Kernel probability estimation for binomial and multinomial data
- Published
- Accepted
- Subject Areas
- Statistics
- Keywords
- time series analysis, proportions, binomial data, multinomial data, nonparametric methods, kernel estimation
- Copyright
- © 2015 Jensen
- Licence
- This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, reproduction and adaptation in any medium and for any purpose provided that it is properly attributed. For attribution, the original author(s), title, publication source (PeerJ PrePrints) and either DOI or URL of the article must be cited.
- Cite this article
- 2015. Kernel probability estimation for binomial and multinomial data. PeerJ PrePrints 3:e1156v1 https://doi.org/10.7287/peerj.preprints.1156v1
Abstract
Kernel-based smoothers have enjoyed considerable success in the estimation of both probability densities and event frequencies. Existing procedures can be modified to yield a similar kernel-based estimator of instantaneous probability over the course of a binomial or multinomial time series. The resulting nonparametric estimate can be described in terms of one bandwidth per outcome alternative, facilitating both the understanding and reporting of results relative to more sophisticated methods for binomial outcome estimation. Also described is a method for sample size estimation, which in turn can be used to obtain credible intervals for the resulting estimate given mild assumptions. One application of this analysis is to model response accuracy in tasks with heterogeneous trial types. An example is presented from a study of transitive inference, showing how kernel probability estimates provide a method for inferring response accuracy during the first trial following training. This estimation procedure is also effective in describing the multinomial responses typical in the study of choice and decision making. An example is presented showing how the procedure may be used to describe changing distributions of choices over time when eight response alternatives are simultaneously available.
Author Comment
This preprint is deposited with the intent to submit to PeerJ.
Supplemental Information
Matlab Function & Vignette
A standalone Matlab function, as well as a vignette for performing analysis of the types shown in Figures 2 through 4.