predict-est.mixedDiffusion-method: Prediction for a hierarchical (mixed) diffusion process model

In SimoneHermann/BaPreStoPro: Bayesian Prediction of Stochastic Processes

Description

Bayesian prediction of a stochastic process model dY_t = b(φ_j,t,Y_t)dt + γ \widetilde{s}(t,Y_t)dW_t, φ_j~N(μ, Ω).

Usage

## S4 method for signature 'est.mixedDiffusion'
predict(object, t, Euler.interval = FALSE,
  level = 0.05, burnIn, thinning, b.fun.mat, which.series = c("new",
  "current"), y.start, ind.pred, M2pred = 10, cand.length = 1000,
  pred.alg = c("Distribution", "Trajectory", "simpleTrajectory",
  "simpleBayesTrajectory"), sample.length, grid, plot.prediction = TRUE)

Arguments

object	class object of MCMC samples: "est.mixedDiffusion", created with method estimate,mixedDiffusion-method
t	vector of time points to make predictions for
Euler.interval	if TRUE: simple prediction intervals with Euler are made (in one step each)
level	level of the prediction intervals
burnIn	burn-in period
thinning	thinning rate
b.fun.mat	matrix-wise definition of drift function (makes it faster)
which.series	which series to be predicted, new one ("new") or further development of current one ("current")
y.start	optional, if missing, first (which.series = "new") or last observation variable ("current") is taken
ind.pred	index of series to be predicted, optional, if which.series = "current" and ind.pred missing, the last series is taken
M2pred	optional, if current series to be predicted and t missing, M2pred variables will be predicted with the observation time distances
cand.length	length of candidate samples (if method = "vector")
pred.alg	prediction algorithm, "Distribution", "Trajectory", "simpleTrajectory" or "simpleBayesTrajectory"
sample.length	number of samples to be drawn, default is the number of posterior samples
grid	fineness degree of sampling approximation
plot.prediction	if TRUE, prediction intervals are plotted

References

Hermann, S. (2016a). BaPreStoPro: an R Package for Bayesian Prediction of Stochastic Processes. SFB 823 discussion paper 28/16.

Hermann, S. (2016b). Bayesian Prediction for Stochastic Processes based on the Euler Approximation Scheme. SFB 823 discussion paper 27/16.

Examples

mu <- 2; Omega <- 0.4; phi <- matrix(rnorm(21, mu, sqrt(Omega)))
model <- set.to.class("mixedDiffusion",
         parameter = list(phi = phi, mu = mu, Omega = Omega, gamma2 = 0.1),
         b.fun = function(phi, t, x) phi*x, sT.fun = function(t, x) x)
t <- seq(0, 1, by = 0.01)
data <- simulate(model, t = t)
est_mixdiff <- estimate(model, t, data[1:20,], 100) # nMCMC should be much larger
plot(est_mixdiff)
## Not run: 
pred_mixdiff <- predict(est_mixdiff, b.fun.mat = function(phi, t, y) phi[,1]*y)
lines(t, data[21,], lwd = 2)
mean(apply(pred_mixdiff$Y, 2, quantile, 0.025) <= data[21, ] &
apply(pred_mixdiff$Y, 2, quantile, 0.975) >= data[21, ])
mean(sapply(1:20, function(i){
   mean(apply(pred_mixdiff$Y, 2, quantile, 0.025) <= data[i, ] &
   apply(pred_mixdiff$Y, 2, quantile, 0.975) >= data[i, ])}))
pred_mixdiff2 <- predict(est_mixdiff, b.fun.mat = function(phi, t, y) phi[,1]*y,
     which.series = "current")
pred_mixdiff3 <- predict(est_mixdiff, b.fun.mat = function(phi, t, y) phi[,1]*y,
     which.series = "current", y.start = data[20, 51], t = t[51:101])

## End(Not run)
pred_mixdiff <- predict(est_mixdiff, Euler.interval = TRUE,
     b.fun.mat = function(phi, t, y) phi[,1]*y); lines(t, data[21,], lwd = 2)
     # one step Euler approximation
pred_mixdiff <- predict(est_mixdiff, pred.alg = "simpleTrajectory",
                        sample.length = 100)
for(i in 1:100) lines(t, pred_mixdiff$Y[i,], col = "grey")
pred_mixdiff <- predict(est_mixdiff, pred.alg = "simpleBayesTrajectory")

# OU
## Not run: 
b.fun <- function(phi, t, y) phi[1]-phi[2]*y; y0.fun <- function(phi, t) phi[3]
mu <- c(10, 1, 0.5); Omega <- c(0.9, 0.01, 0.01)
phi <- sapply(1:3, function(i) rnorm(21, mu[i], sqrt(Omega[i])))
model <- set.to.class("mixedDiffusion",
           parameter = list(phi = phi, mu = mu, Omega = Omega, gamma2 = 0.1),
           y0.fun = y0.fun, b.fun = b.fun, sT.fun = function(t, x) 1)
t <- seq(0, 1, by = 0.01)
data <- simulate(model, t = t)
est <- estimate(model, t, data[1:20,], 2000)
plot(est)
pred <- predict(est, t = seq(0, 1, length = 21),
   b.fun.mat = function(phi, t, y) phi[,1]-phi[,2]*y)
lines(t, data[21,], lwd = 2)
mean(apply(pred$Y, 2, quantile, 0.025) <= data[21, seq(1, length(t), length = 21)] &
     apply(pred$Y, 2, quantile, 0.975) >= data[21, seq(1, length(t), length = 21)])
mean(sapply(1:20, function(i){
    mean(apply(pred$Y, 2, quantile, 0.025) <= data[i, seq(1, length(t), length = 21)] &
    apply(pred$Y, 2, quantile, 0.975) >= data[i, seq(1, length(t), length = 21)])}))

## End(Not run)

SimoneHermann/BaPreStoPro documentation built on May 9, 2019, 1:46 p.m.