dsimpostppt {PPTcirc}

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())

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.

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.

References

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

See Also

postppt.plot, postppt.summary

Examples

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

postppt.summary(z1)
postppt.plot(z1, plot.type= "line" , ylim = c(0,0.8))