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MATLAB Version

Source: vignettes/articles/matlab-version.Rmd
matlab-version.Rmd

Changes from MATLAB Version

This page documents changes from original MATLAB code.

Exploratory Data Analysis (EDA)

Bug Fixes

  • Only show statistically significant change points for the Pettitt and MKS plots.
  • Fix bug causing the MKS test to only identify one change point, even if multiple change points were found to be above the threshold for statistical significance.
  • Fix major bug causing the MKS test to identify change points based on the progressive series instead of the z-statistics of the crossing points.
  • Remove unnecessary rounding in the moving window algorithm for estimating variability.
  • Re-implement the Phillips-Perron and KPSS tests to account for drift and trend.

Framework Changes

  • If serial correlation is identified, do not run the Phillips-Perron and KPSS tests.
  • Add the the Runs test to detect nonlinearity after fitting Sen’s trend estimator.
  • Run change point detection in multiple stages to prevent overpartitioning.

Flood Frequency Analysis (FFA)

Distribution Changes

The R version adds the three parameter Weibull distribution (with location, scale, and shape) parameters.

Model Selection Changes

The L-distance and L-kurtosis selection methods have been improved by using an optimization algorithm to find the parameters with the closest L-moments to the data instead of using a brute force approach. This is more computationally efficient and gives more precise results.

The procedure for computing the Z-statistic selection metric has been changed. If the L-moments of the dataset do not satisfy \(\tau_{4} \leq (1 + 5\tau _{3}^2)/6\), then the Kappa distribution will not be fitted and the candidate distributions that use the dataset will be omitted.

Parameter Estimation Changes

Parameterization of the PE3/LP3 distributions fails for some datasets because MATLAB is unable to handle the large numbers created by the gamma function. To manage this issue, the MATLAB version used the conventional moments (i.e. sample mean/variance/skewness) when this occurred. We avoid this problem in the R version by using the lgamma (log-gamma) function.

The R implementation uses L-BFGS-B for MLE/GMLE parameter estimation instead of Nelder-Mead, since the gradient is well defined for the likelihood functions we are working with. Additionally, the L-BFGS-B method makes it possible to assign bounds to the variables. This modification produced slight improvements to the MLL/GMLL for some datasets.

Uncertainty Quantification

Implement RFPL uncertainty quantification for the Weibull distribution.

Model Assessment Changes

Use the built-in R function approx() to perform log-linear interpolation of the return periods. The MATLAB implementation uses a hard-coded algorithm which behaves unpredictably when the original and interpolated \(x\)-values are equal.