Limits of uncertainty about estimates of probability of ecological events
- Published
- Accepted
- Subject Areas
- Ecology, Statistics, Computational Science
- Keywords
- MCMC, Cumulative distribution function, MaxEnt, exponential, maximum likelihood, species distribution model, quantile function
- Copyright
- © 2014 Keil
- 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
- 2014. Limits of uncertainty about estimates of probability of ecological events. PeerJ PrePrints 2:e446v1 https://doi.org/10.7287/peerj.preprints.446v1
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 \(P_{single}\), which I assume to represent mean \(\mu\) 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.
Author Comment
This is the first version of the manuscript. It has not been submitted to any journal yet.
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.