adaBayes {yuima}

Adaptive Bayes estimator for the parameters in sde model

Description

The adabayes.mcmc class is a class of the yuima package that extends the mle-class.

Usage

adaBayes(yuima, start, prior, lower, upper, method = "mcmc", iteration = NULL,mcmc,
rate =1, rcpp = TRUE, algorithm = "randomwalk",center=NULL,sd=NULL,rho=NULL,
path = FALSE)

Arguments

yuima

a 'yuima' object.

start

initial suggestion for parameter values

prior

a list of prior distributions for the parameters specified by 'code'. Currently, dunif(z, min, max), dnorm(z, mean, sd), dbeta(z, shape1, shape2), dgamma(z, shape, rate) are available.

lower

a named list for specifying lower bounds of parameters

upper

a named list for specifying upper bounds of parameters

method

"nomcmc" requires package cubature

iteration

number of iteration of Markov chain Monte Carlo method

mcmc

number of iteration of Markov chain Monte Carlo method

rate

a thinning parameter. Only the first n^rate observation will be used for inference.

rcpp

Logical value. If rcpp = TRUE (default), Rcpp code will be performed. Otherwise, usual R code will be performed.

algorithm

If algorithm = "randomwalk" (default), the random-walk Metropolis algorithm will be performed. If algorithm = "MpCN", the Mixed preconditioned Crank-Nicolson algorithm will be performed.

center

A list of parameters used to center MpCN algorithm.

sd

A list for specifying the standard deviation of proposal distributions.

path

Logical value when method = "mcmc". If path=TRUE, then the sample path for each variable will be included in the MCMC object in the output.

rho

A parameter used for MpCN algorithm.

Details

Calculate the Bayes estimator for stochastic processes by using the quasi-likelihood function. The calculation is performed by the Markov chain Monte Carlo method. Currently, the Random-walk Metropolis algorithm and the Mixed preconditioned Crank-Nicolson algorithm is implemented.

Slots

mcmc:

is a list of MCMC objects for all estimated parameters.

accept_rate:

is a list acceptance rates for diffusion and drift parts.

call:

is an object of class language.

fullcoef:

is an object of class list that contains estimated parameters.

vcov:

is an object of class matrix.

coefficients:

is an object of class vector that contains estimated parameters.

Note

algorithm = nomcmc is unstable.

Author(s)

Kengo Kamatani with YUIMA project Team

References

Yoshida, N. (2011). Polynomial type large deviation inequalities and quasi-likelihood analysis for stochastic differential equations. Annals of the Institute of Statistical Mathematics, 63(3), 431-479. Uchida, M., & Yoshida, N. (2014). Adaptive Bayes type estimators of ergodic diffusion processes from discrete observations. Statistical Inference for Stochastic Processes, 17(2), 181-219. Kamatani, K. (2017). Ergodicity of Markov chain Monte Carlo with reversible proposal. Journal of Applied Probability, 54(2).

Examples

## Not run: 
set.seed(123)
b <- c("-theta1*x1+theta2*sin(x2)+50","-theta3*x2+theta4*cos(x1)+25")
a <- matrix(c("4+theta5","1","1","2+theta6"),2,2)
true = list(theta1 = 0.5, theta2 = 5,theta3 = 0.3,
            theta4 = 5, theta5 = 1, theta6 = 1)
lower = list(theta1=0.1,theta2=0.1,theta3=0,
             theta4=0.1,theta5=0.1,theta6=0.1)
upper = list(theta1=1,theta2=10,theta3=0.9,
             theta4=10,theta5=10,theta6=10)
start = list(theta1=runif(1),
             theta2=rnorm(1),
             theta3=rbeta(1,1,1),
             theta4=rnorm(1),
             theta5=rgamma(1,1,1),
             theta6=rexp(1))
yuimamodel <- setModel(drift=b,diffusion=a,state.variable=c("x1", "x2"),solve.variable=c("x1","x2"))
yuimasamp <- setSampling(Terminal=50,n=50*10)
yuima <- setYuima(model = yuimamodel, sampling = yuimasamp)
yuima <- simulate(yuima, xinit = c(100,80),
                  true.parameter = true,sampling = yuimasamp)
prior <-
  list(
    theta1=list(measure.type="code",df="dunif(z,0,1)"),
    theta2=list(measure.type="code",df="dnorm(z,0,1)"),
    theta3=list(measure.type="code",df="dbeta(z,1,1)"),
    theta4=list(measure.type="code",df="dgamma(z,1,1)"),
    theta5=list(measure.type="code",df="dnorm(z,0,1)"),
    theta6=list(measure.type="code",df="dnorm(z,0,1)")
  )
set.seed(123)
mle <- qmle(yuima, start = start, lower = lower, upper = upper, method = "L-BFGS-B",rcpp=TRUE)
print(mle@coef)
center<-list(theta1=0.5,theta2=5,theta3=0.3,theta4=4,theta5=3,theta6=3)
sd<-list(theta1=0.001,theta2=0.001,theta3=0.001,theta4=0.01,theta5=0.5,theta6=0.5)
bayes <- adaBayes(yuima, start=start, prior=prior,lower=lower,upper=upper,
                  method="mcmc",mcmc=1000,rate = 1, rcpp = TRUE,
                   algorithm = "randomwalk",center = center,sd=sd,
                   path=TRUE)
print(bayes@fullcoef)
print(bayes@accept_rate)
print(bayes@mcmc$theta1[1:10])

## End(Not run)