Introduction When fitting a nonlinear regression model in R with nls(), the first step is to select an appropriate regression model to fit the observed data, the second step is to find reasonable starting values for the model parameters in order to initialize the nonlinear least-squares (NLS) algorithm. In some ...

Introduction The previous post showcases the rrapply() function in the minimal rrapply-package as a revised and extended version of base rapply() in the context of nested list recursion in R. For quick data exploration of a nested list it can make sense to keep the list in its original nested ...

Introduction The previous post showcases the rrapply() function in the minimal rrapply-package as a revised and extended version of base rapply() in the context of nested list recursion in R. For quick data exploration of a nested list it can make sense to keep the list in its original nested ...

Introduction The nested list below shows a small extract from the Mathematics Genealogy Project highlighting the advisor/student genealogy of several famous mathematicians. The mathematician’s given names are present in the "given" attribute of each list element. The numeric values at the leaf elements are the total number of ...

Introduction The nested list below shows a small extract from the Mathematics Genealogy Project highlighting the advisor/student genealogy of several famous mathematicians. The mathematician’s given names are present in the "given" attribute of each list element. The numeric values at the leaf elements are the total number of ...

Introduction Automatic differentiation Automatic differentiation (AD) refers to the automatic/algorithmic calculation of derivatives of a function defined as a computer program by repeated application of the chain rule. Automatic differentiation plays an important role in many statistical computing problems, such as gradient-based optimization of large-scale models, where gradient calculation ...

Introduction The new gslnls-package provides R bindings to nonlinear least-squares optimization with the GNU Scientific Library (GSL) using the trust region methods implemented by the gsl_multifit_nlinear module. The gsl_multifit_nlinear module was added in GSL version 2.2 (released in August 2016) and the available nonlinear-least squares routines have been ...

Introduction Nonlinear regression model As a model setup, we consider noisy observations \(y_1,\ldots, y_n \in \mathbb{R}\) obtained from a standard nonlinear regression model of the form: \[ \begin{aligned} y_i &\ = \ f(\boldsymbol{x}_i, \boldsymbol{\theta}) + \epsilon_i, \quad i = 1,\ldots, n \end{aligned} \] where \(f: \mathbb{...

Introduction Tha aim of this post is to provide a working approach to perform piecewise constant or step function regression in Stan. To set up the regression problem, consider noisy observations \(y_1, \ldots, y_n \in \mathbb{R}\) sampled from a standard signal plus i.i.d. Gaussian noise model ...

Introduction Selection bias Selection bias occurs when sampled data or subjects in a study have been selected in a way that is not representative of the population of interest. As a consequence, conclusions made about the analyzed sample may be difficult to generalize, as the observed effects could be biased ...