Implementations of Bayesian parametric, nonparametric and semiparametric procedures for univariate and multivariate time series. The package is based on the methods presented in C. Kirch et al (2018) <doi:10.1214/18-BA1126>, A. Meier (2018) <https://opendata.uni-halle.de//handle/1981185920/13470> and Y. Tang et al (2023) <arXiv:2303.11561>. It was supported by DFG grants KI 1443/3-1 and KI 1443/3-2.

The bezier package is a toolkit for working with Bezier curves and splines. The package provides functions for point generation, arc length estimation, degree elevation and curve fitting.

Decomposition of time series into
    trend, seasonal, and remainder components with methods for detecting and
    characterizing abrupt changes within the trend and seasonal components. 'BFAST'
    can be used to analyze different types of satellite image time series and can
    be applied to other disciplines dealing with seasonal or non-seasonal time
    series, such as hydrology, climatology, and econometrics. The algorithm can be
    extended to label detected changes with information on the parameters of the
    fitted piecewise linear models. 'BFAST' monitoring functionality is described
    in Verbesselt et al. (2010) <doi:10.1016/j.rse.2009.08.014>. 'BFAST monitor'
    provides functionality to detect disturbance in near real-time based on 'BFAST'-
    type models, and is described in Verbesselt et al. (2012) <doi:10.1016/j.rse.2012.02.022>.
    'BFAST Lite' approach is a flexible approach that handles missing data
    without interpolation, and will be described in an upcoming paper.
    Furthermore, different models can now be used to fit the
    time series data and detect structural changes (breaks).

Bayes factors represent the ratio of probabilities assigned to data by competing scientific hypotheses. However, one drawback of Bayes factors is their dependence on prior specifications that define null and alternative hypotheses. Additionally, there are challenges in their computation. To address these issues, we define Bayes factor functions (BFFs) directly from common test statistics. BFFs express Bayes factors as a function of the prior densities used to define the alternative hypotheses. These prior densities are centered on standardized effects, which serve as indices for the BFF. Therefore, BFFs offer a summary of evidence in favor of alternative hypotheses that correspond to a range of scientifically interesting effect sizes. Such summaries remove the need for arbitrary thresholds to determine "statistical significance." BFFs are available in closed form and can be easily computed from z, t, chi-squared, and F statistics. They depend on hyperparameters "r" and "tau^2", which determine the shape and scale of the prior distributions defining the alternative hypotheses. Plots of BFFs versus effect size provide informative summaries of hypothesis tests that can be easily aggregated across studies.