Fundamentals and Recent Developments in Approximate Bayesian Computation.

Bayesian inference plays an important role in phylogenetics, evolutionary biology, and in many other branches of science. It provides a principled framework for dealing with uncertainty and quantifying how it changes in the light of new evidence. For many complex models and inference problems, however, only approximate quantitative answers are obtainable. Approximate Bayesian computation (ABC) refers to a family of algorithms for approximate inference that makes a minimal set of assumptions by only requiring that sampling from a model is possible. We explain here the fundamentals of ABC, review the classical algorithms, and highlight recent developments. [ABC; approximate Bayesian computation; Bayesian inference; likelihood-free inference; phylogenetics; simulator-based models; stochastic simulation models; tree-based models.]

Resolving outbreak dynamics using approximate Bayesian computation for stochastic birth-death models.

Earlier research has suggested that approximate Bayesian computation (ABC) makes it possible to fit simulator-based intractable birth-death models to investigate communicable disease outbreak dynamics with accuracy comparable to that of exact Bayesian methods. However, recent findings have indicated that key parameters, such as the reproductive number R, may remain poorly identifiable with these models. Here we show that this identifiability issue can be resolved by taking into account disease-specific characteristics of the transmission process in closer detail. Using tuberculosis (TB) in the San Francisco Bay area as a case study, we consider a model that generates genotype data from a mixture of three stochastic processes, each with its own distinct dynamics and clear epidemiological interpretation.       We show that our model allows for accurate posterior inferences about outbreak dynamics from aggregated annual case data with genotype information. As a byproduct of the inference, the model provides an estimate of the infectious population size at the time the data were collected. The acquired estimate is approximately two orders of magnitude smaller than assumed in earlier related studies, and it is much better aligned with epidemiological knowledge about active TB prevalence. Similarly, the reproductive number R related to the primary underlying transmission process is estimated to be nearly three times larger than previous estimates, which has a substantial impact on the interpretation of the fitted outbreak model.

On the Identifiability of Transmission Dynamic Models for Infectious Diseases.

Understanding the transmission dynamics of infectious diseases is important for both biological research and public health applications. It has been widely demonstrated that statistical modeling provides a firm basis for inferring relevant epidemiological quantities from incidence and molecular data. However, the complexity of transmission dynamic models presents two challenges: (1) the likelihood function of the models is generally not computable, and computationally intensive simulation-based inference methods need to be employed, and (2) the model may not be fully identifiable from the available data. While the first difficulty can be tackled by computational and algorithmic advances, the second obstacle is more fundamental. Identifiability issues may lead to inferences that are driven more by prior assumptions than by the data themselves. We consider a popular and relatively simple yet analytically intractable model for the spread of tuberculosis based on classical IS6110 fingerprinting data. We report on the identifiability of the model, also presenting some methodological advances regarding the inference. Using likelihood approximations, we show that the reproductive value cannot be identified from the data available and that the posterior distributions obtained in previous work have likely been substantially dominated by the assumed prior distribution. Further, we show that the inferences are influenced by the assumed infectious population size, which generally has been kept fixed in previous work. We demonstrate that the infectious population size can be inferred if the remaining epidemiological parameters are already known with sufficient precision.