On small sample Bayesian inference and sequential design for quantal response curves

Tom Leonard and John S. J. Hsu
Additional contact information
Tom Leonard: University of Wisconsin-Madison, Department of Statistics
John S. J. Hsu: University of California, Department of Statistics and Applied Probability

A chapter in Modelling and Prediction Honoring Seymour Geisser, 1996, pp 169-175 from Springer

Abstract: Abstract It is important in many econometric and biological applications to evaluate the effective dose (ED) points in the tails of quantal response curves and the curves according to a sensible criterion. Following Geisser (1971), it seems most sensible to evaluate the posterior mean value function of the response curve, since this also gives predictive probabilities of positive responses across the design region. While plausible, it can be insufficient for small samples to base the calculations upon standard multivariate normal likelihood approximations. Exact determinations, for example, via importance sampling (see Zellner and Rossi, 1984) are needed. Extending Leonard (1982a) it is now also possible to compute the exact posterior distribution of the ED points. These are proposed as “design measures”, since they can be used to sequentially generate further design points. Related procedures (see Leonard, 1982b) yield excellent frequency properties. For example, a total of 40 observations (10 fixed in advance and 30 chosen sequentially) can assess a response curve to 6% accuracy for all design points between the ED60 and ED90 points, with an average of over 90% of the sequentially generated design points falling between the ED60 and ED90 points.

Keywords: Biossay; quantal response curve; posterior mean; effective dose; design measure. (search for similar items in EconPapers)
Date: 1996
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-2414-3_10

Ordering information: This item can be ordered from
http://www.springer.com/9781461224143

DOI: 10.1007/978-1-4612-2414-3_10

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().