IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-642-01039-2_11.html

Probabilistic Knowledge Structures

In: Learning Spaces

Author

Listed:
  • Jean-Claude Falmagne

    (University of California, Irvine, Department of Cognitive Sciences, Institute of Mathematical Behavioral Sciences)

  • Jean-Paul Doignon

    (Université Libre de Bruxelles, Département de Mathématique)

Abstract

The concept of a knowledge structure is a deterministic one. As such, it does not provide realistic predictions of subjects’ responses to the problems of a test. There are two ways in which probabilities must enter in a realistic model. For one, the knowledge states will certainly occur with different frequencies in the population of reference. It is thus reasonable to postulate the existence of a probability distribution on the collection of states. For another, a subject’s knowledge state does not necessarily specify the observed responses. A subject having mastered an item may be careless in responding, and make an error. Also, in some situations, a subject may be able to guess the correct response to a question not yet mastered. In general, it makes sense to introduce conditional probabilities of responses, given the states. A number of simple probabilistic models will be described in this chapter. They will be used to illustrate how probabilistic concepts can be introduced within knowledge space theory. These models will also provide a precise context for the discussion of some technical issues related to parameter estimation and statistical testing. The material in this chapter must be regarded as a preparation for the stochastic theories discussed in Chapters 12, 13 and 14.

Suggested Citation

  • Jean-Claude Falmagne & Jean-Paul Doignon, 2011. "Probabilistic Knowledge Structures," Springer Books, in: Learning Spaces, chapter 11, pages 187-214, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-01039-2_11
    DOI: 10.1007/978-3-642-01039-2_11
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:spr:sprchp:978-3-642-01039-2_11. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.