Estfun: Parameter estimation for some two dimensional diffusions.
In BIPOD: BIPOD (Bayesian Inference for Partially Observed diffusions)

Description Usage Arguments Details Value Author(s) Examples

View source: R/Estfun.r

Applies a Gibbs sampler to parameters and augmented data for two-dimensional stochastic differential equations. Currently the Ornstein-Uhlenbeck, the stochastic FitzHugh-Nagumo model and the extended FitzHugh-Nagumo model are implemented.

Estfun(data, Delta, ImputeN = 5, seed, GibbsN = 1000,
       parKnown = list(), Start = c(0,0,0,0,1,1), diffPriorMean,
       diffPriorCovar, diffRW=diag(2), LatentPathStart,Model = NULL,
       driftPriorMean, driftPriorCovar, driftRW, LatentMeanY0 = 0,
       LatentVarY0 = 1, RWrhoPaths = 1, RWrho2PathPoints = 1)

`data`	Data to estimate parameters from. Matrix or numeric. Dimensions must be n1 or n2 depending on whether second coordinate is observed.
`Delta`	Positive numeric: Time between observations.
`ImputeN`	Positive integer>=3: M-2 is the number of imputed data points between consecutive observed data.
`seed`	Positive integer giving the seed for the random number generator. Defaults to random.
`GibbsN`	Positive integer: Number of iterations of the Gibbs sampler.
`parKnown`	List of named values for the known drift and diffusion parameters.
`Start`	Numerical vector with starting values for the drift and diffusion parameters in the Gibbs sampler.
`diffPriorMean`	numerical vector of length 2. Prior mean for diffusion coefficients
`diffPriorCovar`	2*2 matrix. Prior variance for diffusion coefficients.
`diffRW`	Random walk variance for the MH step for the diffusion ocefficients.
`LatentPathStart`	Numeric of length one or same length as Data. Starting value for the latent path. If LatentPathStart is a single number then all starting values take this value.
`Model`	Charater, specifying the model. Currently the only options are 'OU','FHN' and 'FHN5'.
`driftPriorMean`	prior mean for the drift parameters
`driftPriorCovar`	Prior covariance for the drift parameters
`driftRW`	Covariance matrix for the RW update of the drift parameters
`LatentMeanY0`	Prior mean for the first data point of the unobserved coordinate.
`LatentVarY0`	Prior variance for the first data point of the unobserved coordinate. If 0, the point is fixed at first value of LatentPathStart.
`RWrhoPaths`	Numeric in [0,1]. Parameter for random walk update of the latent path between observation times. The value 0 samples a BB, the value 1 keeps the current value of the (skeleton) path
`RWrho2PathPoints`	Parameter for random walk update of the latent coordinate at observation times. The value 0 samples a middle point of a BB, the value 1 keeps the current value of the points

More details for the help page will be added soon.

An object of class BIPOD.

`Drift`	Output of the Gibbs sampler for the drift parameters.
`Diff`	Output of the Gibbs sampler for the diffusion parameters.
`AccRate1`	Accept/reject (1/0) for each path interval and each iteration of the sampler.
`AccRate2`	Accept/reject (1/0) for each path endpoint of the latent coordinate and each iteration of the sampler. Only valid if second coordinate is latent.
`LatentPath`	Output of the Gibbs sampler for the endpoints of the latent path. Only valid when one coordinate is observed.
`diffAcc`	Accept/reject (1/0) for the MH step of the diffusion coefficient.
`Info`	List with information about the estimated model.
`driftPriormu`	Prior mean of the drift parameters.
`driftPriorOmega`	Prior variance in the drift parameters.
`driftRW`	Random Walk variance for updating drift parameters.

Anders Chr. Jensen

Data <- DiffSim(n=5000,
                start=c(0,0),
                Delta=.001,
                driftpar=c(10,5,1.5,.6),
                Sigma=diag(c(.5,.3)),
                seed=1,
                thin=100,
                Model="FHN")

A <- Estfun(data    = Data[,1],
            Delta   = .001*100,
            ImputeN = 5,
            seed    = 2,
            GibbsN  = 500,
            parKnown = list("drift3"=1.5,"drift4"=.6,"diff2"=.3),
            Start=c(10,10,10,10,1,1),
            diffPriorMean= c(0,0),
            diffPriorCovar= diag(2),
            diffRW = diag(c(.01,.02)),
            LatentPathStart = .5,
            Model="FHN",
            driftPriorMean = NULL,
            driftPriorCovar = NULL,
            driftRW = diag(4),
            LatentMeanY0 = 0,
            LatentVarY0 = 1,
            RWrhoPaths = 0,
            RWrho2PathPoints = 0)

class(A);names(A)
plot(A,type="trace",interval=1,theta=c(10,5,1.5,.6,.5,.3),subset=c(1,2,5))
### plot(A,type="movie",truepath=Data[,2],speed=.01,BY=10,interval=1)