Package BysPrior

BysPriorInf stands for Bayesian Prior Information and allows to define prior information handlers to be used in estimation systems (max-likelihood and bayesian ones).

A prior is a distribution function over a subset of the total set of variables of a model that expresses the knowledge about the phenomena behind the model.

The effect of a prior is to add the logarithm of its likelihood to the logarithm of the likelihood of the global model. So it can be two or more priors over some variables. For example, in order to stablish a truncated normal we can define a uniform over the feasible region and an unconstrainined normal.

In order to be estimated with NonLinGloOpt (max-likelihood) and BysSampler (Bayesian sampler), each prior must define methods to calculate the logarithm of the likelihood (except an additive constant), its gradient and its hessian, and an optional set of constraining inequations, in order to define the feasible region. Each inequation can be linear or not and the gradient and hessian must be also calculated. Note that this implies that priors should be continuous and two times differentiable but this an admisible restricion in almost all cases.

Non informative priors

Let a uniform random variable in a region which likelihood function is

Since the logarithm of the likelihood but a constant is zero, when log-likelihood is not defined for a prior, the default assumed will be the uniform distribution, also called non informative prior.

Domain prior

The easiest way, but one of the most important, to define non informative prior information is to stablish a domain interval for one or more variables.

In this cases, you mustn't to define the log-logarithm nor the constraining inequation functions, but simply it's needed to fix the lower and upper bounds:

Polytope prior

A polytope is defined by a system of arbitrary linear inequalities