Model choice problems using approximate Bayesian computation with applications to pathogen transmission data sets

Bayesian model selection for COVID-19 pandemic state estimation using extended Kalman filters: Case study for Saudi Arabia

Quantifying the uncertainty in data-driven mechanistic models is fundamental in public health applications. COVID-19 is a complex disease that had a significant impact on global health and economies. Several mathematical models were used to understand the complexity of the transmission dynamics under different hypotheses to support the decision-making for disease management. This paper highlights various scenarios of a 6D epidemiological model known as SEIQRD (Susceptible-Exposed-Infected-Quarantined-Recovered-Deceased) to evaluate its effectiveness in prediction and state estimation during the spread of COVID-19 pandemic. Then we investigate the suitability of the classical 4D epidemiological model known as SIRD (Susceptible-Infected-Recovered-Deceased) in the long-term behaviour in order to make a comparison between these models. The primary aim of this paper is to establish a foundational basis for the validity and epidemiological model comparisons in long-term behaviour which may help identify the degree of model complexity that is required based on two approaches viz. the Bayesian inference employing the nested sampling algorithm and recursive state estimation utilizing the Extended Kalman Filter (EKF). Our approach acknowledges the potential imperfections and uncertainties inherent in compartmental epidemiological models. By integrating our proposed methodology, these models can consistently generate predictions closely aligned with the observed data on active cases and deaths. This framework, implemented within the EKF algorithm, offers a robust tool for addressing future, unknown pandemics. Moreover, we present a systematic methodology for time-varying parameter estimation along with uncertainty quantification using Saudi Arabia COVID-19 data and obtain the credible confidence intervals of the epidemiological nonlinear dynamical system model parameters.

Flexible model selection for mechanistic network models

Network models are applied across many domains where data can be represented as a network. Two prominent paradigms for modelling networks are statistical models (probabilistic models for the observed network) and mechanistic models (models for network growth and/or evolution). Mechanistic models are better suited for incorporating domain knowledge, to study effects of interventions (such as changes to specific mechanisms) and to forward simulate, but they typically have intractable likelihoods. As such, and in a stark contrast to statistical models, there is a relative dearth of research on model selection for such models despite the otherwise large body of extant work. In this article, we propose a simulator-based procedure for mechanistic network model selection that borrows aspects from Approximate Bayesian Computation along with a means to quantify the uncertainty in the selected model. To select the most suitable network model, we consider and assess the performance of several learning algorithms, most notably the so-called Super Learner, which makes our framework less sensitive to the choice of a particular learning algorithm. Our approach takes advantage of the ease to forward simulate from mechanistic network models to circumvent their intractable likelihoods. The overall process is flexible and widely applicable. Our simulation results demonstrate the approach's ability to accurately discriminate between competing mechanistic models. Finally, we showcase our approach with a protein-protein interaction network model from the literature for yeast (Saccharomyces cerevisiae).

Approximate Bayesian inference for discretely observed continuous-time multi-state models

Inference for continuous time multi-state models presents considerable computational difficulties when the process is only observed at discrete time points with no additional information about the state transitions. In fact, for general multi-state Markov model, evaluation of the likelihood function is possible only via intensive numerical approximations. Moreover, in real applications, transitions between states may depend on the time since entry into the current state, and semi-Markov models, where the likelihood function is not available in closed form, should be fitted to the data. Approximate Bayesian Computation (ABC) methods, which make use only of comparisons between simulated and observed summary statistics, represent a solution to intractable likelihood problems and provide alternative algorithms when the likelihood calculation is computationally too costly. In this article we investigate the potentiality of ABC techniques for multi-state models both to obtain the posterior distributions of the model parameters and to compare Markov and semi-Markov models. In addition, we will also exploit ABC methods to estimate and compare hidden Markov and semi-Markov models when observed states are subject to classification errors. We illustrate the performance of the ABC methodology both with simulated data and with a real data example.