Laplace's Demon

LaplacesDemon, usually referred to as Laplace's Demon, is a contributed R package for Bayesian inference, and is freely available on the Comprehensive R Archive Network (CRAN). Laplace's Demon allows the choice of Laplace Approximation and four MCMC algorithms to update a Bayesian model according to a user-specified model function. The user-specified model function enables Bayesian inference for any model form, provided the user specifies the likelihood. Laplace's Demon also attempts to assist the user by creating and offering R code, based on a previous model update, that can be copy/pasted and executed. Posterior predictive checks and many other features are included as well. Laplace's Demon 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.

Laplace's Demon 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.

The package provides three vignettes: "BayesianInference", "Examples", and "LaplacesDemon". The BayesianInference vignette introduces Bayesian inference to new users of Laplace's Demon. The Examples vignette provides examples of different model forms. And finally, the LaplacesDemon vignette is a tutorial to the software.

There are also screencasts available on YouTube. This should get you started. Enjoy.