NGSSEML (version 1.0)

SmoothingF: Smoothing Distribution (Procedure) of the Latent States

Description

The function SmoothingF gives an exact sample of the posterior distribution of the latent states condiotinal on the static parameters or marginal.

Usage

SmoothingF(formula,data,na.action="na.omit",pz=NULL,nBreaks=NULL,
 model="Poisson",StaPar=NULL,Type="Cond",a0=0.01,b0=0.01,
 amp=FALSE,samples=1,ci=0.95,splot=FALSE)

Arguments

formula

an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted.

data

a data frame containing the variables in the model. The variables are: - the time series of interest Yt (first column of the data frame). the explanatory time series to be inserted in the model. - Xt must be always specified as a matrix of order n by p (after Yt). - the explanatory time series to be inserted in the mean of volatility model. Zt must be always specified as a matrix of order n by p (after Xt). - a censoring indicator of the event (a vector), only for the PEM. If the model is the PEM, put the variable Event in the secon column of tha data frame after Yt, and he explanatory time series after the variable Event. The value 1 indicates failure.

na.action

a function which indicates what should happen when the data contain NAs. The default is set by the na.action setting of options, and is na.fail if that is unset. Optional argument.

pz

the number of the explanatory time series to be inserted in the mean of volatility model. Default: NULL. Optional argument.

nBreaks

the number of breaks used to build a vector with the interval limits, only for the PEM. Optional argument.

model

the chosen model for the observations. The options are: Poisson, Normal, Gamma, Weibull, Generalized Gamma, Laplace, GED and PEM models.

StaPar

a numeric vector of initial values for the static parameters. Optional argument.

Type

the chosen distribution of the lantent states. There are 2 options: conditional on the static parameters and marginal ("Marg"). The default is conditional ("Cond").

a0

the shape parameter of the initial Gamma distribution. Optional argument. DDefault: a0=0.01.

b0

the scale parameter of the initial Gamma distribution. Optional argument. Default: b0=0.01.

amp

the interval width is taken in account in the estimation of parameter w which controls the loss of information over time, only for the PEM. For more details see Santos et al. (2017). Default: FALSE. Optional argument.

samples

the number of samples drawn from the joint posterior distribution of the latent states, given a point of the static parameters (StaPar). Optional argument. Default: samples = 1.

ci

the nominal level of confidence interval for the parameters. Optional argument. Default: ci=0.95.

splot

Create a plot with the point and interval estimates of the states. Optional argument.

Value

mdata

This function returns an exact sample of the join distribution of the states. If the number of samples is greater than 1, some summaries of the state samples are returned.

Details

Typical usages are

SmoothingF(Ytm~Trend+CosAnnual+SinAnnual+CosSemiAnnual+SinSemiAnnual,
data=data.frame(Ytm,Xtm),model="Poisson",Type="Cond",a0=0.01,b0=0.01,samples=1,ci=0.95)

References

Gamerman, D., Santos, T. R., and Franco, G. C. (2013). A Non-Gaussian Family of State-Space Models with Exact Marginal Likelihood. Journal of Time Series Analysis, 34(6), 625-645.

Santos T. R., Gamerman, D., Franco, G. C. (2017). Reliability Analysis via Non-Gaussian State-Space Models. IEEE Transactions on Reliability, 66, 309-318.

See Also

FilteringF LikeF ngssm.mle ngssm.bayes

Examples

# NOT RUN {
###############################################################################
##
## CLASSICAL ESTIMATION
##
###############################################################################

################################################################################
##
## PEM Example: the GTE data 
##
################################################################################
library(NGSSEML)
data(gte_data)
Ytm=gte_data$V1
Xtm=NULL
Ztm=NULL
model="PEM"
amp=FALSE
Eventm=gte_data$V2        
Breakm=GridP(Ytm, Eventm, nT = NULL)
LabelParTheta=c("w")
StaPar=c(0.73)
a0=0.01
b0=0.01
ci=0.95
fit=ngssm.mle(Ytm~1,data=data.frame(Ytm,Eventm),model=model,StaPar=StaPar,
nBreaks=NULL,amp=amp,a0=a0,b0=b0,ci=ci,LabelParTheta=LabelParTheta)
estopt=fit[[1]][1]
set.seed(10)
MeanSmooth=SmoothingF(Ytm~1,data=data.frame(Ytm,Eventm),model=model,
a0=0.01,b0=0.1,amp=FALSE,samples=1000,ci=0.95,splot=FALSE,StaPar=estopt) 

#Smoothing:
set.seed(1000)
fits=SmoothingF(Ytm~1,data=data.frame(Ytm,Eventm),model=model,Type="Cond",
a0=0.01,b0=0.1,ci=0.95,samples=1,splot=FALSE,StaPar=estopt)
##PlotF function:
PlotF(Ytm~1,data=data.frame(Ytm,Eventm),model=model,plotYt=FALSE,
axisxdate=Breakm[1:17],Proc="Smooth",Type="Cond",distl="Filter",a0=0.01,b0=0.1,
ci=0.95,posts=estopt,Typeline='s',
cols=c("black","blue","lightgrey"),xxlab="Time to Failure (Days)",yylab="Failure rate",
yylim=c(0,0.008),xxlim=c(0,139),Lty=c(1,2,1),Lwd=c(2,2,2),Cex=0.68)

###############################################################################
##
## BAYESIAN ESTIMATION
##
###############################################################################

###############################################################################
##PEM
##GTE Data
###############################################################################
#library(NGSSEML)
### Inputs: 
data(gte_data)
Ytm=gte_data$V1
Eventm=gte_data$V2   
Breakm=GridP(Ytm, Eventm, nT = NULL)
Xtm=NULL
Ztm=NULL
model="PEM"
amp=FALSE
LabelParTheta=c("w")
StaPar=c(0.73)
p=length(StaPar)
nn=length(Breakm)
a0=0.01
b0=0.1
p=length(StaPar)
pointss=5    ### points
nsamplex=100 ## Multinomial sampling posterior
ci=0.95
alpha=1-ci
#Fit:
#Bayesian:
fitbayes=ngssm.bayes(Ytm~1,data=data.frame(Ytm,Eventm),model=model,
pz=NULL,StaPar=StaPar,amp=amp,a0=a0,b0=b0,prw=c(1,1),prnu=NULL,prchi=NULL,
prmu=NULL,prbetamu=NULL,prbetasigma=NULL,ci=ci,pointss=pointss,nsamplex=nsamplex,
postplot=FALSE,contourplot=FALSE,LabelParTheta=LabelParTheta)
posts=fitbayes[[2]]
#Smoothing:
set.seed(1000)
fits=SmoothingF(Ytm~1,data=data.frame(Ytm,Eventm),model=model,pz=NULL,
StaPar=posts,Type="Marg",a0=a0,b0=b0,ci=ci,samples=1,splot=FALSE)
###############################################################################
 
# }