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

In DiffusionRgqd: Inference and Analysis for Generalized Quadratic Diffusions

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.

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

Value

A data frame with summary of model output. See Details.

Author(s)

Etienne A.D. Pienaar: [e-mail]

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))
 
#===============================================================================

DiffusionRgqd documentation built on May 2, 2019, 3:26 a.m.