beast  R Documentation 
A Bayesian model averaging algorithm called BEAST to decompose time series or 1D sequential data into individual components, such as abrupt changes, trends, and periodic/seasonal variations. BEAST is useful for changepoint detection (e.g., breakpoints, joinpoints, or structural breaks), nonlinear trend analysis, time series decomposition, and time series segmentation.
beast(
y,
start = 1,
deltat = 1,
season = c("harmonic", "svd", "dummy", "none"),
period = NULL,
scp.minmax = c(0,10), sorder.minmax = c(0,5),
tcp.minmax = c(0,10), torder.minmax = c(0,1),
sseg.min = NULL, sseg.leftmargin = NULL, sseg.rightmargin = NULL,
tseg.min = NULL, tseg.leftmargin = NULL, tseg.rightmargin = NULL,
method = c( 'bayes', 'bic', 'aic', 'aicc', 'hic',
'bic0.25', 'bic0.5', 'bic1.5', 'bic2' ),
detrend = FALSE,
deseasonalize = FALSE,
mcmc.seed = 0,
mcmc.burnin = 200,
mcmc.chains = 3,
mcmc.thin = 5,
mcmc.samples = 8000,
precValue = 1.5,
precPriorType = c('componentwise','uniform','constant','orderwise'),
hasOutlier = FALSE,
ocp.minmax = c(0,10),
print.param = TRUE,
print.progress = TRUE,
print.warning = TRUE,
quiet = FALSE,
dump.ci = FALSE,
dump.mcmc = FALSE,
gui = FALSE,
...
)
y 
a vector for an evenlyspaced regular time series. Missing values such as NA and NaN are allowed.
If a list of multiple time series is provided for 
start 
numeric (default to 1.0) or 
deltat 
numeric (default to 1.0) or string; the time interval between consecutive data points. Its unit should be consistent with 
season 
characters (default to 'harmonic'); specify if

period 
numeric or string. Specify the period for the seasonal/periodic component in 
scp.minmax 
a vector of 2 integers (>=0); the min and max number of seasonal changepoints (scp) allowed in segmenting the seasonal component. 
sorder.minmax 
a vector of 2 integers (>=1); the min and max harmonic orders considered to fit the seasonal component. 
tcp.minmax 
a vector of 2 integers (>=0); the min and max number of trend changepoints (tcp) allowed in segmenting the trend component. If the min and max changepoint numbers are equal, BEAST assumes a constant number of changepoints and won't infer the posterior probability of the number of changepoints for the trend, but it still estimates the occurrence probability of the changepoints over time (i.e., the most likely times at which these changepoints occur in the trend). If both the min and max numbers are set to 0, no changepoints are allowed; then a global polynomial trend is used to fit the trend component, but still, the most likely polynomial order will be inferred if torder.minmax[1] is not equal to torder.minmax[2]. 
torder.minmax 
a vector of 2 integers (>=0); the min and max orders of the polynomials considered to fit the trend component. The 0th order corresponds to a constant term/a flat line and the 1st order is a line. If 
sseg.min 
an integer (>0); the min segment length allowed between two neighboring season changepoints. That is, when fitting a piecewise harmonic seasonal model, two changepoints are not allowed to occur within a time window of length 
sseg.leftmargin 
an integer (>=0); the number of leftmost data points excluded for seasonal changepoint detection. That is, when fitting a piecewise harmonic seasonal model, no changepoints are allowed in the starting window/segment of length 
sseg.rightmargin 
an integer (>=0); the number of rightmost data points excluded for seasonal changepoint detection. That is, when fitting a piecewise harmonic seasonal model, no changepoints are allowed in the ending window/segment of length 
tseg.min 
an integer (>0); the min segment length allowed between two neighboring trend changepoints. That is, when fitting a piecewise polynomial trend model, two changepoints are not allowed to occur within a time window of length 
tseg.leftmargin 
an integer (>=0); the number of leftmost data points excluded for trend changepoint detection. That is, when fitting a piecewise polynomial trend model, no changepoints are allowed in the starting window/segment of length 
tseg.rightmargin 
an integer (>=0); the number of rightmost data points excluded for trend changepoint detection. That is, when fitting a piecewise polynomial trend model, no changepoints are allowed in the ending window/segment of length 
method 
a string (default to 'bayes'); specify the method for formulating model posterior probability.

detrend 
logical; If 
deseasonalize 
logical; If 
mcmc.seed 
integer (>=0); the seed for the random number generator used for Monte Carlo Markov Chain (mcmc). If 
mcmc.chains 
integer (>0); the number of MCMC chains. 
mcmc.thin 
integer (>0); a factor to thin chains (e.g., if thinningFactor=5, samples will be taken every 3 iterations) 
mcmc.burnin 
integer (>0); the number of burnin samples discarded at the start of each chain 
mcmc.samples 
integer (>=0); the number of samples collected per MCMC chain. The total number of iterations is 
precValue 
numeric (>0); the hyperparameter of the precision prior; the default value is 1.5. 
precPriorType 
characters. It takes one of 'constant', 'uniform', 'componentwise' (the default), and 'orderwise'. Below are the differences between them.

hasOutlier 
boolean; if true, fit a model with an outlier component that refers to potential spikes or dips at isolated data points: Y = trend + outlier + error if season='none',and Y = trend + season + outlier + error if season ~= 'none'. 
ocp.minmax 
a vector of 2 integers (>=0); the min and max numbers of outliertype changepoints (ocp) allowed in the time seriestrend component. Ocp refers to spikes or dips at isolated times that can't be modeled as trends or seasonal terms. 
print.param 
boolean. If 
print.progress 
boolean;If 
print.warning 
boolean;If 
quiet 
boolean. If 
dump.ci 
boolean; If 
dump.mcmc 
boolean; If 
gui 
boolean. If 
... 
additional parameters. There are many more settings for the implementation but not made available in the beast() interface; please use the function 
The output is an object of class "beast". It is a list, consisting of the following variables. Its structure is the same as the outputs from the other two alternative functions beast.irreg
and beast123
. In the explanations below, we assume the input y
is a single time series of length N
:
time 
a vector of size 
data 
a vector, matrix, or 3D array; this is a copy of the input 
marg_lik 
numeric; the average of the model marginal likelihood; the greater marg_lik, the better the fitting for a given time series; that is, 1 will be better than 10; 10 better than 1 and 10. 
R2 
numeric; the Rsquare of the model fitting. 
RMSE 
numeric; the RMSE of the model fitting. 
sig2 
numeric; the estimated variance of the model error. 
trend 
a list object consisting of various outputs related to the estimated trend component:

season 
a list object consisting of various outputs related to the estimated seasonal/periodic component:

The three functions beast
(), beast.irreg
(), and beast123
() are essentially the same BEAST algorithm but with different APIs. There is a onetoone correspondence between the parameters for beast() and beast.irreg() and the 'metadata', 'prior','mcmc', and 'extra' objects in the beast123() interface. Examples are:
start <> metadata$startTime
deltat <> metadata$deltaTime
deseasonalize <> metadata$deseasonalize
hasOutlier <> metadata$hasOutlierCmpnt
scp.minmax[1] <> prior$seasonMinOrder
scp.minmax[2] <> prior$seasonMaxOrder
sseg.min <> prior$seasonMinSepDist
tcp.torder[1] <> prior$trendMinOrder
tseg.leftmargin <> prior$trendLeftMargin
mcmc.seed <> mcmc$seed
dump.ci <> extra$computeCredible
Experts should use the the beast123 function.
Zhao, K., Wulder, M.A., Hu, T., Bright, R., Wu, Q., Qin, H., Li, Y., Toman, E., Mallick, B., Zhang, X. and Brown, M., 2019. Detecting changepoint, trend, and seasonality in satellite time series data to track abrupt changes and nonlinear dynamics: A Bayesian ensemble algorithm. Remote Sensing of Environment, 232, p.111181 (the beast algorithm paper).
Zhao, K., Valle, D., Popescu, S., Zhang, X. and Mallick, B., 2013. Hyperspectral remote sensing of plant biochemistry using Bayesian model averaging with variable and band selection. Remote Sensing of Environment, 132, pp.102119 (the Bayesian MCMC scheme used in beast).
Hu, T., Toman, E.M., Chen, G., Shao, G., Zhou, Y., Li, Y., Zhao, K. and Feng, Y., 2021. Mapping finescale human disturbances in a working landscape with Landsat time series on Google Earth Engine. ISPRS Journal of Photogrammetry and Remote Sensing, 176, pp.250261(a beast application paper).
beast
, beast.irreg
, beast123
, minesweeper
, tetris
, geeLandsat
library(Rbeast)
#Example 1#
# 'googletrend_beach' is the monthly Google Trend popularity of searching for 'beach'
# in the US from 2004 to 2022. Sudden changes in the time series coincide with known
# extreme weather events (e.g., 2006 North American Blizzard, 2011 US hottest summer
# on record, Record warm January in 2016) or the covid19 outbreak.
out < beast(googletrend_beach)
plot(out)
plot(out, vars=c('t','slpsgn') ) # plot the trend and probability of slope sign only.
# In the slpsgn panel, the upper red portion refers to
# probability of trend slope being positive, the middle
# green to the prob of slope being zero, and the lower
# blue to the probability of slope being negative.
# Run "?plot.beast" for details on the plot function.
#Example 2#
# Yellowstone is a halfmonthly satellite time series of 774 NDVI(vegetation greeness)
# observations starting from July 115,1981(i.e., start=c(1981,7,7)) at a Yellowstone
# forest site. It has 24 data points per year (i.e., freq=24). Note that the beast
# function hanldes only evenlyspaced regular time series. Irregular data need to be
# first aggegrated at a regular time interval of your choicethe aggregation
# functionality is implemented in beast.irreg() and beast123().
data(Yellowstone)
plot( 1981.5+(0:773)/24, Yellowstone, type='l') # A sudden drop in greenness in 1988
# due to the 1988 Yellowstone Fire
# Yellowstone is not a object of class 'ts' but a pure vector without time attributes.
# Below, no extra argument is supplied, so default values (i.e.,start=1, deltat=1) are
# used and the time is 1:774. 'period' is missing and so is guessed via autocorrelation.
# Use of autocorrelation to compute the period of a cyclic time series is not always
# reliable, so it is suggested to always supply 'period' directly, as in Example 2 and
# Example 3.
o = beast(Yellowstone) # By defualt, the times assumed to be 1:length(Yellowstone)
# and a periodic component is assumed (season='harmonic')
plot(o)
#o = beast(Yellowstone, quiet=TRUE) # print no warning messages
#o = beast(Yellowstone, quiet=TRUE, print.progress=FALSE) # print nothing
#Example 3#
# The time info such as start,delta,and period is explicitly provided. 'start' can be
# given as (1) a fractional number, (2) a vector comprising year, month,& day, or (3)
# a R's Date. In (1), the unit of start and deltat does not necessarily refer to time and can
# be arbitrary (e.g., a sequence of data observed at evenlyspaced distaces along a
# transect or a elevation gradient)
# (1) Unknown unit such that 1981.5137 can be interpreted arbitrarily
o=beast(Yellowstone, start=1981.5137, deltat=1/24, period=1.0)
# Use a string to explictly specify a time unit so that times are intepreted as dates
# o=beast(Yellowstone, start=1981.5137, deltat='1/24 year', period=1.0) # 1.0 = 1 yr
# o=beast(Yellowstone, start=1981.5137, deltat='0.5 mon', period=1.0) # 1.0 = 1 yr
# o=beast(Yellowstone, start=1981.5137, deltat=1/24, period='1 yr') # 1/24 = 1/24 yr
# o=beast(Yellowstone, start=1981.5137, deltat=1/24, period='365 days')# 1/24 = 1/24 yr
# (2) start is provided as YMD, the unit is year: deltat=1/24 year=0.5 month
# o=beast(Yellowstone, start=c(1981,7,7), deltat=1/24, period=1.0)
# (3) start is provided as Date, the unit is year: deltat=1/24 year=0.5 month
#o=beast(Yellowstone, start=as.Date('198177'), deltat=1/24, period=1.0)
print(o) # o is a R LIST object with many fields
str(o) # See a list of fields in o
plot(o) # plot many variables
plot(o, vars=c('y','s','t') ) # plot the Y, seasonal, and trend components only
plot(o, vars=c('s','scp','samp','t','tcp','tslp'))# Plot some selected variables in
# 'o'. Type "?plot.beast" to see
# more about vars
plot(o, vars=c('s','t'),col=c('red','blue') ) # Specify colors of selected subplots
plot(o$time, o$season$Y,type='l') # directly plot output: the fitted season
plot(o$time, o$season$cpOccPr) # directly plot output: season chgpt prob
plot(o$time, o$trend$Y,type='l') # directly plot output: the fitted trend
plot(o$time, o$trend$cpOccPr) # directly plot output: trend chgpt occurrence prob
plot(o$time, o$season$order) # directly plot output: avg harmonic order
plot(o, interactive=TRUE) # manually choose which variables to plot
#Example 4#
# Specify other arguments explicitly. Default values are used for missing parameters.
# Note that beast(), beast.irreg(), and beast123() call the same internal C/C++ library,
# so in beast(), the input parameters will be converted to metadata, prior, mcmc, and
# extra parameters as explained for the beast123() function. Or type 'View(beast)' to
# check the parameter assignment in the code.
# In R's terminology, the number of datapoints per period is also called 'freq'. In this
# version, the 'freq' argument is obsolete and replaced by 'period'.
# period=deltat*number_of_datapoints_per_period = 1.0*24=24 because deltat is set to 1.0 by
# default and this signal has 24 samples per period.
o = beast(Yellowstone, period=24.0, mcmc.samples=5000, tseg.min=20)
# period=deltat*number_of_datapoints_per_period = 1/24*24=1.0.
# o = beast(Yellowstone, deltat=1/24 period=1.0, mcmc.samples=5000, tseg.min=20)
o = beast(
Yellowstone, # Yellowstone: a pure numeric vector wo time info
start = 1981.51,
deltat = 1/24,
period = 1.0, # Period=delta*number_of_datapoints_per_period
season = 'harmonic', # Periodic compnt exisits,fitted as a harmonic curve
scp.minmax = c(0,3), # Min and max numbers of seasonal changpts allowed
sorder.minmax = c(1,5), # Min and max harmonic orders allowed
sseg.min = 24, # The min length of segments btw neighboring chnpts
# '24' means 24 datapoints; the unit is datapoint.
sseg.leftmargin= 40, # No seasonal chgpts allowed in the starting 40 datapoints
tcp.minmax = c(0,10),# Min and max numbers of changpts allowed in the trend
torder.minmax = c(0,1), # Min and maxx polynomial orders to fit trend
tseg.min = 24, # The min length of segments btw neighboring trend chnpts
tseg.leftmargin= 10, # No trend chgpts allowed in the starting 10 datapoints
deseasonalize = TRUE, # Remove the global seasonality before fitting the beast model
detrend = TRUE, # Remove the global trend before fitting the beast model
mcmc.seed = 0, # A seed for mcmc's random nummber generator; use a
# nonzero integer to reproduce results across runs
mcmc.burnin = 500, # Number of initial iterations discarded
mcmc.chains = 2, # Number of chains
mcmc.thin = 3, # Include samples every 3 iterations
mcmc.samples = 6000, # Number of samples taken per chain
# total iteration: (500+3*6000)*2
print.param = FALSE # Do not print the parameters
)
plot(o)
plot(o,vars=c('t','slpsgn') ) # plot only trend and slope sign
plot(o,vars=c('t','slpsgn'), relative.heights =c(.8,.2) ) # run "?plot.beast" for more info
plot(o, interactive=TRUE)
#Example 5#
# Run an interactive GUI to visualize how BEAST is samplinig from the possible model
# spaces in terms of the numbers and timings of seasonal and trend changepoints.
# The GUI inferface allows changing the option parameters interactively. This GUI is
# only available on Win x64 machines, not Mac or Linux.
## Not run:
beast(Yellowstone, period=24, gui=TRUE)
## End(Not run)
#Example 6#
# Apply beast to trendonly data. 'Nile' is the ANNUAL river flow of the river
# Nile at Aswan since 1871. It is a 'ts' object; its time attributes (start=1871,
# end=1970,frequency=1) are used to replace the usersupplied start,deltat, and freq,
# if any.
data(Nile)
plot(Nile)
attributes(Nile) # a ts object with time attributes (i.e., tsp=(start,end,freq)
o = beast(Nile) # start=1871, delta=1, and freq=1 taken from Nile itself
plot(o)
o = beast(Nile, # the same as above. The usersupplied values (i.e., 2023,
start=2023, # 9999) are ignored bcz Nile carries its own time attributes.
period=9999, # Its frequency tag is 1 (i.e., trendonly), so season='none'
season='harmonic' # is used instead of the supplied 'harmonic'
)
#Example 7#
# NileVec is a pure data vector. The first run below is WRONG bcz NileVec was assumed
# to have a perodic component by default and beast gets a best estimate of freq=6 while
# the true value is freq=1. To fit a trendonly model, season='none' has to be explicitly
# specified, as in the 2nd & 3rd funs.
NileVec = as.vector(Nile) # NileVec is not a ts obj but a pure numeric data vector
o = beast(NileVec) # WRONG WAY to call: No time attributes available to interpret
# NileVec. By default, beast assumes season='harmonic', start=1,
# & deltat=1. 'freq' is missing and guessed to be 6 (WRONG).
plot(o) # WRONG Results: The result has a suprious seasonal component
o=beast(NileVec,season='none') # The correct way to call: Use season='none' for trendonly
# analysis; the default time is the integer indices
# "1:length(NileVec)'.
print(o$time)
o=beast(NileVec, # Recommended way to call: The true time attributes are
start = 1871, # given explicitly through start and deltat (or freq if
deltat = 1, # there is a cyclic/seasonal cmponent).
season = 'none')
print(o$time)
plot(o)
#Example 8#
# beast can handle missing data. co2 is a monthly time series (i.e.,freq=12) starting
# from Jan 1959. We generate some missing values at random indices
## Not run:
data(co2)
attributes(co2) # A ts object with time attributes (i.e., tsp)
badIdx = sample( 1:length(co2), 50) # Get a set of random indices
co2[badIdx] = NA # Insert some data gaps
out=beast(co2) # co2 is a ts object and its 'tsp' time attributes are used to get the
# true time info. No need to specify 'start','deltat', & freq explicity.
out=beast(co2, # The supplied time/period values will be ignored bcz
start = c(1959,1,15),# co2 is a ts object; the correct period = 1 will be
deltat = 1/12, # used.
period = 365)
print(out)
plot(out)
## End(Not run)
#Example 9#
# Apply beast to time serislike sequence data: the unit of sequences is not
# necessarily time.
data(CNAchrom11) # DNA copy number alterations in Chromesome 11 for cell line GM05296
# The data is orderd by genomic position (not time), and the values
# are the log2based intensity ratio of copy numbers between the sample
# the reference. A value of zero means no gain or loss in copy number.
o = beast(CNAchrom11,season='none') # season is a misnomer here bcz the data has nothing
# to do with time. Regardless, we fit only a trend.
plot(o)
#Example 10#
# Apply beast to time serislike data: the unit of sequences is not necessarily time.
# Age of Death of Successive Kings of England
# If the data link is deprecated, install the time series data library instead,
# which is available at https://pkg.yangzhuoranyang.com/tsdl/
# install.packages("devtools")
# devtools::install_github("FinYang/tsdl")
# kings = tsdl::tsdl[[293]]
kings = scan("http://robjhyndman.com/tsdldata/misc/kings.dat",skip=3)
out = beast(kings,season='none')
plot(out)
#Example 11#
# Another example from the tsdl data library
# Number of monthly births in New York from Jan 1946 to Dec 1959
# If the data link becomes invalid, install the time series data package instead
# install.packages("devtools")
# devtools::install_github("FinYang/tsdl")
# kings = tsdl::tsdl[[534]]
births = scan("http://robjhyndman.com/tsdldata/data/nybirths.dat")
out = beast(births,start=c(1946,1,15), deltat=1/12 )
plot(out) # the result is wrong bcz the guessed freq via autocorrelation by beast
# is 2 rather than 12, so we recommend always specifying 'freq' explicitly
# for those time series with a periodic component, as shown below.
out = beast(births,start=c(1946,1,15), deltat=1/12, freq =12 )
out = beast(births,start=c(1946,1,15), deltat=1/12, period=1.0 )
plot(out)
#Example 12#
# Daily confirmed COVID19 new cases and deaths across the globe
## Not run:
data(covid19)
plot(covid19$date, covid19$newcases, type='l')
newcases = sqrt( covid19$newcases ) # Apply a square roottransformation
# This ts varies periodically every 7 days. 7 days can't be precisely represented
# in the unit of year bcz some years has 365 days and others has 366. BEAST can hanlde
# this in two ways.
#(1) Use the date number as the time unitthe num of days lapsed since 19700101.
datenum = as.numeric(covid19$date)
o = beast(newcases, start=min(datenum), deltat=1, period=7)
o$time = as.Date(o$time, origin='19700101') # Convert from integers to Date.
plot(o)
#(2) Use strings to explicitly specify deltat and period with a unit.
startdate = covid19$date[1]
o = beast(newcases, start=startdate, deltat='1day', period='7days')
plot(o)
## End(Not run)
#Example 13#
# The old API interface of beast is still made available but NOT recommended. It is
# kept mainly to ensure the working of the sample code on Page 475 in the text
# Ecological Metods by Drs. Southwood and Henderson.
## Not run:
# The interface as shown here will be deprecated and NOT recommended.
beast(Yellowstone, 24) #24 is the freq: number of datapoints per period
# Specify the model or MCMC parameters through opt as in Rbeast v0.2
opt=list() #Create an empty list to append individual model parameters
opt$period=24 #Period of the cyclic component (i.e.,freq in the new version)
opt$minSeasonOrder=2 #Min harmonic order allowed in fitting season component
opt$maxSeasonOrder=8 #Max harmonic order allowed in fititing season component
opt$minTrendOrder=0 #Min polynomial order allowed to fit trend (0 for constant)
opt$maxTrendOrder=1 #Max polynomial order allowed to fit trend (1 for linear term)
opt$minSepDist_Season=20#Min separation time btw neighboring season changepoints
opt$minSepDist_Trend=20 #Min separation time btw neighboring trend changepoints
opt$maxKnotNum_Season=4 #Max number of season changepoints allowed
opt$maxKnotNum_Trend=10 #Max number of trend changepoints allowed
opt$omittedValue=NA #A customized value to indicate bad/missing values in the time
#series, in additon to those NA or NaN values.
# The following parameters used to configure the reverisiblejump MCMC (RJMCC) sampler
opt$chainNumber=2 #Number of parallel MCMC chains
opt$sample=1000 #Number of samples to be collected per chain
opt$thinningFactor=3 #A factor to thin chains
opt$burnin=500 #Number of burnin samples discarded at the start
opt$maxMoveStepSize=30 #For the move proposal, the max window allowed in jumping from
#the current changepoint
opt$resamplingSeasonOrderProb=0.2 #The probability of selecting a resampling proposal
#(e.g., resample seasonal harmonic order)
opt$resamplingTrendOrderProb=0.2 #The probability of selecting a resampling proposal
#(e.g., resample trend polynomial order)
opt$seed=65654 #A seed for the random generator: If seed=0,random numbers differ
#for different BEAST runs. Setting seed to a chosen nonzero integer
#will allow reproducing the same result for different BEAST runs.
beast(Yellowstone, opt)
## End(Not run)
#Example 14#
# Fit a model with an outlier component: Y = trend + outlier + error.
# Outliers here refer to spikes or dips at isolated points that can't be capatured by the
# trend
## Not run:
NileVec = as.vector(Nile)
NileVec[50] = NileVec[50] + 1500 # Add an artificial spike at t=50
o = beast(NileVec, season='none', hasOutlier=TRUE)
plot(o)
## End(Not run)
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