Publications by anspiess
Introducing ‘propagate’
With this post, I want to introduce the new ‘propagate’ package on CRAN. It has one single purpose: propagation of uncertainties (“error propagation”). There is already one package on CRAN available for this task, named ‘metRology’ (http://cran.r-project.org/web/packages/metRology/index.html). ‘propagate’ has some additional funct...
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I’ll take my NLS with weights, please…
Today I want to advocate weighted nonlinear regression. Why so? Minimum-variance estimation of the adjustable parameters in linear and non-linear least squares requires that the data be weighted inversely as their variances . Only then is the BLUE (Best Linear Unbiased Estimator) for linear regression and nonlinear regression with small errors (...
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Error propagation based on interval arithmetics
I added an interval function to my ‘propagate’ package (now on CRAN) that conducts error propagation based on interval arithmetics. It calculates the uncertainty of a model by using interval arithmetics based on (what I call) a “combinatorial sequence grid evaluation” approach, thereby avoiding the classical dependency problem that often ...
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Introducing: Orthogonal Nonlinear Least-Squares Regression in R
With this post I want to introduce my newly bred ‘onls’ package which conducts Orthogonal Nonlinear Least-Squares Regression (ONLS): http://cran.r-project.org/web/packages/onls/index.html. Orthogonal nonlinear least squares (ONLS) is a not so frequently applied and maybe overlooked regression technique that comes into question when one encoun...
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Linear regression with random error giving EXACT predefined parameter estimates
When simulating linear models based on some defined slope/intercept and added gaussian noise, the parameter estimates vary after least-squares fitting. Here is some code I developed that does a double transform of these models as to obtain a fitted model with EXACT defined parameter estimates a (intercept) and b (slope). It does so by: 1) Fitting...
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Monte Carlo-based prediction intervals for nonlinear regression
Calculation of the propagated uncertainty using (1), where is the gradient and the covariance matrix of the coefficients , is called the “Delta Method” and is widely applied in nonlinear least-squares (NLS) fitting. However, this method is based on first-order Taylor expansion and thus assummes linearity around . The second-order approach...
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