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Bayesian changepoint detection and time series decomposition

Project description

Rbeast: A Python package for Bayesian changepoint 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, 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 implemented in C/C++ but accessible from R, Python, Matlab, and Octave. Run the following to install:

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

Quick Usage

One-liner code for Python, Matlab and R. Check for more details.

# 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 Python

A package Rbeast has been deposited here at PyPI: Install from a binary wheel using:

  pip install Rbeast

Currently, binary wheel files were built for common OS platforms and CPU architectures (e.g., Linux, Windows, and macOS for both x86_64 and arm64 CPUs). If the pre-built wheel doesn't work on your computer, please try to install from the source:

pip install Rbeast --no-binary :none:

The installation from sources requires a C/C++ compiler (e.g., gcc, and clang) to build the binary package, which should be hassle-free on Linux ( with gcc) or Mac (with clang or xcode) and may be tricky on Windows systems. If needed, contact Kaiguang Zhao ( to help build the package for your specific OS platforms and Python versions.

Run and test Rbeast in Python

Import the Rbeast package as rb:

import Rbeast as rb

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

nile, year = rb.load_example('nile')                     # nile is a 1d Python array or numpy vector
o          = rb.beast( nile, start=1871, season='none')  # season='none' bcz the data has no seasonal/periodic component
rb.plot(o, title='Annual streamflow of the Nile River')

# Print a list of fields in the output variable (e.g,, o.RMSE, o.trend.cp, o.time, and o.tend.cpOccPr)
# Check the R manual for expalanations of the output ( 
o                                                        # this is equivalent to "print(o)"                                    
# A wrong way to call beast for nile: If the 'season' arg is missing, the default season='harmonic' is used such that
# there is a seasonal component to be fit. But the Nile data is a trend-only signal with no periodic component
o = rb.beast(nile, start=1871 )  
rb.plot(o)      # the result is wrong. Use season='none' when calling beast for trend-only data                                 

The second example is a monthly time series of the Google Search popularity of beach over the US. This 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, deltat=1/12, period = 1.0)       # the time unit is uknown or arbitrary
o = rb.beast(beach, start= 2004, deltat=1/12, period ='1.0 year') # the time unit is fractional year

The third example is a stack of 1066 satellite NDVI images over time, with a spatial dimenion of 10 rows x 9 cols: Each pixel is an IRREGULAR time series of 1066 NDVI values with periodic variations at a period of 1.0 year. When running, BEAST will first aggragate the irregular time series into regular ones at a specified time interaval of deltat (in this example, we choose deltat=1/12 year =1 month, but you may choose other intervals, depending on the needs).

ndvi3d, datestr,year = rb.load_example('imagestack')  # ndvi is a numpy array of shape (484,10,20); the 1st dim refers to the time

metadata                = rb.args() # create an empty object to stuff the attributes: "metadata  = lambda: None" also works
metadata.time           = year      # times of individulal images/data points: the unit here is fractional year (e.g., 2004.232)
metadata.deltaTime      = 1/12      # regular interval used to aggregate the irregular time series (1/12 = 1/12 year = 1 month)
metadata.period         = 1.0       # the period is 1.0 year, so freq= 1.0 /(1/12) = 12 data points per period
metadata.whichDimIsTime = 1         # the dimension of the input ndvi is (484,10,20): which dim refers to the time. whichDimIsTime is a 1-based index  

o = rb.beast123(ndvi3d, metadata, [], [], []) # rb.beast123(data, metadata, prior, mcmc, extra): default values used if not supplied

rb.print(o[4, 6])                 # print the (5-th row, 7-th col) pixel: Python uses 0-based indices.
rb.plot(o[4, 6])                  # plot the (5-th row, 7-th col) pixel: Python uses 0-based indices.

figure, axes = rb.plot(o[4, 6])   # plot the (5-th row, 7-th col) pixel: Python uses 0-based indices.
rb.plot( o[4, 7], fig = figure)   # plot the (5-th row, 8-th col)pixel: Setting fig=figure will use the existing figure to plot

Below is another way to supply the time info:

ndvi3d, datestr,year = rb.load_example('imagestack') 

metadata              = lambda: None # create an empty object to stuff the attributes: "metadata  = rb.args()" also works
metadata.time         = rb.args( )   # create an empty object to stuff the 'datestr' and 'strfmt' attributes
metadata.time.datestr = datestr      # datestr is a list of file names (e.g., s2_ndvi_2018-01-03.tif) that contain the date info
metadata.time.strfmt  = 'LT05_018032_20110726.yyyy-mm-dd'  # the format used to extract the year (YYYY), month (mm), and day (dd) from the strings
metadata.deltaTime    = 1/12        # regular interval used to aggregate the irregular time series (1/12 = 1/12 year = 1 month)
metadata.period       = 1.0         # the period is 1.0 year, so freq= 1.0 /(1/12) = 12 data points per period
metadata.whichDimIsTime = 1         # the dimension of the input ndvi is (484,10,20): which dim refers to the time. whichDimIsTime is a 1-based index  

extra = rb.args(                             # a set of options to specify the outputs or computational configurations
               dumpInputData    = True,    # make a copy of the aggregated input data in the beast ouput
               numThreadsPerCPU = 2,       # Paralell  computing: use 2 threads per cpu core
               numParThreads    = 0        # `0` means using all CPU cores: total num of ParThreads = numThreadsPerCPU * core Num           
# Instead of using "extra=lambda:None;  extra.dumpInputData=True; ...", the above directly specifies the attribues in the object creation function

o = rb.beast123(ndvi3d, metadata, [], [], extra)  # rb.beast123(data, metadata, prior, mcmc, extra): default values used for prior and mcmc if missing


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


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/bugs with the software, please report the issue. Providing a 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 to report issues or request feature enhancements. Alternatively, use the Issues tracker on GitHub.

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.

Discipline Publication Title
Remote Sensing Li, J., Li, Z., Wu, H., and You, N., 2022. Trend, seasonality, and abrupt change detection method for land surface temperature time-series analysis: Evaluation and improvement. Remote Sensing of Environment, 10.1016/j.rse.2022.113222
Population Ecology Henderson, P. A. (2021). Southwood's Ecological Methods (5th edition). Oxford University Press., page 475-476
Cardiology Ozier, D., Rafiq, T., de Souza, R. and Singh, S.M., 2023. Use of Sacubitril/Valsartan Prior to Primary Prevention Implantable Cardioverter Defibrillator Implantation. CJC Open.
Spatial Ecology Laurin, G.V., Cotrina-Sanchez, A., Belelli-Marchesini, L., Tomelleri, E., Battipaglia, G., Cocozza, C., Niccoli, F., Kabala, J.P., Gianelle, D., Vescovo, L. and Da Ros, L., 2024. Comparing ground below-canopy and satellite spectral data for an improved and integrated forest phenology monitoring system. Ecological Indicators, 158, p.111328.
Psychophysiology Michela, A., 2024. The heart on duty: Training police officers in action using a biofeedback virtual-reality game (Doctoral dissertation, Sl: sn).
Ecology Mehri, S., Alesheikh, A.A. and Lotfata, A., 2024. Abiotic factors impact on oak forest decline in Lorestan Province, Western Iran. Scientific Reports, 14(1), p.3973.
Paleoclimatology Wauthy, S., Tison, J.L., Inoue, M., El Amri, S., Sun, S., Fripiat, F., Claeys, P. and Pattyn, F., 2024. Spatial and temporal variability of environmental proxies from the top 120 m of two ice cores in Dronning Maud Land (East Antarctica). Earth System Science Data, 16(1), pp.35-58.
Paleoclimatology Anastasia Zhuravleva et al., 2023. Caribbean salinity anomalies contributed to variable North Atlantic circulation and climate during the Common Era. Science Advances, DOI:10.1126/sciadv.adg2639
Phenometrics Laurin, G.V., Cotrina-Sanchez, A., Belelli-Marchesini, L., Tomelleri, E., Battipaglia, G., Cocozza, C., Niccoli, F., Kabala, J.P., Gianelle, D., Vescovo, L. and Da Ros, L., 2024. Comparing ground below-canopy and satellite spectral data for an improved and integrated forest phenology monitoring system. Ecological Indicators, 158, p.111328.
Anthropocene Science Thomas, E.R., Vladimirova, D.O., Tetzner, D.R., Emanuelsson, D.B., Humby, J., Turner, S.D., Rose, N.L., Roberts, S.L., Gaca, P. and Cundy, A.B., 2023. The Palmer ice core as a candidate Global boundary Stratotype Section and Point for the Anthropocene series. The Anthropocene Review, p.20530196231155191.
Enviornmental Engineering Ganji, A., Saeedi, M., Lloyd, M., Xu, J., Weichenthal, S. and Hatzopoulou, M., 2024. Air pollution prediction and backcasting through a combination of mobile monitoring and historical on-road traffic emission inventories. Science of The Total Environment, 915, p.170075.
Biomedical Engineering Saghbiny, E., Da Silva, J., Leblanc, L., Bobbio, C., Morel, G.G., Vialle, R. and Tamadazte, B., 2023, September. Breach detection in spine surgery based on cutting torque with ex-vivo experimental validation. In Conference on New Technologies for Computer and Robot Assisted Surgery.
Political Science Reuning, K., Whitesell, A. and Hannah, A.L., 2022. Facebook algorithm changes may have amplified local republican parties. Research & Politics, 9(2), p.20531680221103809.
Geography Lyu, R., Pang, J., Zhang, J. and Zhang, J., 2024. The impacts of disturbances on mountain ecosystem services: Insights from BEAST and Bayesian network. Applied Geography, 162, p.103143.
Watershed Hydrology Sakizadeh, M., Milewski, A. and Sattari, M.T., 2023. Analysis of Long-Term Trend of Stream Flow and Interaction Effect of Land Use and Land Cover on Water Yield by SWAT Model and Statistical Learning in Part of Urmia Lake Basin, Northwest of Iran. Water, 15(4), p.690.
Oceanography Oehlert, A.M., Hunter, H., Riopelle, C. and Purkis, S.J., 2023. Perturbation to North Atlantic Ocean-Climate Dynamics Tripled Whitings Mud Production in the Bahamas. Journal of Geophysical Research: Oceans, 128(11), p.e2023JC020021.
Hydraulic Engineering Xu, X., Yang, J., Ma, C., Qu, X., Chen, J. and Cheng, L., 2022. Segmented modeling method of dam displacement based on BEAST time series decomposition. Measurement, 202, p.111811.
Social Media Barrie, C., Ketchley, N., Siegel, A. and Bagdouri, M., 2023. Measuring Media Freedom.
Political Economy Benchimol, J. and Palumbo, L., 2023. Sanctions and Russian Online Prices.
Physiology Shakeel, M., Brockmann, A. Temporal effects of sugar intake on fly local search and honey bee dance behaviour. J Comp Physiol A (2023).
Ichthyology Kaeding, L.R., 2023. Climate-change and nonnative-piscivore impacts on a renowned Oncorhynchus metapopulation, requirements for metapopulation recovery, and similarities to anadromous salmonid metapopulations. Aquatic Sciences, 85(4), p.88.
Remote Sensing Mulverhill, C., Coops, N.C. and Achim, A., 2023. Continuous monitoring and sub-annual change detection in high-latitude forests using Harmonized Landsat Sentinel-2 data. ISPRS Journal of Photogrammetry and Remote Sensing, 197, pp.309-319.
Physical Chemistry Faran, M. and Bisker, G., 2023. Nonequilibrium Self-Assembly Time Forecasting by the Stochastic Landscape Method. The Journal of Physical Chemistry B.
Analytical Chemistry Simic, M., Neuper, C., Hohenester, U. and Hill, C., 2023. Optofluidic force induction as a process analytical technology. Analytical and Bioanalytical Chemistry, pp.1-11.
Ecosystem Sciences Lyu, R., Zhao, W., Pang, J., Tian, X., Zhang, J. and Wang, N., 2022. Towards a sustainable nature reserve management: Using Bayesian network to quantify the threat of disturbance to ecosystem services. Ecosystem Services, 58, p.101483.
Environmental Sciences Nickerson, S., Chen, G., Fearnside, P., Allan, C.J., Hu, T., de Carvalho, L.M. and Zhao, K., 2022. Forest loss is significantly higher near clustered small dams than single large dams per megawatt of hydroelectricity installed in the Brazilian Amazon. Environmental Research Letters.
Geology Fan, X., Goeppert, N. and Goldscheider, N., 2023. Quantifying the historic and future response of karst spring discharge to climate variability and change at a snow-influenced temperate catchment in central Europe. Hydrogeology Journal, pp.1-17.
Wildlife Smith, Matthew M., and Jonathan N. Pauli. "Connectivity maintains genetic diversity and population persistence within an archipelagic refugia even under declining lake ice." Mechanisms of species recovery for a forest carnivore in a changing landscape: 173.
Climate Sciences Duke, N.C., Mackenzie, J.R., Canning, A.D., Hutley, L.B., Bourke, A.J., Kovacs, J.M., Cormier, R., Staben, G., Lymburner, L. and Ai, E., 2022. ENSO-driven extreme oscillations in mean sea level destabilise critical shoreline mangroves—An emerging threat. PLOS Climate, 1(8), p.e000003
Finance Candelaria, Christopher A., Shelby M. McNeill, and Kenneth A. Shores. (2022). What is a School Finance Reform? Uncovering the ubiquity and diversity of school finance reforms using a Bayesian changepoint estimator.(EdWorkingPaper: 22-587). Retrieved from Annenberg Institute at Brown University:
Public health Linnell, K., Fudolig, M., Schwartz, A., Ricketts, T.H., O'Neil-Dunne, J.P., Dodds, P.S. and Danforth, C.M., 2022. Spatial changes in park visitation at the onset of the pandemic. arXiv preprint arXiv:2205.15937.
Biometerology Li, Y., Liu, Y., Bohrer, G., Cai, Y., Wilson, A., Hu, T., Wang, Z. and Zhao, K., 2022. Impacts of forest loss on local climate across the conterminous United States: Evidence from satellite time-series observations. Science of The Total Environment, 802, p.149651.
Applied Math Ferguson, Daniel, and Francois G. Meyer. Probability density estimation for sets of large graphs with respect to spectral information using stochastic block models. arXiv preprint arXiv:2207.02168 (2022).
Transportation Science Delavary, M., Kalantari, A.H., Mohammadzadeh Moghaddam, A., Fakoor, V., Lavalliere, M. and Wilhelm Siebert, F., 2023. Road traffic mortality in Iran: longitudinal trend and seasonal analysis, March 2011-February 2020. International Journal of Injury Control and Safety Promotion, pp.1-12.
Water quality He, Ziming, Jiayu Yao, Yancen Lu, and Danlu Guo. "Detecting and explaining long-term changes in river water quality in south eastern Australia." Hydrological Processes: e14741.
Air quality Wu, S., Yao, J., Wang, Y. and Zhao, W., 2023. Influencing factors of PM2. 5 concentrations in the typical urban agglomerations in China based on wavelet perspective. Environmental Research, p.116641.
Hydrology Zohaib, M. and Choi, M., 2020. Satellite-based global-scale irrigation water use and its contemporary trends. Science of The Total Environment, 714, p.136719.
Energy Engineering Lindig, S., Theristis, M. and Moser, D., 2022. Best practices for photovoltaic performance loss rate calculations. Progress in Energy, 4(2), p.022003.
Virology Shen, L., Sun, M., Song, S., Hu, Q., Wang, N., Ou, G., Guo, Z., Du, J., Shao, Z., Bai, Y. and Liu, K., 2022. The impact of anti-COVID19 nonpharmaceutical interventions on hand, foot, and mouth disease—A spatiotemporal perspective in Xi'an, northwestern China. Journal of medical virology.
Pharmaceutical Sciences Patzkowski, M.S., Costantino, R.C., Kane, T.M., Nghiem, V.T., Kroma, R.B. and Highland, K.B., 2022. Military Health System Opioid, Tramadol, and Gabapentinoid Prescription Volumes Before and After a Defense Health Agency Policy Release. Clinical Drug Investigation, pp.1-8.
Geography Cai, Y., Liu, S. and Lin, H., 2020. Monitoring the vegetation dynamics in the Dongting Lake Wetland from 2000 to 2019 using the BEAST algorithm based on dense Landsat time series. Applied Sciences, 10(12), p.4209.
Oceanography Pitarch, J., Bellacicco, M., Marullo, S. and Van Der Woerd, H.J., 2021. Global maps of Forel-Ule index, hue angle and Secchi disk depth derived from 21 years of monthly ESA Ocean Colour Climate Change Initiative data. Earth System Science Data, 13(2), pp.481-490.
Photovoltaics Micheli, L., Theristis, M., Livera, A., Stein, J.S., Georghiou, G.E., Muller, M., Almonacid, F. and Fernadez, E.F., 2021. Improved PV soiling extraction through the detection of cleanings and change points. IEEE Journal of Photovoltaics, 11(2), pp.519-526.
Climate Sciences White, J.H., Walsh, J.E. and Thoman Jr, R.L., 2021. Using Bayesian statistics to detect trends in Alaskan precipitation. International Journal of Climatology, 41(3), pp.2045-2059.
Field Hydrology Merk, M., Goeppert, N. and Goldscheider, N., 2021. Deep desiccation of soils observed by long-term high-resolution measurements on a large inclined lysimeter. Hydrology and Earth System Sciences, 25(6), pp.3519-3538.
Forest Ecology Moreno-Fernandez, D., Viana-Soto, A., Camarero, J.J., Zavala, M.A., Tijerin, J. and Garcia, M., 2021. Using spectral indices as early warning signals of forest dieback: The case of drought-prone Pinus pinaster forests. Science of The Total Environment, 793, p.148578.
Atmospheric Sciences Tingwei, C., Tingxuan, H., Bing, M., Fei, G., Yanfang, X., Rongjie, L., Yi, M. and Jie, Z., 2021. Spatiotemporal pattern of aerosol types over the Bohai and Yellow Seas observed by CALIOP. Infrared and Laser Engineering, 50(6), p.20211030.
Terrestrial ecology Dashti, H., Pandit, K., Glenn, N.F., Shinneman, D.J., Flerchinger, G.N., Hudak, A.T., de Graaf, M.A., Flores, A., Ustin, S., Ilangakoon, N. and Fellows, A.W., 2021. Performance of the ecosystem demography model (EDv2. 2) in simulating gross primary production capacity and activity in a dryland study area. Agricultural and Forest Meteorology, 297, p.108270.
Statistics Storath, M. and Weinmann, A., 2023. Smoothing splines for discontinuous signals. Journal of Computational and Graphical Statistics, (just-accepted), pp.1-26.
Environmental Engineering Bainbridge, R., Lim, M., Dunning, S., Winter, M.G., Diaz-Moreno, A., Martin, J., Torun, H., Sparkes, B., Khan, M.W. and Jin, N., 2022. Detection and forecasting of shallow landslides: lessons from a natural laboratory. Geomatics, Natural Hazards and Risk, 13(1), pp.686-704.
Hydrology Yang, X., Tian, S., You, W. and Jiang, Z., 2021. Reconstruction of continuous GRACE/GRACE-FO terrestrial water storage anomalies based on time series decomposition. Journal of Hydrology, 603, p.127018.
Landscape Ecology Adams, B.T., Matthews, S.N., Iverson, L.R., Prasad, A.M., Peters, M.P. and Zhao, K., 2021. Spring phenological variability promoted by topography and vegetation assembly processes in a temperate forest landscape. Agricultural and Forest Meteorology, 308, p.108578.

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