BIPOD (version 0.2.1)

Estfun: Parameter estimation for some two dimensional diffusions.

Description

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.

Usage

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)

Arguments

data

Data to estimate parameters from. Matrix or numeric. Dimensions must be n*1 or n*2 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

Value

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.

Details

More details for the help page will be added soon.

Examples

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)