Identifying Changes in Mean and Variance
Calculates the optimal positioning and (potentially) number of changepoints for data using the user specified method.
- A vector, ts object 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.
- Choice of "None", "SIC", "BIC", "MBIC", AIC", "Hannan-Quinn", "Asymptotic", "Manual" and "CROPS" penalties. If Manual is specified, the manual penalty is contained in the pen.value parameter. If Asymptotic is specified, the theoretical type I error is contained in the pen.value parameter. If CROPS is specified, the penalty range is contained in the pen.value parameter; note this is a vector of length 2 which contains the minimum and maximum penalty value. Note CROPS can only be used if the method is "PELT". The predefined penalties listed DO count the changepoint as a parameter, postfix a 0 e.g."SIC0" to NOT count the changepoint as a parameter.
- The theoretical type I error e.g.0.05 when using the Asymptotic penalty. A vector of length 2 (min,max) if using the CROPS penalty. 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, diffparam=difference in number of alternatve and null parameters.
- Choice of "AMOC", "PELT", "SegNeigh" or "BinSeg".
- 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.
- The assumed test statistic / distribution of the data. Currently only "Normal", "Gamma", "Exponential" and "Poisson" are supported.
Logical. If TRUE then an object of class
- Logical. If TRUE and class=TRUE then parameter estimates are returned. If FALSE or class=FALSE no parameter estimates are returned.
- Value of the assumed known shape parameter required when test.stat="Gamma".
- Positive integer giving the minimum segment length (no. of observations between changes), default is the minimum allowed by theory.
This function is used to find changes in mean and variance for data using the test statistic specified in the test.stat parameter. The changes are found using the method supplied which can be single changepoint (AMOC) or multiple changepoints using exact (PELT or SegNeigh) or approximate (BinSeg) methods. A changepoint is denoted as the first observation of the new segment / regime.
class=TRUEthen an object of S4 class "cpt" is returned. The slot
cptscontains the changepoints that are returned. For
class=FALSEthe structure is as follows.If data is a vector (single dataset) then a vector/list is returned depending on the value of 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 method.If method is AMOC then a vector (one dataset) or matrix (multiple datasets) is returned, the columns are:If method is PELT then a vector is returned containing the changepoint locations for the penalty supplied. This always ends with n. If the penalty is CROPS then a list is returned with elements:If method is SegNeigh then a list is returned with elements:If method is BinSeg then a list is returned with elements:
Change in Normal mean and variance: Chen, J. and Gupta, A. K. (2000) Parametric statistical change point analysis, Birkhauser
Change in Gamma shape parameter: Chen, J. and Gupta, A. K. (2000) Parametric statistical change point analysis, Birkhauser
Change in Exponential model: Chen, J. and Gupta, A. K. (2000) Parametric statistical change point analysis, Birkhauser
Change in Poisson model: Chen, J. and Gupta, A. K. (2000) Parametric statistical change point analysis, Birkhauser
PELT Algorithm: Killick R, Fearnhead P, Eckley IA (2012) Optimal detection of changepoints with a linear computational cost, JASA 107(500), 1590--1598
CROPS: Haynes K, Eckley IA, Fearnhead P (2014) Efficient penalty search for multiple changepoint problems (in submission), arXiv:1412.3617
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
MBIC: Zhang, N. R. and Siegmund, D. O. (2007) A Modified Bayes Information Criterion with Applications to the Analysis of Comparative Genomic Hybridization Data. Biometrics 63, 22-32.
# Example of a change in scale parameter (mean and variance) at 100 in simulated gamma data set.seed(1) x=c(rgamma(100,shape=1,rate=1),rgamma(100,shape=1,rate=5)) cpt.meanvar(x,penalty="SIC",method="AMOC",test.stat="Gamma",class=FALSE,shape=1) # returns 97 to #show that the null hypothesis was rejected and the change in scale parameter is at 97 ans=cpt.meanvar(x,penalty="AIC",method="AMOC",test.stat="Gamma",shape=1) cpts(ans) # returns 97 to show that the null hypothesis was rejected, the change in scale parameter is at 97 # Example of multiple changes in mean and variance at 50,100,150 in simulated normal data set.seed(1) x=c(rnorm(50,0,1),rnorm(50,5,3),rnorm(50,10,1),rnorm(50,3,10)) cpt.meanvar(x,penalty="Manual",pen.value="4*log(n)",method="BinSeg",Q=5,class=FALSE) # returns optimal number of changepoints is 4, locations are 50,100,150,152. # Example of using the CROPS penalty in the above example set.seed(1) x=c(rnorm(50,0,1),rnorm(50,5,3),rnorm(50,10,1),rnorm(50,3,10)) out=cpt.meanvar(x,pen.value=c(2*log(length(x)),100*log(length(x))),penalty="CROPS",method="PELT") cpts.full(out) # returns 6 segmentations for penalty values between 2log(n) and 100log(n). # We find segmentations with 9, 7, 4, 3, 1 and 0 changepoints. # Note that the empty final row indicates no changepoints. pen.value.full(out) # gives associated penalty transition points # CROPS does not give an optimal set of changepoints thus we may wish to explore further plot(out,diagnostic=TRUE) # looks like the segmentation with 4 changepoints, 50,100,150,200 is the most appropriate plot(out,ncpts=3) # 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(rnorm(50,0,1),rnorm(50,5,3),rnorm(50,10,1),rnorm(50,3,10)) y=rnorm(200,0,1) z=rbind(x,y) cpt.meanvar(z,penalty="Asymptotic",pen.value=0.01,method="SegNeigh",Q=5,class=FALSE) # returns list #that has two elements, the first has 3 changes in mean and variance at 50,100,150 and the second #has no changes in mean or variance ans=cpt.meanvar(z,penalty="Asymptotic",pen.value=0.01,method="PELT") cpts(ans[]) # same results as for the SegNeigh method. cpts(ans[]) # same results as for the SegNeigh method.