Tag: linear regression
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Reaction rate inference
Consider the toy example set of reactions\begin{align*}S_0 &\xrightarrow{k_1} S_1 + S_2\\S_2 &\xrightarrow{k_2}S_3 + S_4\\S_1 + S_3 &\xrightarrow{k_3} S_5\end{align*}We have (noisy) data on the concentrations of the species as a function of time. We want to infer the rates $k_1$ to $k_3$. Let’s write the derivatives:\begin{align*}\dot S_0 &=- k_1 S_0\\\dot S_1 &= k_1 S_0 -k_3 S_1…
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The equivalent kernel for non-zero prior mean
This note is a brief addendum to Section 3.3 of Bishop on Bayesian Linear Regression. Some of the derivations in that section assume, for simplicity, that the prior mean on the weights is zero. Here we’ll relax this assumption and see what happens to the equivalent kernel. Background The setting in that section is that,…