# R

## New nonlinear least squares solvers in R with {gslnls}

Introduction Solving a nonlinear least squares problem consists of minimizing a least squares objective function made up of residuals $$g_1(\boldsymbol{\theta}), \ldots, g_n(\boldsymbol{\theta})$$ that are nonlinear functions of the parameters of interest $$\boldsymbol{\theta} = (\theta_1,\ldots, \theta_p)'$$:

## Mesmerizing multi-scale Turing patterns in R with Rcpp

This post showcases several multi-scale Turing patterns generated in R with Rcpp(Armadillo). The generating process, inspired by (McCabe 2010), consists of multi-scale convolutions with respect to short-range activator kernels and long-range inhibitor kernels, computed efficiently in the Fourier domain using RcppArmadillo. Starting from an almost homogeneous state, the algorithm generates regular 2D Turing patterns with smoothly varying behavior across multiple scales that are quite fascinating to look at.

## Automatic differentiation in R with Stan Math

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 by means of numeric differentiation (i.

## GSL nonlinear least squares fitting in R

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.

## Asymptotic confidence intervals for NLS regression in R

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 $$f: \mathbb{R}^k \times \mathbb{R}^p \to \mathbb{R}$$ is a known nonlinear function of the independent variables $$\boldsymbol{x}_1,\ldots,\boldsymbol{x}_n \in \mathbb{R}^k$$ and the unknown parameter vector $$\boldsymbol{\theta} \in \mathbb{R}^p$$ that we aim to estimate.

## Step function regression in Stan

Introduction The 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.

## Estimating reaction kinetics with Stan and R

Introduction In chemical kinetics, the rate of a solid-state reaction is generally modeled by a reaction rate law (or rate equation) of the form: $\frac{d\alpha}{dt} \ = \ k \cdot f(\alpha)\ = \ Ae^{-E_a/RT} \cdot f(\alpha)$

## Fitting the Heckman selection model with Stan and R

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 towards the sample and do not necessarily extend well to the population that we intended to analyze.

## Tracking Stan sampling progress in Shiny

Introduction The previous post demonstrates the use of pre-compiled Stan models in interactive R Shiny applications to avoid unnecessary Stan model (re-)compilation on application start-up.

## Running compiled Stan models in Shiny

Introduction The aim of this post is to provide a short step-by-step guide on writing interactive R Shiny-applications that include models written in Stan using rstan and rstantools.