LaplacesDemon

LaplacesDemon is a contributed R package for Bayesian inference, and is freely available on the Comprehensive R Archive Network (CRAN). Often referred to as Laplace's Demon, LaplacesDemon is a complete environment for Bayesian inference within R.

LaplacesDemon includes dozens of MCMC algorithms, Laplace Approximation with multiple optimization algorithms, scores of examples, dozens of additional probability distributions, numerous MCMC diagnostics, Bayes factors, posterior predictive checks, a variety of plots, elicitation, parameter and variable importance, and numerous additional utility functions. LaplacesDemon seeks to be generalizable and user-friendly to Bayesians, especially Laplacians.

In 1814, Laplace published his "Essai philosophique sur les probabilites", which introduced a mathematical system of inductive reasoning based on probability. In it, the Bayesian interpretation of probability was developed independently by Laplace, much more thoroughly than Bayes, so some "Bayesians" refer to Bayesian inference as Laplacian inference. This is a translation of a quote in the introduction to this work:

"We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes" (Laplace, 1814).

The 'intellect' has been referred to by future biographers as Laplace's Demon. In this quote, Laplace expresses his philosophical belief in hard determinism and his wish for a computational machine that is capable of estimating the universe.

LaplacesDemon is designed without consideration for hard determinism, but instead with a lofty goal toward facilitating high-dimensional Bayesian (or Laplacian) inference, posing as its own intellect that is capable of impressive analysis.

References

• Laplace P (1814). "Essai Philosophique sur les Probabilites." English translation in Truscott, F.W. and Emory, F.L. (2007) from (1902) as "A Philosophical Essay on Probabilities". ISBN 1602063281, translated from the French 6th ed. (1840).