changepoint (version 0.3)

multiple.meanvar.gamma: Multiple Changes in Mean and Variance - Gamma Data (i.e. change in scale parameter)

Description

Calculates the optimal positioning and number of changepoints for Gamma data using the user specified method.

Usage

multiple.meanvar.gamma(data,shape=1, mul.method="PELT",penalty="SIC",value=0,Q=5,class=TRUE,param.estimates=TRUE)

Arguments

data

A vector or matrix containing the data within which you wish to find a changepoint. If data is a matrix, each row is considered a separate dataset.

shape

Numerical value of the true shape parameter for the data. Either single value or vector of length nrow(data). If data is a matrix and shape is a single value, the same shape parameter is used for each row.

mul.method

Choice of "PELT", "SegNeigh" or "BinSeg".

penalty

Choice of "None", "SIC", "BIC", "AIC", "Hannan-Quinn" and "Manual" penalties. If Manual is specified, the manual penalty is contained in the value parameter.

value

The value of the penalty when using the Manual penalty option. This can be a numeric value or text giving the formula to use. Available variables are, n=length of original data, null=null likelihood, alt=alternative likelihood, tau=proposed changepoint,

Q

The maximum number of changepoints to search for using the "BinSeg" method. The maximum number of segments (number of changepoints + 1) to search for using the "SegNeigh" method.

class

Logical. If TRUE then an object of class cpt is returned.

param.estimates

Logical. If TRUE and class=TRUE then parameter estimates are returned. If FALSE or class=FALSE no parameter estimates are returned.

Value

• If class=TRUE then an object of S4 class "cpt" is returned. The slot cpts contains the changepoints that are solely returned if class=FALSE. The structure of cpts is as follows.

  If data is a vector (single dataset) then a vector/list is returned depending on the value of mul.method. If data is a matrix (multiple datasets) then a list is returned where each element in the list is either a vector or list depending on the value of mul.method.

  If mul.method is PELT then a vector is returned:

• cpt
  Vector containing the changepoint locations for the penalty supplied. This always ends with n.
• If mul.method is SegNeigh then a list is returned with elements:
• cps
  Matrix containing the changepoint positions for 1,...,Q changepoints.
• op.cpts
  The optimal changepoint locations for the penalty supplied.
• like
  Value of the -2*log(likelihood ratio) + penalty for the optimal number of changepoints selected.
• If mul.method is BinSeg then a list is returned with elements:
• cps
  2xQ Matrix containing the changepoint positions on the first row and the test statistic on the second row.
• op.cpts
  The optimal changepoint locations for the penalty supplied.
• pen
  Penalty used to find the optimal number of changepoints.

Details

This function is used to find multiple changes in mean and variance for data that is assumed to be Gamma distributed. The changes are found using the method supplied which can be exact (PELT or SegNeigh) or approximate (BinSeg).

References

Change in Gamma shape parameter: Chen, J. and Gupta, A. K. (2000) Parametric statistical change point analysis, Birkhauser

PELT Algorithm: Killick, R. and Fearnhead, P. and Eckley, I.A. (2011) An exact linear time search algorithm for multiple changepoint detection, Submitted

Binary Segmentation: Scott, A. J. and Knott, M. (1974) A Cluster Analysis Method for Grouping Means in the Analysis of Variance, Biometrics 30(3), 507--512

Segment Neighbourhoods: Auger, I. E. And Lawrence, C. E. (1989) Algorithms for the Optimal Identification of Segment Neighborhoods, Bulletin of Mathematical Biology 51(1), 39--54

See Also

multiple.meanvar.norm,cpt.meanvar,PELT.meanvar.gamma,binseg.meanvar.gamma,single.meanvar.gamma,segneigh.meanvar.gamma,cpt

Examples

# Example of multiple changes in mean and variance at 50,100,150 in simulated Gamma data
set.seed(1)
x=c(rgamma(50,shape=1,rate=1),rgamma(50,shape=1,rate=3),rgamma(50,shape=1,rate=1),rgamma(50,shape=1,rate=10))
multiple.meanvar.gamma(x,shape=1,mul.method="BinSeg",penalty="Manual",value="2*log(n)",Q=5,class=FALSE) # returns optimal number of changepoints is 3, locations are 47,104,150.

# Example multiple datasets where the first row has multiple changes in mean and variance and the second row has no change in mean or variance
set.seed(1)
x=c(rgamma(50,shape=1,rate=1),rgamma(50,shape=1,rate=3),rgamma(50,shape=1,rate=1),rgamma(50,shape=1,rate=10))
y=rgamma(200,shape=1,rate=1)
z=rbind(x,y)
multiple.meanvar.gamma(z,shape=1,mul.method="SegNeigh",penalty="SIC",Q=5,class=FALSE) # returns list that has two elements, the first has 4 changes in mean and variance at 47,102,151,172 and the second has no changes in mean or variance
ans=multiple.meanvar.gamma(z,shape=1,mul.method="PELT",penalty="SIC") 
cpts(ans[[1]]) # same results as for the SegNeigh method.
cpts(ans[[2]]) # same results as for the SegNeigh method.