seqMC: seqMC creates a seqMC object

Description Usage Arguments Value Examples

View source: R/seqMC.R

Description

seqMC creates a seqMC object

Usage

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seqMC(f, logprob_y_given_x, x0, y0, sample_method = c("systematic",
  "residual", "bootstrap"))

Arguments

f

function, when called with parameter t (time point) and x_t (state vector at time t), it would return x_(t+1)

logprob_y_given_x

function, when called with parameter t (time point), y_t (observation vector at time t) and x_t (state vector at time t), it would return the conditional log_probability: log(Prob(y_t | x_t ))

x0

matrix, sample of state vector at time 0, each col is a sample of state at time 0.

y0

observation at time 0 (can be missing).

sample_method

character, specify sample method in the resample stage. Default systematic, means "systematic resampling".

Value

a seqMC object, which can be updated at each time point. e.g. obj = update(ojb, y)

Examples

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f <- function(t, x) {
 0.5 * x + 25 * x / (1 + x * x) + 8.0 * cos(1.2 * (t-1)) + rnorm(length(x), sd=sqrt(10.0))
}

logprob_y_given_x <- function(t, y, x) {
	 as.numeric(-(y - x * x / 20.0)**2/2.0)
}

x0 = matrix(rnorm(4000, sd=2), nrow=1, ncol=4000)

mod = seqMC(f, logprob_y_given_x, x0)

### simulate true path ###
x0 = 0.1
T = 50
x = rep(0.0, T)
x[1] = f(0, x0)
for (t in 1:(T-1)) {
	 x[t+1] = f(t, x[t])
}
y = x * x / 20 + rnorm(length(x))

### estimate the posterior of state vector given y[t] ####
xhat = sapply(1:T, function(t) {
   mod <<- update(mod, y[t])
   estimate.seqMC(mod)
})

plot(x, ylim=c(-40, 40), pch='*')
lines(xhat[1,])
lines(xhat[2,], lty='dotted')
lines(xhat[3,], lty='dotted')

chuanwen/seqMC documentation built on June 26, 2017, 7:35 p.m.