Tag: inference
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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 inference model when missing observations
The inference model isn’t giving good performance. But is this because we’re missing data? In the inference model, the recorded output activity is related to the input according to $$ (\sigma^2 \II + \AA \AA^T) \bLa = \YY,$$where we’ve absorbed $\gamma$ into $\AA$. We can model this as $N$ observations of $\yy$ given $\bla$, where$$…