BEAST: A Bayesian Ensemble Algorithm for Change-Point Detection and Time Series Decomposition

BEAST (Bayesian Estimator of Abrupt change, Seasonality, and Trend) is a fast, generic Bayesian model averaging algorithm to decompose time series or 1D sequential data into individual components, such as abrupt changes, trends, and periodic/seasonal variations, as described in Zhao et al. (2019). BEAST is useful for changepoint detection (e.g., breakpoints, structural breaks,joinpoints, regime shifts, or anomalies), trend analysis, time series decomposition (e.g., trend vs seasonality), time series segmentation, and interrupted time series analysis. See a list of selected studies using BEAST .

Quick Installation > BEAST was impemented in C/C++ but accessible from R, Python, Matlab, and Octave. Install it as follows:

• Python: pip install Rbeast
  
• Matlab: eval(webread('http://b.link/rbeast',weboptions('cert','')))
• Octave: eval(webread('http://b.link/rbeast'))
  
• R lang: install.packages("Rbeast")

Quick Usage

One-liner code for Python, Matlab and R:

# Python example
import Rbeast as rb; (Nile, Year)=rb.load_example('nile'); o=rb.beast(Nile,season='none'); rb.plot(o)

# Matlab/Octave example
load('Nile'); o = beast(Nile, 'season','none'); plotbeast(o)

# R example
library(Rbeast); data(Nile); o = beast(Nile); plot(o)

Installation for R

Rbeast in CRAN-TASK-VIEW: [Time Series Analysis] [Bayesian inference] [Environmetrics]

An R package Rbeast has been deposited at CRAN. ( On CRAN, there is another Bayesian time-series package named “beast”, which has nothing to do with the BEAST algorithim. Our package is Rbeast. Also, Rbeast has nothing to do with the famous “Bayesian evolutionary analysis by sampling trees” aglorithm.) Install Rbeast in R using

install.packages("Rbeast")

Run and test Rbeast in R

The main functions in Rbeast are beast(Y, ...), beast.irreg(Y, ...), and beast123(Y, metadata, prior, mcmc, extra). The code snippet below provides a starting point for the basic usage.

library(Rbeast)
data(Nile)                       #  annual streamflow of the Nile River    
out = beast(Nile, season='none') #  'none': trend-only data without seasonlaity   
print(out)                   
plot(out)
?Rbeast                          # See more details about the usage of `beast`    
     
tetris()                         # if you dare to waste a few moments of your life 
minesweeper()                    # if you dare to waste a few more moments of your life 

Installation for Matlab

Install the Matlab version of BEAST automatically to a local folder of your choice by running ```Matlab
beastPath = ‘C:'
eval( webread(’http://b.link/rbeast’) )

%%%%%%%%%%%%%%%%%%%%%%%%%%% Note on Automatic Installtion %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 1. Write permission needed for your chosen path; the variable name must be ‘beastPath’. % % 2. If webread has a certificate error, run the following line instead: % eval( webread( ‘http://b.link/rbeast’, weboptions(‘cert’,’’) ) ) % % 3. If the automatic installation fails, please manually download all the files (see blow) %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ``> The above will download all the files in the [Rbeast\Matlab folder at Github](https://github.com/zhaokg/Rbeast) to the chosen folder: ifbeastPathis missing, a default temporary folder (e.g.,C:$user_name$for Windows 10) will be used. If the automatic script fails, please download the Matlab files from [Github](https://github.com/zhaokg/Rbeast) manually. These files include a Matlab mex library compiled from the C soure code (e.g.,Rbeast.mexw64for Windows,Rbeast.mexa64for Linux,Rbeast.mexmaci64for MacOS) and some Matlab wrapper functions (e.g.,beast.m, andbeast123.m`) similar to the R interface, as well as some test datasets (e.g., Nile.mat, and co2.mat).

We generated the Matlab mex binary library on our own machines with Win10, Ubuntu 22.04, and macOS High Sierra. If they fail on your machine, the mex library can be compiled from the C source code files under Rbeast\Source. If needed, we are happy to work with you to compile for your specific OS or machines. Additional information on compilations from the C source is also given below.

Run and test Rbeast in Matlab

The Matlab API is similar to those of R. Below is a quick example: Matlab help beast help beast123 load('Nile.mat') % annual streamflow of the Nile River startin from year 1871 out = beast(Nile, 'season', 'none','start', 1871) % trend-only data without seasonality printbeast(out) plotbeast(out) ## Installation for Octave

The same as for Matlab. Now, only Windows platforms are supported. If needed for other platforms (e.g., Octave in Linux and Mac), please contact the author at zhao.1423@osu.edu for support.

Installation for Python

A package Rbeast has been deposited at PyPI: https://pypi.org/project/Rbeast/. Run the command below in a console to install:

  pip install Rbeast

Binary wheel files were built on Windows, MacOS, and Linux for Python version 3.7 to 3.11 (either x86_64 or arm64 CPU). If the installation fails, please install from the source to build the package using pip install Rbeast --no-binary :none:, which requies a C/C++ compliler (e.g., requiring gcc on Linux or xcode on Mac). If needed, contact Kaiguang Zhao (zhao.1423@osu.edu) to help build the package for your OS platform and Python version.

Run and test Rbeast in Python

Nile is annual streamflow of the River Nile, starting from Year 1871. As annual observations, it has no periodic component (i.e., season='none').

import Rbeast as rb                                       # Import the Rbeast package as `rb`
nile, year = rb.load_example('nile')                      # a sample time series
o          = rb.beast( nile, start=1871, season='none')
rb.plot(o)
rb.print(o)
o  # see a list of output fields in the output variable o

The second example googletrend is a monthly time series of the Google Search popularity of the word beach over the US. This monthly time series is reguarly-spaced (i.e., deltat=1 month =1/12 year); it has a cyclyic component with a period of 1 year. That is, the number of data points per period is period / deltat = 1 year / 1 month = 1/(1/12) = 12.

beach, year = rb.load_example('googletrend')
o = rb.beast(beach, start= 2004.0, deltat=1/12, period = 1.0)       # the time unit is unknown or arbitrary
o = rb.beast(beach, start= 2004.0, deltat=1/12, period ='1.0 year') # the time unit is fractional year
o = rb.beast(beach, start= 2004.0, deltat='1 month', period =1.0)   # the time unit is fractional year
rb.plot(o)
rb.print(o)

Installation for Julia/IDL (yet to come)

Wrappers in Julia and IDL are being developed: We welcome contributions and help from interested developers. If interested, contact Kaiguang Zhao at zhao.1423@osu.edu.

Description of BEAST

Interpretation of time series data is affected by model choices. Different models can give different or even contradicting estimates of patterns, trends, and mechanisms for the same data–a limitation alleviated by the Bayesian estimator of abrupt change,seasonality, and trend (BEAST) of this package. BEAST seeks to improve time series decomposition by forgoing the “single-best-model” concept and embracing all competing models into the inference via a Bayesian model averaging scheme. It is a flexible tool to uncover abrupt changes (i.e., change-points), cyclic variations (e.g., seasonality), and nonlinear trends in time-series observations. BEAST not just tells when changes occur but also quantifies how likely the detected changes are true. It detects not just piecewise linear trends but also arbitrary nonlinear trends. BEAST is applicable to real-valued time series data of all kinds, be it for remote sensing, finance, public health, economics, climate sciences, ecology, and hydrology. Example applications include its use to identify regime shifts in ecological data, map forest disturbance and land degradation from satellite imagery, detect market trends in economic data, pinpoint anomaly and extreme events in climate data, and unravel system dynamics in biological data. Details on BEAST are reported in Zhao et al. (2019). The paper is available at https://go.osu.edu/beast2019.

Note on computation

As a Bayesian algorithm, BEAST is fast and is possibly among the fastest implementations of Bayesian time-series analysis algorithms of the same nature. (But it is still slower, compared to nonBayesian methods.) For applications dealing with a few to thousands of time series, the computation won’t be an practical concern. But for remote sensing/geospatial applications that may easily involve millions or billions of time series, computation will be a big challenge for Desktop computer users. We suggest first testing BEAST on a single time series or small image chips first to determine whether BEAST is appropriate for your applications and, if yes, estimate how long it may take to process the whole image.

In any case, for those users handling stacked time-series images, do not use beast or beast.irreg. Use beast123 instead, which can handle 3D data cubes and allow parallel computing. We also welcome consultation with Kaiguang Zhao (zhao.1423@osu.edu) to give specific suggestions if you see some value of BEAST for your applications.

Reference

• Zhao, K., Wulder, M. A., Hu, T., Bright, R., Wu, Q., Qin, H., Li, Y., Toman, E., Mallick B., Zhang, X., & Brown, M. (2019). Detecting change-point, trend, and seasonality in satellite time series data to track abrupt changes and nonlinear dynamics: A Bayesian ensemble algorithm. Remote Sensing of Environment, 232, 111181. (the BEAST 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.102-119. (the mcmc sampler used for BEAST)

• Hu, T., Toman, E.M., Chen, G., Shao, G., Zhou, Y., Li, Y., Zhao, K. and Feng, Y., 2021. Mapping fine-scale human disturbances in a working landscape with Landsat time series on Google Earth Engine. ISPRS Journal of Photogrammetry and Remote Sensing, 176, pp.250-261. (an application paper)

Compilation from C source code (for developers and experts only)

Though not needed but if preferred, the code can be compiled for your specific machines. Check the Rbeast folder at GitHub for details.

Reporting Bugs or getting help

BEAST is distributed as is and without warranty of suitability for application. The one distributed above is still a beta version, with potential room for further improvement. If you encounter flaws with the software (i.e. bugs) please report the issue. Providing a detailed description of the conditions under which the bug occurred will help to identify the bug, you can directly email its maintainer Dr. Kaiguang Zhao at zhao.1423@osu.edu. Alternatively, Use the Issues tracker on GitHub to report issues with the software and to request feature enhancements.

Acknowledgement:

BEAST is developed by Yang Li, Tongxi Hu, Xuesong Zhang, and Kaiguang Zhao. The development of BEAST received supported through Microsoft Azure for Research (CRM0518513) and a USGS 104B grant and a Harmful Algal Bloom Research Initiative grant from the Ohio Department of Higher Education. The contribution of Xuesong Zhang was supported through USDA-ARS.

Selected publications using BEAST/Rbeast

Despite being published originally for ecological and enviornmental applications, BEAST is developed as a generic tool applicable to time series or time-series-like data arising from all disciplines. BEAST is not a heuristic algorithm but a rigorous statistical model. Below is a list of selected peer-reviewed pulications that used BEAST for statistical data analysis.