| Title: | High-Dimensional Multiscale Online Changepoint Detection |
|---|---|
| Description: | Implements the algorithm in Chen, Wang and Samworth (2020) <arxiv:2003.03668> for online detection of sudden mean changes in a sequence of high-dimensional observations. It also implements methods by Mei (2010) <doi:10.1093/biomet/asq010>, Xie and Siegmund (2013) <doi:10.1214/13-AOS1094> and Chan (2017) <doi:10.1214/17-AOS1546>. |
| Authors: | Yudong Chen, Tengyao Wang, Richard J. Samworth |
| Maintainer: | Yudong Chen <[email protected]> |
| License: | GPL-3 |
| Version: | 1.1 |
| Built: | 2024-12-01 08:40:16 UTC |
| Source: | CRAN |
Accessor functions to attributes of class ChangepointDetector
data_dim(detector) ocdMethod(detector) n_obs(detector) patience(detector) param(detector) thresholds(detector) baselineMean(detector) baselineSD(detector) tracked(detector) statistics(detector) status(detector)data_dim(detector) ocdMethod(detector) n_obs(detector) patience(detector) param(detector) thresholds(detector) baselineMean(detector) baselineSD(detector) tracked(detector) statistics(detector) status(detector)
detector |
Object of S3 class 'ChangepointDetector' |
Obtain various attributes of the class 'ChangepointDetector'
This function implements the getData function to
perform the online changepoint detection for the 'Chan' class.
Chan_update(x_new, X_recent, CUSUM, p0, w, lambda)Chan_update(x_new, X_recent, CUSUM, p0, w, lambda)
x_new |
a new data point |
X_recent |
matrix of |
CUSUM |
tail partial sums of different lengths to be tracked online |
p0 |
sparsity parameter |
w |
window parameter |
lambda |
a tuning parameter for the 'Chan' method |
a list of
stat: test statistic for the 'Chan' class.
X_recent: the updated X_recent matrix
CUSUM: the updated CUSUM matrix
Chan, H. P. (2017) Optimal sequential detection in multi-stream data. Ann. Statist., 45, 2736–2763.
Constructor for the ChangepointDetector S3 class
ChangepointDetector(dim, method = c("ocd", "Mei", "XS", "Chan"), thresh, patience = 5000, MC_reps = 100, beta = 1, sparsity = "auto", b = beta/sqrt(dim), p0 = 1/sqrt(dim), w = 200, lambda = sqrt(8) - 2)ChangepointDetector(dim, method = c("ocd", "Mei", "XS", "Chan"), thresh, patience = 5000, MC_reps = 100, beta = 1, sparsity = "auto", b = beta/sqrt(dim), p0 = 1/sqrt(dim), w = 200, lambda = sqrt(8) - 2)
dim |
Data dimension, all new data must be of this dimension |
method |
Four methods are implemented: |
thresh |
A numeric vector or the character string 'MC'. If 'MC' is
specified then the correct threshold will be computed by Monte Carlo
simulation (the |
patience |
Required patience (average run length without change) of the online changepoint procedure. This is optional if the thresholds for detection are manually specified, but is required if Monte Carlo thresholds are used. |
MC_reps |
Number of Monte Carlo repetitions to use to estimate the
thresholds. Only used when |
beta |
lower bound on the l_2 norm of the vector of mean change to be
detected. This argument is used by the |
sparsity |
Parameter used by the |
b |
Lower bound on the per-coordinate magnitude of mean change be
detected. This argument is used by the 'Mei' method. If |
p0 |
A real number between 0 and 1. Sparsity parameter used by |
w |
Window size parameter used by |
lambda |
A tuning parameter used by the |
This function is a wrapper. The new_OCD,
new_Mei, new_XS and new_Chan carry
out the actual constructor implementation.
An object of S3 class 'ChangepointDetector'. Depending on the
method argument specified, the object also belongs to a subclass
'OCD', 'Mei', 'XS' or 'Chan' corresponding to method='ocd'. It
contains the following attributes:
class - S3 class and subclass
data_dim - data dimension
method - method used for changepoint detection
param - a list of parameters used in the specific method: beta
and sparsity for method ocd; b for method Mei;
p0 and w for method XS; p0, w and
lambda for method Chan.
threshold - a named vector of thresholds used for detection (see the
thresh argument)
n_obs - number of observations, initialised to 0
baseline_mean - vector of pre-change mean, initialised to a vector of 0,
can be estimated by setting the changepoint detector into baseline mean and
standard deviation estimating status, see setStatus, or set
directly using setBaselineMean.
baseline_sd - vector of standard deviation, initialised to a vector of 1,
can be estimated by setting the changepoint detector into baseline mean and
standard deviation estimating status, see setStatus, or set
directly using setBaselineSD.
tracked - a list of information tracked online by the changepoint
detector: matrices A
and tail for method ocd; vector R for method Mei;
matrices X_recent and CUSUM for methods XS and Chan.
statistics - a named vector of test statistics for changepoint
detection: statistics with names diag, off_d and off_s
for method ocd (note if sparsity is 'dense' or
'sparse', then only (S^diag, S^off,d)
and (S^diag, S^off,s) are included in stat respectively.);
statistics with names max and sum for
method Mei; a single numeric value for methods XS and Chan.
status - one of the following: 'estimating' (the detector is estimating the baseline mean and standard deviation with new data points), 'monitoring' (the detector is detecting changes from the baseline mean from new data points) and an integer recording the time of declaration of changepoint.
Chen, Y., Wang, T. and Samworth, R. J. (2020) High-dimensional multiscale online changepoint detection Preprint. arxiv:2003.03668.
Mei, Y. (2010) Efficient scalable schemes for monitoring a large number of data streams. Biometrika, 97, 419–433.
Xie, Y. and Siegmund, D. (2013) Sequential multi-sensor change-point detection. Ann. Statist., 41, 670–692.
Chan, H. P. (2017) Optimal sequential detection in multi-stream data. Ann. Statist., 45, 2736–2763.
accessor functions such as data_dim, the main function
for processing a new data point getData, other methods for the
ChangepointDetector class including reset,
setBaselineMean, setBaselineSD,
setStatus, normalisedStatistics and
checkChange.
detector_ocd <- ChangepointDetector(dim=100, method='ocd', thresh=c(11.6, 179.5, 54.9), beta=1) detector_Mei <- ChangepointDetector(dim=100, method='Mei', thresh=c(8.6, 125.1), b=0.1) detector_XS <- ChangepointDetector(dim=100, method='XS', thresh=55.1) detector_Chan <- ChangepointDetector(dim=100, method='Chan', thresh=8.7)detector_ocd <- ChangepointDetector(dim=100, method='ocd', thresh=c(11.6, 179.5, 54.9), beta=1) detector_Mei <- ChangepointDetector(dim=100, method='Mei', thresh=c(8.6, 125.1), b=0.1) detector_XS <- ChangepointDetector(dim=100, method='XS', thresh=55.1) detector_Chan <- ChangepointDetector(dim=100, method='Chan', thresh=8.7)
Check if a mean change has occurred.
checkChange(detector)checkChange(detector)
detector |
Object of class 'Changepoint Detector' |
The normalisedStatistics funcrtion is used to check if
any of the test statistics are above the threshold level. If this happens, the
status of the detector is changed to record the time of change and a message
is printed to the standard output declaring the change.
Updated object detector
normalisedStatistics, setStatus,
This is the main function for the 'ChangepointDetector' class.
getData(detector, x_new) ## S3 method for class 'OCD' getData(detector, x_new) ## S3 method for class 'Mei' getData(detector, x_new) ## S3 method for class 'XS' getData(detector, x_new) ## S3 method for class 'Chan' getData(detector, x_new)getData(detector, x_new) ## S3 method for class 'OCD' getData(detector, x_new) ## S3 method for class 'Mei' getData(detector, x_new) ## S3 method for class 'XS' getData(detector, x_new) ## S3 method for class 'Chan' getData(detector, x_new)
detector |
Object of class 'Changepoint Detector' |
x_new |
A new data point. It must be of the same dimension as
specified in the data_dim attribute of |
If the status of the detector object is 'estimating', the new
data point is used to update the current estimate of pre-change mean and
standard deviation. If the status of the detector object is monitoring',
the new data point is used to detect if a mean change has occurred.
Updated object detector
OCD: Process a new data for subclass 'OCD'
Mei: Process a new data for subclass 'Mei'
XS: Process a new data for subclass 'XS'
Chan: Process a new data for subclass 'Chan'
setBaselineMean for updating the pre-change mean
estimate, setBaselineSD for updating the standard deviation
estimate, checkChange for checking for change.
Compute Monte Carlo thresholds for the Chan method
MC_Chan(dim, patience, p0, w, lambda, MC_reps)MC_Chan(dim, patience, p0, w, lambda, MC_reps)
dim |
Data dimension |
patience |
Nominal patience of the procedure |
p0 |
Assumed fraction of nonzero coordinates of change. |
w |
Window size |
lambda |
Tuning parameter for Chan (2017) method |
MC_reps |
number of Monte Carlo repetitions to use |
A numeric vector of computed thresholds.
Compute Monte Carlo thresholds for the Mei method
MC_Mei(dim, patience, b, MC_reps)MC_Mei(dim, patience, b, MC_reps)
dim |
Data dimension |
patience |
Nominal patience of the procedure |
b |
lLwer bound on per-coordinate magnitude of change |
MC_reps |
Number of Monte Carlo repetitions to use |
A numeric vector of computed thresholds.
Compute Monte Carlo thresholds for the OCD method
MC_ocd(dim, patience, beta, sparsity, MC_reps)MC_ocd(dim, patience, beta, sparsity, MC_reps)
dim |
Data dimension |
patience |
Nominal patience of the procedure |
beta |
Lower bound on l_2 norm of change |
sparsity |
Sparsity parameter for the OCD method |
MC_reps |
Number of Monte Carlo repetitions to use |
A numeric vector of computed thresholds.
Compute Monte Carlo thresholds for the XS method
MC_XS(dim, patience, p0, w, MC_reps)MC_XS(dim, patience, p0, w, MC_reps)
dim |
Data dimension |
patience |
Nominal patience of the procedure |
p0 |
Assumed fraction of nonzero coordinates of change. |
w |
Window size |
MC_reps |
number of Monte Carlo repetitions to use |
A numeric vector of computed thresholds.
This function implements the getData function to
perform the online changepoint detection for the 'Mei' class.
Mei_update(x_new, R, b)Mei_update(x_new, R, b)
x_new |
a new data point |
R |
vector of of tail CUSUMs that will be tracked and updated online |
b |
a user specified lower bound on per-coordinate magnitude of the vector of change to be detected. |
a list of
stat: a vector of 2 test statistics for the 'Mei' class.
R: the updated R vector
Mei, Y. (2010) Efficient scalable schemes for monitoring a large number of data streams. Biometrika, 97, 419–433.
construtor for subclass 'Chan' in class 'ChangepointDetector'
new_Chan(dim, thresh, p0, w, lambda)new_Chan(dim, thresh, p0, w, lambda)
dim |
Data dimension, all new data must be of this dimension |
thresh |
Detection threshold. A positive real number. |
p0 |
A sparsity parameter between 0 and 1. It is the assumed fraction of
nonzero coordinates of change. Default to |
w |
Window size parameter. Number of most recent data points to keep track in memory. Default is 200. |
lambda |
A tuning parameter used by the Chan (2017) method. Default is
|
It is preferred to use ChangepointDetector for
construction.
An object of S3 subclass 'Chan' in class 'ChangepointDetector'.
Chan, H. P. (2017) Optimal sequential detection in multi-stream data. Ann. Statist., 45, 2736–2763.
detector <- new_Chan(dim=100, thresh=8.7, p0=0.1, w=200, lambda=sqrt(8)-2)detector <- new_Chan(dim=100, thresh=8.7, p0=0.1, w=200, lambda=sqrt(8)-2)
constructor of subclass 'Mei' in class 'ChangepointDetector'
new_Mei(dim, thresh, b)new_Mei(dim, thresh, b)
dim |
Data dimension, all new data must be of this dimension |
thresh |
Detection threshold. A numeric vector of length two (corresponding to the max and sum statistics) should be specified. |
b |
Lower bound on the per-coordinate magnitude of mean change be detected. |
It is preferred to use ChangepointDetector for
construction.
An object of S3 subclass 'Mei' in class 'ChangepointDetector'.
Mei, Y. (2010) Efficient scalable schemes for monitoring a large number of data streams. Biometrika, 97, 419–433.
detector <- new_Mei(dim=100, thresh=c(8.6, 125.1), b=0.1)detector <- new_Mei(dim=100, thresh=c(8.6, 125.1), b=0.1)
constructor of subclass 'OCD' in class 'ChangepointDetector'
new_OCD(dim, thresh, beta, sparsity)new_OCD(dim, thresh, beta, sparsity)
dim |
Data dimension, all new data must be of this dimension |
thresh |
A numeric vector of length 3 (corresponding to the diagonal statistic, off-diagonal dense statistic and off-diagonal sparse statistic) should be specifiied. |
beta |
Lower bound on the l_2 norm of the vector of mean change to be detected. |
sparsity |
If |
It is preferred to use ChangepointDetector for
construction.
An object of S3 subclass 'OCD' in class 'ChangepointDetector'.
Chen, Y., Wang, T. and Samworth, R. J. (2020) High-dimensional multiscale online changepoint detection Preprint. arxiv:2003.03668.
detector <- new_OCD(dim=100, thresh=c(11.6, 179.5, 54.9), beta=1, sparsity='auto')detector <- new_OCD(dim=100, thresh=c(11.6, 179.5, 54.9), beta=1, sparsity='auto')
constructor of subclass 'XS' in class 'ChangepointDetector'
new_XS(dim, thresh, p0, w)new_XS(dim, thresh, p0, w)
dim |
Data dimension, all new data must be of this dimension |
thresh |
Detection threshold. A positive real number. |
p0 |
A sparsity parameter between 0 and 1. It is the assumed fraction of
nonzero coordinates of change. Default to |
w |
Window size parameter. Number of most recent data points to keep track in memory. Default is 200. |
It is preferred to use ChangepointDetector for
construction.
An object of S3 subclass 'XS' in class 'ChangepointDetector'.
Xie, Y. and Siegmund, D. (2013) Sequential multi-sensor change-point detection. Ann. Statist., 41, 670–692.
detector <- new_XS(dim=100, thresh=55.1, p0=0.1, w=200)detector <- new_XS(dim=100, thresh=55.1, p0=0.1, w=200)
Compute maximum ratio between detection statistic and its threshold
normalisedStatistics(detector)normalisedStatistics(detector)
detector |
Object of class 'Changepoint Detector' |
maximum of the ratio between the current test statistics and their respective thresholds.
The ocd package provides the S3 class ChangepointDetector that
processes data sequentially using the getData function and
aims to detect change as soon as it occurs online subject to false alarm
rates.
Chen, Y., Wang, T. and Samworth, R. J. (2020) High-dimensional multiscale online changepoint detection Preprint. arxiv:2003.03668.
ChangepointDetector for detailed usage.
set.seed(2020) p <- 100 thresh <- setNames(c(11.62, 179.48, 54.87), c('diag', 'off_d', 'off_s')) detector <- ChangepointDetector(dim=p, method='ocd', beta=1, thresh=thresh) old_mean <- rnorm(p); new_mean <- old_mean + c(rnorm(p/4), rep(0,3*p/4)) / sqrt(p/4) # using functional semantics native in R detector <- setStatus(detector, 'estimating') for (i in 1:10000){ x_new <- rnorm(p, mean=old_mean) detector <- getData(detector, x_new) } print(detector) detector <- setStatus(detector, 'monitoring') for (i in 1:200){ x_new <- rnorm(p, old_mean * (i < 100) + new_mean * (i>=100)) detector <- getData(detector, x_new) } print(detector) ## Not run: # alternative way to write the above using the piping semantics library(magrittr) detector %<>% reset detector %<>% setStatus('estimating') for (i in 1:10000){ x_new <- rnorm(p, mean=old_mean) detector %<>% getData(x_new) } detector %>% print detector %<>% setStatus('monitoring') for (i in 1:200){ x_new <- rnorm(p, old_mean * (i < 100) + new_mean * (i>=100)) detector %<>% getData(x_new) } detector %>% print ## End(Not run)set.seed(2020) p <- 100 thresh <- setNames(c(11.62, 179.48, 54.87), c('diag', 'off_d', 'off_s')) detector <- ChangepointDetector(dim=p, method='ocd', beta=1, thresh=thresh) old_mean <- rnorm(p); new_mean <- old_mean + c(rnorm(p/4), rep(0,3*p/4)) / sqrt(p/4) # using functional semantics native in R detector <- setStatus(detector, 'estimating') for (i in 1:10000){ x_new <- rnorm(p, mean=old_mean) detector <- getData(detector, x_new) } print(detector) detector <- setStatus(detector, 'monitoring') for (i in 1:200){ x_new <- rnorm(p, old_mean * (i < 100) + new_mean * (i>=100)) detector <- getData(detector, x_new) } print(detector) ## Not run: # alternative way to write the above using the piping semantics library(magrittr) detector %<>% reset detector %<>% setStatus('estimating') for (i in 1:10000){ x_new <- rnorm(p, mean=old_mean) detector %<>% getData(x_new) } detector %>% print detector %<>% setStatus('monitoring') for (i in 1:200){ x_new <- rnorm(p, old_mean * (i < 100) + new_mean * (i>=100)) detector %<>% getData(x_new) } detector %>% print ## End(Not run)
This function implements the getData function to
perform the online changepoint detection for the 'OCD' class.
ocd_update(x_new, A, tail, beta, sparsity)ocd_update(x_new, A, tail, beta, sparsity)
x_new |
a new data point |
A |
matrix of tail CUSUMs that will be tracked and updated online |
tail |
matrix of tail lengths that will be tracked and updated online |
beta |
a user specified lower bound on the l_2 norm of the vector of change to be detected. |
sparsity |
a user specified mode parameter. If the vector of change is known to be dense or sparse, then one should set sparsity to 'dense' or 'sparse' accordingly, otherwise, the default choice sparsity='auto' will run the algorithm adaptive to the sparsity level. |
a list of
stat: a vector of the test statistics for the 'OCD' class
A: the updated A matrix
tail: the updated tail matrix
Chen, Y., Wang, T. and Samworth, R. J. (2020) High-dimensional multiscale online changepoint detection Preprint. arxiv:2003.03668.
Processed data from 39 ground motion sensors at 13 stations near Parkfield, California from 2.00-2.16am on December 23, 2004, with an earthquake measured at duration magnitude 1.47Md hit near Atascadero, California at 02:09:54.01.
data(ParkfieldSensors)data(ParkfieldSensors)
A matrix with 39 columns and 14998 rows, with each column corresponding to a sensor and each row corresponding to a time after 2am. Column names corresponds to names of the sensors and row names are number of seconds after 2am.
HRSN (2014), High Resolution Seismic Network. UC Berkeley Seismological Laboratory. Dataset. doi:10.7932/HRSN.
data(ParkfieldSensors) head(ParkfieldSensors) ## Not run: plot(c(0, nrow(ParkfieldSensors) * 0.064), c(0, ncol(ParkfieldSensors)+1), pch=' ', xlab='seconds after 2004-12-23 02:00:00', ylab='sensor measurements') x <- as.numeric(rownames(ParkfieldSensors)) for (j in 1:ncol(ParkfieldSensors)){ y <- ParkfieldSensors[, j] y <- (y - max(ParkfieldSensors)) / diff(range(ParkfieldSensors)) + 0.5 + j points(x, y, pch='.') } abline(v = 9 * 60 + 54.01, col='blue', lwd=2, lty=3) # earthquake time library(magrittr) p <- ncol(ParkfieldSensors) train_ind <- as.numeric(rownames(ParkfieldSensors)) <= 240 train <- ParkfieldSensors[train_ind, ] test <- ParkfieldSensors[!train_ind, ] # tuning parameters gamma <- 24 * 60 * 60 / 0.064 # patience = 1 day beta <- 150 # use theoretical thresholds suggested in Chen, Wang and Samworth (2020) psi <- function(t){p - 1 + t + sqrt(2 * (p - 1) * t)} th_diag <- log(24*p*gamma*log2(4*p)) th_off_s <- 8*log(24*p*gamma*log2(2*p)) th_off_d <- psi(th_off_s/4) thresh <- setNames(c(th_diag, th_off_d, th_off_s), c('diag', 'off_d', 'off_s')) # initialise ocd detector detector <- ChangepointDetector(dim=p, method='ocd', beta=beta, thresh=thresh) # use training data to update baseline mean and standard deviation detector %<>% setStatus('estimating') for (i in 1:nrow(train)) { detector %<>% getData(train[i, ]) } # find changepoint in the test data detector %<>% setStatus('monitoring') for (i in 1:nrow(test)) { detector %<>% getData(test[i, ]) if (is.numeric(detector %>% status)) break } if (is.numeric(detector %>% status)) { time_declared <- 240 + detector %>% status * 0.064 abline(v = time_declared, col='orange', lwd=2, lty=3) # detection time cat('Change detected', time_declared, 'seconds after 2am.\n') } ## End(Not run)data(ParkfieldSensors) head(ParkfieldSensors) ## Not run: plot(c(0, nrow(ParkfieldSensors) * 0.064), c(0, ncol(ParkfieldSensors)+1), pch=' ', xlab='seconds after 2004-12-23 02:00:00', ylab='sensor measurements') x <- as.numeric(rownames(ParkfieldSensors)) for (j in 1:ncol(ParkfieldSensors)){ y <- ParkfieldSensors[, j] y <- (y - max(ParkfieldSensors)) / diff(range(ParkfieldSensors)) + 0.5 + j points(x, y, pch='.') } abline(v = 9 * 60 + 54.01, col='blue', lwd=2, lty=3) # earthquake time library(magrittr) p <- ncol(ParkfieldSensors) train_ind <- as.numeric(rownames(ParkfieldSensors)) <= 240 train <- ParkfieldSensors[train_ind, ] test <- ParkfieldSensors[!train_ind, ] # tuning parameters gamma <- 24 * 60 * 60 / 0.064 # patience = 1 day beta <- 150 # use theoretical thresholds suggested in Chen, Wang and Samworth (2020) psi <- function(t){p - 1 + t + sqrt(2 * (p - 1) * t)} th_diag <- log(24*p*gamma*log2(4*p)) th_off_s <- 8*log(24*p*gamma*log2(2*p)) th_off_d <- psi(th_off_s/4) thresh <- setNames(c(th_diag, th_off_d, th_off_s), c('diag', 'off_d', 'off_s')) # initialise ocd detector detector <- ChangepointDetector(dim=p, method='ocd', beta=beta, thresh=thresh) # use training data to update baseline mean and standard deviation detector %<>% setStatus('estimating') for (i in 1:nrow(train)) { detector %<>% getData(train[i, ]) } # find changepoint in the test data detector %<>% setStatus('monitoring') for (i in 1:nrow(test)) { detector %<>% getData(test[i, ]) if (is.numeric(detector %>% status)) break } if (is.numeric(detector %>% status)) { time_declared <- 240 + detector %>% status * 0.064 abline(v = time_declared, col='orange', lwd=2, lty=3) # detection time cat('Change detected', time_declared, 'seconds after 2am.\n') } ## End(Not run)
Printing methods for the 'ChangepointDetector' class
## S3 method for class 'ChangepointDetector' print(x, ...)## S3 method for class 'ChangepointDetector' print(x, ...)
x |
object of the 'ChangepointDetector' class |
... |
other arguments used in |
Reset changepoint detector to initial state
reset(detector) ## S3 method for class 'OCD' reset(detector) ## S3 method for class 'Mei' reset(detector) ## S3 method for class 'XS' reset(detector) ## S3 method for class 'Chan' reset(detector)reset(detector) ## S3 method for class 'OCD' reset(detector) ## S3 method for class 'Mei' reset(detector) ## S3 method for class 'XS' reset(detector) ## S3 method for class 'Chan' reset(detector)
detector |
Object of class 'Changepoint Detector' |
Updated object detector
OCD: Reset object of subclass 'OCD'
Mei: Reset object of subclass 'Mei'
XS: Reset object of subclass 'XS'
Chan: Reset object of subclass 'Chan'
Set baseline mean
setBaselineMean(detector, mean)setBaselineMean(detector, mean)
detector |
Object of class 'Changepoint Detector' |
mean |
vector of pre-change mean, must be of the same dimension as
specified in the data_dim attribute of |
Updated object detector
Set baseline standard deviation
setBaselineSD(detector, sd)setBaselineSD(detector, sd)
detector |
Object of class 'Changepoint Detector' |
sd |
vector of standard deviation, must be of the same dimension as
specified in the data_dim attribute of |
Updated object detector
Set changepoint detector status
setStatus(detector, new_status)setStatus(detector, new_status)
detector |
Object of class 'Changepoint Detector' |
new_status |
'estimating' or 'monitoring' |
If the status is set to 'estimating', new observations are used to update current estimate of pre-change mean and standard deviation. If the status is set to 'monitoring', new observations are used to check if mean change has occurred.
Updated object detector
compute new mean and sd from old ones with one additional observation
update_param(old_mean, old_sd, x_new, n_obs)update_param(old_mean, old_sd, x_new, n_obs)
old_mean |
vector of old means |
old_sd |
vector of old standard deviation |
x_new |
new observation vector |
n_obs |
total number of observations (including x_new) |
list of two vectors: new mean and new standard deviation
This function implements the getData function to
perform the online changepoint detection for the 'XS' class.
XS_update(x_new, X_recent, CUSUM, p0, w)XS_update(x_new, X_recent, CUSUM, p0, w)
x_new |
a new data point |
X_recent |
matrix of |
CUSUM |
tail partial sums of different lengths to be tracked online |
p0 |
sparsity parameter |
w |
window parameter |
a list of
stat: test statistic for the 'XS' class.
X_recent: the updated X_recent matrix
CUSUM: the updated CUSUM matrix
Xie, Y. and Siegmund, D. (2013) Sequential multi-sensor change-point detection. Ann. Statist., 41, 670–692.