Limits of uncertainty about estimates of probability of ecological events
Author and article information
Abstract
Probability (P) of binomial event is a commonly estimated quantity in ecology. Recently, interest has moved to estimation and communication of the associated uncertainty about the estimates of P. Here I use the principle of maximum entropy to introduce truncated exponential probability density function f(P) on a closed interval [0,1] that gives expectation of the uncertainty, given that the only information we have is a single-number estimate Psingle, which I assume to represent mean μ of an unknown probability density distribution of P. This expectation puts an upper bound on the maximum uncertainty about P. I also present the associated cumulative distribution function, quantile function, and random number generator. I demonstrate the MaxEnt f(P) on a species distribution model predicting probability of a species' occurrence on a geographic map. The MaxEnt f(P) presented here can be used to make conservative probabilistic statements about probability statements, and it can be used as an alternative to beta distribution, and as the least informative prior distribution of P in Bayesian modelling.
Cite this as
2014. Limits of uncertainty about estimates of probability of ecological events. PeerJ PrePrints 2:e446v1 https://doi.org/10.7287/peerj.preprints.446v1Author comment
This is the first version of the manuscript. It has not been submitted to any journal yet.
Sections
Supplemental Information
Supplement S1: A .pdf document containing R code of the probability density function, cumulative distribbution function, quantile function and random number generator
This is .pdf intended mostly for printing purposes. An identical raw-text version of these codes is also provided in Supplement S2.
Supplement S2: All source codes and raw data used for the study
This .zip file contains all the raw data and codes (with detailed comments) used for this study. Specifically, there are: (1) .html, .md and .rmd versions of the source code. The .html file is most user friendly (just open in a web browser). The .rmd file can be opened by R-studio (and compiled by Knitr). (2) ESRI raster file of the mean annual temperature of the Czech Republic region (from WorldClim), (3) shapefile of the Czech Republic boundaries, (4) .txt file containing the JAGS model description, (4) complete LaTeX codes of the main text, including all of the .pdf vesrions of the figures.
Additional Information
Competing Interests
The author has no competing interest.
Author Contributions
Petr Keil conceived and designed the experiments, performed the experiments, analyzed the data, wrote the paper, prepared figures and/or tables, reviewed drafts of the paper.
Grant Disclosures
The following grant information was disclosed by the authors:
European Union's Seventh Framework Programme (FP7/2007-2013) under REA Grant agreement no. 302868.
Funding
The research leading to these results has received funding from People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme (FP7/2007-2013) under REA Grant agreement no. 302868. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
