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 $\boldsymbol{\theta} = (\theta_1,\ldots, \theta_p)'$: $$ \boldsymbol{\theta}^* \ = \ \arg \min_{\boldsymbol{\theta}} \frac{1}{2} \Vert g(\boldsymbol{\theta}) \Vert^2 $$ In the context of regression, this problem is usually formulated as: $$ \begin{align} \boldsymbol{\theta}^* & \ = \ \arg \min_{\boldsymbol{\theta}} \frac{1}{2} \Vert \boldsymbol{y} - f(\boldsymbol{\theta}) \Vert^2 \\ & \ = \ \arg \min_{\boldsymbol{\theta}} \frac{1}{2} \sum_{i = 1}^n (y_i - f_i(\boldsymbol{\theta}))^2 \end{align} $$

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Hypothesis Testing: Fishing for Trouble

Introduction “Can you check if this is significant?” It was a seemingly innocuous question from a dangerous source: a semi data-literate scientist. The kind who believed, deep in his heart, that small p-values were “good” and large p-values were “erroneous”. On this day, the man in question had come forth with a large, complex multivariate dataset. He’d manually combed the data, visually inspected it, and hand-picked a hypothesis. “Can you check if this is significant?

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