Bayesian inference of chemical reaction network parameters given reaction degeneracy: an approximate analytic solution

JohnVastola

Harvard University

"Bayesian inference of chemical reaction network parameters given reaction degeneracy: an approximate analytic solution"

Although chemical reaction networks (CRN) provide performant and biophysically plausible models for explaining single-cell genomic data, inference of reaction network parameters in this setting usually assumes available data points can be viewed as independent samples from a steady state distribution. Less is known about how to perform efficient parameter inference in the case that there is a continuous-time data stream, which adds complexity like nontrivial correlations between samples from different times. In the continuous-time setting, one has two natural questions: (i) given a set of reactions that could plausibly explain the observed data stream, what are reasonable estimates of the associated reaction rate parameters? and (ii) what is the minimal set of reactions necessary to explain the data? Both questions can be formalized as Bayesian inference problems, with the former concerning the inference of a model-dependent parameter posterior, and the latter concerning ‘structure’ inference. If one can assume each possible reaction has a different stoichiometry vector, there is a well-known analytic solution to both problems; if reactions can have the same stoichiometry vector (i.e., there is reaction degeneracy), both problems become substantially more difficult, and no analytic solution is known. We present the first approximate analytic solution to both problems, which is valid when the number of observations becomes sufficiently large. In its regime of validity, this solution allows its user to avoid expensive likelihood computations that can involve summing over an exponentially large number of terms. We discuss interesting consequences of this solution, like the fact that ‘simpler’ models with fewer reactions are preferred over more complex ones, and the fact that the parameter posteriors of non-identifiable models are strongly prior-dependent.
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