  The transition density of a stochastic, logistic population growth model with
multiplicative intrinsic noise is analytically intractable. Inferring model
parameter values by fitting such stochastic differential equation (SDE) models
to data therefore requires relatively slow numerical simulation. Where such
simulation is prohibitively slow, an alternative is to use model approximations
which do have an analytically tractable transition density, enabling fast
inference. We introduce two such approximations, with either multiplicative or
additive intrinsic noise, each derived from the linear noise approximation of
the logistic growth SDE. After Bayesian inference we find that our fast LNA
models, using Kalman filter recursion for computation of marginal likelihoods,
give similar posterior distributions to slow arbitrarily exact models. We also
demonstrate that simulations from our LNA models better describe the
characteristics of the stochastic logistic growth models than a related
approach. Finally, we demonstrate that our LNA model with additive intrinsic
noise and measurement error best describes an example set of longitudinal
observations of microbial population size taken from a typical, genome-wide
screening experiment.
