initialize {FVDDPpkg}

Initialize Fleming-Viot dependent Dirichlet Processes by setting hyperparameters

Description

Initialize Fleming-Viot dependent Dirichlet Processes by setting hyperparameters

Usage

initialize(theta, sampling.f, density.f, atomic)

Arguments

theta

The intensity of the centering measure, in the sense of Bayesian Nonparametrics.

sampling.f

A function to sample from the centering. Its unique argument must be the amount of values to be drawn.

density.f

A function to compute the value of the density function or mass function of the centering. It has to be consistent with sampling.f.

atomic

A boolean value stating whether the centering is atomic or not.

Value

A list containing the input (renamed as theta, P0.sample, P0.density, and is.atomic) and three empty slots that will contain the information once the FVDDP is updated with data. In particular, they are:

• y.star: a vector of unique values

• M: a matrix of multiplicities, represented as row vectors

• w: a vector of weights associated to each row of the matrix of multiplicities. Such list repesents a n object of the fvddp class.

References

Papaspiliopoulos O, Ruggiero M (2014). “Optimal filtering and the dual process.” Bernoulli, 20(4). doi:10.3150/13-bej548.

Papaspiliopoulos O, Ruggiero M, Spanò D (2016). “Conjugacy properties of time-evolving Dirichlet and gamma random measures.” Electronic Journal of Statistics, 10(2), 3452 – 3489. doi:10.1214/16-EJS1194.

Examples

#initiization with an atomic measure (Pois(3))
initialize(theta = 1, sampling.f = function(x) rpois(x, 3),
           density.f = function(x) dpois(x, 3), atomic = TRUE)

#initialization with a non-atomic measure (N(-1, 3))
initialize(theta = 3, sampling.f = function(x) rnorm(x, -1, 3),
           density.f = function(x) dnorm(x, -1, 3), atomic = FALSE)