MFT.rate {MFT}

MFT.rate

Description

The multiple filter test for rate change detection in point processes on the line.

Usage

MFT.rate(Phi, m = 0, cutout = TRUE, autoset.d_H = TRUE, S = NULL,
  E = NULL, d = NULL, H = NULL, alpha = 0.05,
  method = "asymptotic", sim = 10000, rescale = FALSE, Q = NA,
  blocksize = NA, perform.CPD = TRUE, print.output = TRUE)

Arguments

Phi

numeric vector of increasing events, input point process

m

non-negative integer, dependence parameter: serial corellation rho up to order m estimated

cutout

logical, if TRUE for every point, for which the estimated rho becomes negative, the h-neighborhood of G (resp. R) is set to zero. This might only occur, if m > 0

autoset.d_H

logical, automatic choice of window size H and step size d

S

numeric, start of time interval, default: Smallest multiple of d that lies beyond min(Phi)

E

numeric, end of time interval, default: Smallest multiple of d that lies beyond max(Phi), needs E > S.

d

numeric, > 0, step size delta at which processes are evaluated. d is automatically set if autoset.d_H = TRUE

H

vector, window set H, all elements must be increasing ordered multiples of d, the smallest element must be >= d and the largest =< (T/2). H is automatically set if autoset.d_H = TRUE

alpha

numeric, in (0,1), significance level

method

either "asymptotic", "bootstrap" or "fixed", defines how threshold Q is derived, default: "asymptotic", If "asymptotic": Q is derived by simulation of limit process L (Brownian motion); possible set number of simulations (sim), If "bootstrap": Q is derived by (Block)-Bootstrapping; possibly set number of simulations (sim) and blocksize (blocksize), If "fixed": Q may be set manually (Q)

sim

integer, > 0, No of simulations of limit process (for approximation of Q), default = 10000

rescale

logical, if TRUE statistic G is rescaled to statistic R, default = FALSE

Q

numeric, rejection threshold, default: Q is simulated according to sim and alpha.

blocksize

NA or integer >= 1, if method == 'bootstrap', blocksize determines the size of blocks (number of life times) for bootstrapping

perform.CPD

logical, if TRUE change point detection algorithm is performed

print.output

logical, if TRUE results are printed to the console

Value

invisible

M

test statistic

Q

rejection threshold

method

how threshold Q was derived, see 'Arguments' for detailed description

sim

number of simulations of the limit process (approximation of Q)

blocksize

size of blocks (number of life times) for bootstrapping (approximation of Q)

rescale

states whether statistic G is rescaled to R

m

order of respected serial correlation (m-dependence)

CP

set of change points estmated by the multiple filter algorithm, increasingly ordered in time

rate

estimated mean rates between adjacent change points

S

start of time interval

E

end of time interval

Tt

length of time interval

H

window set

d

step size delta at which processes were evaluated

alpha

significance level

cutout

states whether cutout was used (see 'Arguments')

perform.CPD

logical, if TRUE change point detection algorithm was performed

tech.var

list of technical variables with processes Phi and G_ht or R_ht

type

type of MFT which was performed: "rate"

Author(s)

Michael Messer, Stefan Albert, Solveig Plomer and Gaby Schneider

References

Michael Messer, Marietta Kirchner, Julia Schiemann, Jochen Roeper, Ralph Neininger and Gaby Schneider (2014). A multiple filter test for the detection of rate changes in renewal processes with varying variance. The Annals of Applied Statistics 8(4): 2027-67 <doi:10.1214/14-AOAS782>

Michael Messer, Kaue M. Costa, Jochen Roeper and Gaby Schneider (2017). Multi-scale detection of rate changes in spike trains with weak dependencies. Journal of Computational Neuroscience, 42 (2), 187-201. <doi:10.1007/s10827-016-0635-3>

See Also

MFT.variance, MFT.m_est, plot.MFT, summary.MFT, MFT.mean, MFT.peaks

Examples

# Rate change detection in Poisson process 
# with three change points (at t = 250, 600 and 680)
set.seed(0)
Phi1 <- runif(rpois(1,lambda=390),0,250)
Phi2 <- runif(rpois(1,lambda=380),250,600)
Phi3 <- runif(rpois(1,lambda=200),600,680)
Phi4 <- runif(rpois(1,lambda=400),680,1000)
Phi  <- sort(c(Phi1,Phi2,Phi3,Phi4)) 
mft  <- MFT.rate(Phi)
plot(mft)