Efficient Statistical Inference for Stochastic Reaction Processes

We address the problem of estimating unknown model parameters and state variables in stochastic reaction processes when only sparse and noisy measurements are available. Using an asymptotic system size expansion for the backward equation, we derive an efficient approximation for this problem. We demonstrate the validity of our approach on model systems and generalize our method to the case when some state variables are not observed.

Figure 1

Inference results for a Lotka-Volterra process with parameters given in Table . Symbols denote noisy observations, thick lines show the posterior mean, and the 95% confidence region for parameters fixed at their maximum-likelihood values is surrounded by dotted lines. For comparison, the original process is plotted as a thin line. Parameter estimates for this data set: $\alpha =(6.1\pm 1.3)\times {10}^{-3}$, $\beta =(2.6\pm 0.5)\times {10}^{-4}$, $\gamma =(4.1\pm 0.9)\times {10}^{-3}$, $\delta =(1.8\pm 0.4)\times {10}^{-4}$.

Figure 2

Inference results for the genetic autoregulatory network with parameters given in Table . Symbols and lines as in Fig. 1. Results of parameter estimation for this data set: $\alpha =1.9\times {10}^{-1}$, $\beta =6.8\times {10}^{-3}$, $\gamma =3.0\times {10}^{-2}$, $\delta =4.2\times {10}^{-3}$, $x_c=19.7$.