Bayesian inference for a partially observed birth–death process using data on proportions

• Published in: Australian & New Zealand journal of statistics 2018-06, Vol.60 (2), p.157-173
• Main Authors: Boys, Richard J., Ainsworth, Holly F., Gillespie, Colin S.
• Format: Article
• Language: English
• Subjects: Bayesian analysis; Biological activity; Biological models (mathematics); Gaussian process; Organic chemistry; Parameter estimation; partial observation; sparse emulator; Statistical inference
• ISSN: 1369-1473; 1467-842X
• DOI: 10.1111/anzs.12230

Summary Stochastic kinetic models are often used to describe complex biological processes. Typically these models are analytically intractable and have unknown parameters which need to be estimated from observed data. Ideally we would have measurements on all interacting chemical species in the process, observed continuously in time. However, in practice, measurements are taken only at a relatively few time‐points. In some situations, only very limited observation of the process is available, for example settings in which experimenters can only observe noisy observations on the proportion of cells that are alive. This makes the inference task even more problematic. We consider a range of data‐poor scenarios and investigate the performance of various computationally intensive Bayesian algorithms in determining the posterior distribution using data on proportions from a simple birth‐death process. The performance of algorithms for determining the posterior distribution in data‐poor scenarios using a simple birth‐death process.