makeChangePointModel: Creates a CPM S4 Object

In cpm: Sequential and Batch Change Detection Using Parametric and Nonparametric Methods

Description

This function is used to create a change point model (CPM) S4 object. The CPM object can be used to process a sequence of data, one observation at a time. The CPM object maintains its state between each observation, and can be queried to obtain the D_{k,t} statistics, and to test whether a change has been detected.

Note that this function is part of the S4 object section of the cpm package, which allows for more precise control over the change detection process. For many simple change detection applications this extra complexity will not be required, and the detectChangePoint and processStream functions should be used instead.

For a fuller overview of this function including a description of the CPM framework and examples of how to use the various functions, please consult the package manual "Parametric and Nonparametric Sequential Change Detection in R: The cpm Package" available from www.gordonjross.co.uk

Usage

     makeChangePointModel(cpmType, ARL0=500, startup=20, lambda=NA) 
     

Arguments

cpmType	The type of CPM which is to be created. Possible arguments are: Student: Student-t test statistic, as in [Hawkins et al, 2003]. Use to detect mean changes in a Gaussian sequence. Bartlett: Bartlett test statistic, as in [Hawkins and Zamba, 2005]. Use to detect variance changes in a Gaussian sequence. GLR: Generalized Likelihood Ratio test statistic, as in [Hawkins and Zamba, 2005b]. Use to detect both mean and variance changes in a Gaussian sequence. Exponential: Generalized Likelihood Ratio test statistic for the Exponential distribution, as in [Ross, 2013]. Used to detect changes in the parameter of an Exponentially distributed sequence. GLRAdjusted and ExponentialAdjusted: Identical to the GLR and Exponential statistics, except with the finite-sample correction discussed in [Ross, 2013] which can lead to more powerful change detection. FET: Fishers Exact Test statistic, as in [Ross and Adams, 2012b]. Use to detect parameter changes in a Bernoulli sequence. Mann-Whitney: Mann-Whitney test statistic, as in [Ross et al, 2011]. Use to detect location shifts in a stream with a (possibly unknown) non-Gaussian distribution. Mood: Mood test statistic, as in [Ross et al, 2011]. Use to detect scale shifts in a stream with a (possibly unknown) non-Gaussian distribution. Lepage: Lepage test statistics in [Ross et al, 2011]. Use to detect location and/or shifts in a stream with a (possibly unknown) non-Gaussian distribution. Kolmogorov-Smirnov: Kolmogorov-Smirnov test statistic, as in [Ross et al 2012]. Use to detect arbitrary changes in a stream with a (possibly unknown) non-Gaussian distribution. Cramer-von-Mises: Cramer-von-Mises test statistic, as in [Ross et al 2012]. Use to detect arbitrary changes in a stream with a (possibly unknown) non-Gaussian distribution.
ARL0	Determines the ARL_0 which the CPM should have, which corresponds to the average number of observations before a false positive occurs, assuming that the sequence does not undergo a chang. Because the thresholds of the CPM are computationally expensive to estimate, the package contains pre-computed values of the thresholds corresponding to several common values of the ARL_0. This means that only certain values for the ARL_0 are allowed. Specifically, the ARL_0 must have one of the following values: 370, 500, 600, 700, ..., 1000, 2000, 3000, ..., 10000, 20000, ..., 50000.
startup	The number of observations after which monitoring begins. No change points will be flagged during this startup period. This must be set to at least 20.
lambda	A smoothing parameter which is used to reduce the discreteness of the test statistic when using the FET CPM. See [Ross and Adams, 2012b] in the References section for more details on how this parameter is used. Currently the package only contains sequences of ARL0 thresholds corresponding to lambda=0.1 and lambda=0.3, so using other values will result in an error. If no value is specified, the default value will be 0.1.

Value

A CPM S4 object. The class of this object will depend on the value which has been passed as the cpmType argument.

Author(s)

Gordon J. Ross [e-mail]

References

Hawkins, D. , Zamba, K. (2005) – A Change-Point Model for a Shift in Variance, Journal of Quality Technology, 37, 21-31

Hawkins, D. , Zamba, K. (2005b) – Statistical Process Control for Shifts in Mean or Variance Using a Changepoint Formulation, Technometrics, 47(2), 164-173

Hawkins, D., Qiu, P., Kang, C. (2003) – The Changepoint Model for Statistical Process Control, Journal of Quality Technology, 35, 355-366.

Ross, G. J., Tasoulis, D. K., Adams, N. M. (2011) – A Nonparametric Change-Point Model for Streaming Data, Technometrics, 53(4)

Ross, G. J., Adams, N. M. (2012) – Two Nonparametric Control Charts for Detecting Arbitary Distribution Changes, Journal of Quality Technology, 44:102-116

Ross, G. J., Adams, N. M. (2013) – Sequential Monitoring of a Proportion, Computational Statistics, 28(2)

Ross, G. J., (2014) – Sequential Change Detection in the Presence of Unknown Parameters, Statistics and Computing 24:1017-1030

Ross, G. J., (2015) – Parametric and Nonparametric Sequential Change Detection in R: The cpm Package, Journal of Statistical Software, forthcoming

See Also

processObservation, changeDetected, cpmReset.

Examples

#generate a sequence containing a single change point
x <- c(rnorm(100,0,1),rnorm(100,1,1))

#use a Student CPM
cpm <- makeChangePointModel(cpmType="Student", ARL0=500)

for (i in 1:length(x)) {

  #process each observation in turn
  cpm <- processObservation(cpm,x[i])
  
  if (changeDetected(cpm)) {
    print(sprintf("change detected at observation %s",i))
    break
  }
}
     

cpm documentation built on Nov. 16, 2020, 9:13 a.m.