to this class. In this paper we propose an iterative approach to solve these problems. This approach has been successfully applied to emission tomography (Ma, 2008). The popular EM algorithm can also be used for indirect density estimation, but it requires that observations follow Poisson distributions. Our method does not involve such assumptions; rather, it is established simply from the Bayes conditional probability model and is termed the Iterative Bayes (IB) algorithm. Under certain regularity conditions, this algorithm converges to the positively constrained solution minimizing the Kullback-Leibler distance, an asymmetric measure involving both logarithmic and linear scales of dissimilarities between two probability distributions.

Suggested Citation

  • Ma, Jun, 2011. "Indirect density estimation using the iterative Bayes algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1180-1195, March.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:3:p:1180-1195
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(10)00361-0
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Qian, Zhiguang & Shapiro, Alexander, 2006. "Simulation-based approach to estimation of latent variable models," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1243-1259, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Crucinio, Francesca R. & De Bortoli, Valentin & Doucet, Arnaud & Johansen, Adam M., 2024. "Solving a class of Fredholm integral equations of the first kind via Wasserstein gradient flows," Stochastic Processes and their Applications, Elsevier, vol. 173(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      Corrections

      All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:55:y:2011:i:3:p:1180-1195. See general information about how to correct material in RePEc.

      If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

      If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

      For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

      Please note that corrections may take a couple of weeks to filter through the various RePEc services.

      IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.