On the relationship between Bayesian error bars and the input data density

C. K. I. Williams, C. Qazaz, Christopher M. Bishop, H. Zhu

    Research output: Chapter in Book/Published conference outputChapter


    We investigate the dependence of Bayesian error bars on the distribution of data in input space. For generalized linear regression models we derive an upper bound on the error bars which shows that, in the neighbourhood of the data points, the error bars are substantially reduced from their prior values. For regions of high data density we also show that the contribution to the output variance due to the uncertainty in the weights can exhibit an approximate inverse proportionality to the probability density. Empirical results support these conclusions.
    Original languageEnglish
    Title of host publicationFourth International Conference on Artificial Neural Networks, 1995
    Place of PublicationCambridge
    Number of pages6
    ISBN (Print)0852966415
    Publication statusPublished - 26 Jun 1995
    EventProc. Fourth International Conference on Artificial Neural Networks -
    Duration: 26 Jun 199526 Jun 1995

    Publication series

    NameIEE Conference Publication
    PublisherInstitute of Electrical and Electronics Engineers (IEEE)


    ConferenceProc. Fourth International Conference on Artificial Neural Networks

    Bibliographical note

    ©1995 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.


    • Bayes methods
    • neural nets
    • prediction theory
    • ayesian error bars
    • error bars
    • high data densit
    • input data density
    • linear regression models
    • probability density


    Dive into the research topics of 'On the relationship between Bayesian error bars and the input data density'. Together they form a unique fingerprint.

    Cite this