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.

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.

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:
\[ \frac{d\alpha}{dt} \ = \ k \cdot f(\alpha)\ = \ Ae^{-E_a/RT} \cdot f(\alpha) \]

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.

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.

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.