bsad {bsamGP}  R Documentation 
This function fits a semiparametric model, which consists of parametric and nonparametric components, for estimating density using a logistic Gaussian process.
bsad(x, xmin, xmax, nint, MaxNCos, mcmc = list(), prior = list(),
smoother = c('geometric', 'algebraic'),
parametric = c('none', 'normal', 'gamma', 'laplace'), marginal.likelihood = TRUE,
verbose = FALSE)
x 
a vector giving the data from which the density estimate is to be computed. 
xmin 
minimum value of x. 
xmax 
maximum value of x. 
nint 
number of grid points for plots (need to be odd). The default is 201. 
MaxNCos 
maximum number of Fourier coefficients. 
mcmc 
a list giving the MCMC parameters.
The list includes the following integers (with default values in parentheses):

prior 
a list giving the prior information. The list includes the following parameters
(default values specify the noninformative prior):

smoother 
types of smoothing priors for Fourier coefficients. See Details. 
parametric 
specifying a distribution of the parametric part to be test. 
marginal.likelihood 
a logical variable indicating whether the log marginal likelihood is calculated. 
verbose 
a logical variable. If 
This generic function fits a semiparametric model, which consists of parametric and nonparametric, for density estimation (Lenk, 2003):
f(x  \beta, Z) = \frac{\exp[h(x)^\top\beta + Z(x)]}{\int_\mathcal{X} \exp[h(y)^\top\beta + Z(y)]dG(y)}
where Z
is a zero mean, secondorder Gaussian process with bounded, continuous covariance function. i.e.,
E[Z(x), Z(y)] = \sigma(x,y), \quad \int_\mathcal{X}ZdG = 0 ~~(a.s.)
Using the KarhunenLoeve Expansion, Z
is represented as infinite series with random coefficients
Z(x) = \sum_{j=1}^\infty \theta_j\varphi_j(x),
where \{\varphi_j\}
is the cosine basis, \varphi_j(x)=\sqrt{2}\cos[j\pi G(x)]
.
For the random Fourier coefficients of the expansion, two smoother priors are assumed (optional),
\theta_j  \tau, \gamma \sim N(0, \tau^2\exp[j\gamma]), ~ j \ge 1 ~ (geometric ~smoother)
\theta_j  \tau, \gamma \sim N(0, \tau^2\exp[ln(j+1)\gamma]), ~ j \ge 1 ~ (algebraic ~smoother)
The coefficient \beta
have the popular normal prior,
\beta  m_{0,\beta}, V_{0,\beta} \sim N(m_{0,\beta}, V_{0,\beta})
To complete the model specification, independent hyper priors are assumed,
\tau^2  r_0, s_0 \sim IGa(r_0/2, s_0/2)
\gamma  w_0 \sim Exp(w_0)
Note that the posterior algorithm is based on computing a discrete version of the likelihood over a fine mesh on \mathcal{X}
.
An object of class bsad
representing the Bayesian spectral analysis density estimation model fit.
Generic functions such as print
, fitted
and plot
have methods to show the results of the fit.
The MCMC samples of the parameters in the model are stored in the list mcmc.draws
,
the posterior samples of the fitted values are stored in the list fit.draws
, and
the MCMC samples for the log marginal likelihood are saved in the list loglik.draws
.
The output list also includes the following objects:
post.est 
posterior estimates for all parameters in the model. 
lmarg 
log marginal likelihood. 
ProbProbs 
posterior probability of models. 
call 
the matched call. 
mcmctime 
running time of Markov chain from 
Jo, S., Choi, T., Park, B. and Lenk, P. (2019). bsamGP: An R Package for Bayesian Spectral Analysis Models Using Gaussian Process Priors. Journal of Statistical Software, 90, 310320.
Lenk, P. (2003) Bayesian semiparametric density estimation and model verification using a logistic Gaussian process. Journal of Computational and Graphical Statistics, 12, 548565.
## Not run:
############################
# Old Faithful geyser data #
############################
data(faithful)
attach(faithful)
# mcmc parameters
mcmc < list(nblow = 10000,
smcmc = 1000,
nskip = 10,
ndisp = 1000,
kappaloop = 5)
# fits BSAD model
fout < bsad(x = eruptions, xmin = 0, xmax = 8, nint = 501, mcmc = mcmc,
smoother = 'geometric', parametric = 'gamma')
# Summary
print(fout); summary(fout)
# fitted values
fit < fitted(fout)
# predictive density plot
plot(fit, ask = TRUE)
detach(faithful)
## End(Not run)