E_alpha {BayesTreePrior}

Expected value of the number of bottom nodes in the unrealistic case where we assume that the number of variables and possible splits are infinite (therefore P(T) is not dependent on the design matrix X) and \beta=0 (Case #1).

Description

Expected value of the number of bottom nodes in the unrealistic case where we assume that the number of variables and possible splits are infinite (therefore P(T) is not dependent on the design matrix X) and \beta=0 (Case #1).

Usage

E_alpha(alpha)

Arguments

alpha

base parameter of the tree prior, alpha \in [0,1).

Value

Returns the expected value of the number of bottom nodes.

References

Jolicoeur-Martineau, A. (Currently in revision, expected 2016) Etude d'une loi a priori pour les arbres binaires de regression (Study on the prior distribution of binary regression trees) (Master thesis). UQAM university.

See Also

Var_alpha

Examples

E_alpha(.30)
E_alpha(.45)
E_alpha(.499)
E_alpha(.75)