DiffusionRgqd (version 0.1.3)

GQD.dic: Summarize MCMC Selection Output for a List of GQD.mcmc or BiGQD.mcmc objects.

Description

GQD.dic() summarizes the MCMC output from a list of GQD.mcmc() objects. This may be used to neatly summarize the MCMC output of various models fitted to a given dataset.

Usage

GQD.dic(model.list, type = "col")

Arguments

model.list

A list of GQD.mcmc() objects.

type

Shoould output be of row ('row') or column ('col') format.

Value

Details

GQD.dic() summarizes the output from various models fitted via GQD.mcmc(). By ranking them according to DIC. [=] indicates which model has the minimal DIC.

	Elapsed_Time	Time_Homogeneous	p	DIC	pD
N	Model 1	00:00:47	No	5.00	389.30
3.92	201	Model 2	00:01:00	No	5.00
[=]386.45	4.13	201	Model 3	00:02:50	No
5.00	391.37	3.94	201		Elapsed_Time

References

Updates available on GitHub at https://github.com/eta21.

See Also

GQD.mcmc

Examples

#===============================================================================
# Simulate a time inhomogeneous diffusion.
#-------------------------------------------------------------------------------

 data(SDEsim1)
 attach(SDEsim1)
 par(mfrow=c(1,1))
 expr1=expression(dX[t]==2*(5+3*sin(0.5*pi*t)-X[t])*dt+0.5*sqrt(X[t])*dW[t])
 plot(Xt~time,type='l',col='blue',xlab='Time (t)',ylab=expression(X[t]),main=expr1)


 #------------------------------------------------------------------------------
 # Define coefficients of model 1
 #------------------------------------------------------------------------------

  # Remove any existing coeffients. If none are pressent NAs will be returned, but
  # this is a safeguard against overlapping.
    GQD.remove()

  # Define time dependant coefficients. Note that all functions have a single argument.
  # This argument has to be `t' in order for the dependancy to be recognized.
  # theta does not have to be defined as an argument.

  G0 <- function(t){theta[1]*(theta[2]+theta[3]*sin(0.25*pi*t))}
  G1 <- function(t){-theta[1]}
  Q0 <- function(t){theta[4]*theta[4]}

  theta.start   <-  c(1,1,1,1)                     # Starting values for the chain
  proposal.sds  <-  c(0.8,0.1,0.1,0.1)             # Std devs for proposal distributions
  mesh.points   <-  10                             # Number of mesh points
  updates       <-  50000                          # Perform 50000 updates

  priors=function(theta){dnorm(theta[1],5,5)}
  m1 <- GQD.mcmc(Xt,time,mesh=mesh.points,theta=theta.start,sds=proposal.sds,
                 updates=updates)

 
 #------------------------------------------------------------------------------
 # Define coefficients of model 2
 #------------------------------------------------------------------------------

  GQD.remove()
  G0 <- function(t){theta[1]*(theta[2]+theta[3]*sin(0.25*pi*t))}
  G1 <- function(t){-theta[1]}
  Q1 <- function(t){theta[4]*theta[4]}

  proposal.sds  <-  c(0.8,0.1,0.1,0.1)
  m2 <- GQD.mcmc(Xt,time,mesh=mesh.points,theta=theta.start,sds=proposal.sds,
                 updates=updates)

  # Checkthe parameter estimates:
  GQD.estimates(m2,thin = 200)
 #------------------------------------------------------------------------------
 # Summarize the output from the models.
 #------------------------------------------------------------------------------

 GQD.dic(list(m1,m2))
 
#===============================================================================