dsimpostppt: Posterior projected Polya Tree distribution

Description

Performs posterior inference for a given a circular dataset with the Projected Polya Tree via a MCMC algorithm.

Usage

dsimpostppt(datafile,units = c("radians", "degrees", "hours"),
mm = 4, mu = c(0, 0), sig = 1, aa = 1, delta = 1.1,
it = 500, bi = 50, ti = 2, kapa = 0.5, ha = 0, hm = 0,
c0 = 1, c1 = 2, iota = 6, mu0 = 0, taum = 1, control.circular = list())

Value

An object of class postppt.circ whose underlying structure is a list containing the following components:

x: points where the density is evaluated.
predictive: predicitive density estimated with the projected Polya tree.
quantile2.5 quantile97.5: lower and upper 95% credible interval limits.
stats: descriptive statistics: mean direction and concentration of each MCMC density.
cpo: conditional predictive ordinate statistic for the data.
LMPL: logarithm of the pseudo marginal likelihood statistic.
aa.sims: vector of simulated alphas when ha=1.
mu.sims: matrix of simulated bivariate means when hm=1.
acceptancerate: Acceptance rate of MH step for the latent resultants.
acceptancerate_aa: Acceptance rate of MH step for alpha.
data: original dataset.

Arguments

datafile: the data from which the estimate is to be computed. The object is circular or will be coerced to circular.
units: units of the support: "radians", "degrees" or "hours".
mm: number of finite levels of the Polya tree
mu: mean vector of the projected bivariate normal centering distribution.
sig: precision of the projected bivariate normal centering distribution.
aa: alpha. Standard deviation parameter of the projected Polya tree.
delta: controls of the speed at which the variances of the branching probabilities move down in the tree, rho(m)=m^delta.
it: number of iterations for MCMC.
bi: number of burn in iterations for MCMC.
ti: thinning parameter of the MCMC chain.
kapa: tunning parameter in the MH proposal distribution for the latent resultants R.
ha: logical. If TRUE alpha will be assigned Ga(c0,c1) hyper-prior distribution.
hm: logical. If TRUE mu will be assigned N(mu0,taum) independent hyper-prior distributions for each coordinate.
c0, c1: shape and rate hyper-parameters of the gamma prior distribution for alpha. These will be used only when ha=1.
iota: tunning parameter in the MH proposal distribution for alpha.
mu0, taum: mean and precision hyper-parameters of the independent normal prior distribution for each coordinate of mu. These will be used only when hm=1.
control.circular: the attribute used to coerced the resulting. object. See circular.

References

Nieto-Barajas, L.E. & Nunez-Antonio, G. (2019). Projected Polya tree. https://arxiv.org/pdf/1902.06020.pdf

Examples

Run this code

data(tapir)
#It is advised to increase the number of iterations for a better fitting
z1 <- dsimpostppt(tapir, units = "radians", it = 5, ti =1, bi=0, ha = 1, hm =1)
class(z1)
length(z1$acceptancerate)
z1$acceptancerate
# \donttest{
postppt.summary(z1)
postppt.plot(z1, plot.type= "line" , ylim = c(0,0.8))
# }