adaBayes | R Documentation |
The adabayes.mcmc
class is a class of the yuima package that extends the mle-class
.
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)
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 |
|
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 |
algorithm |
If |
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 |
rho |
A parameter used for MpCN algorithm. |
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.
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.
algorithm = nomcmc
is unstable.
Kengo Kamatani with YUIMA project Team
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).
## 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)
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