Nested sampling for Bayesian model comparison in the context of Salmonella disease dynamics

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.

Likelihood-free nested sampling for parameter inference of biochemical reaction networks

The development of mechanistic models of biological systems is a central part of Systems Biology. One major challenge in developing these models is the accurate inference of model parameters. In recent years, nested sampling methods have gained increased attention in the Systems Biology community due to the fact that they are parallelizable and provide error estimates with no additional computations. One drawback that severely limits the usability of these methods, however, is that they require the likelihood function to be available, and thus cannot be applied to systems with intractable likelihoods, such as stochastic models. Here we present a likelihood-free nested sampling method for parameter inference which overcomes these drawbacks. This method gives an unbiased estimator of the Bayesian evidence as well as samples from the posterior. We derive a lower bound on the estimators variance which we use to formulate a novel termination criterion for nested sampling. The presented method enables not only the reliable inference of the posterior of parameters for stochastic systems of a size and complexity that is challenging for traditional methods, but it also provides an estimate of the obtained variance. We illustrate our approach by applying it to several realistically sized models with simulated data as well as recently published biological data. We also compare our developed method with the two most popular other likeliood-free approaches: pMCMC and ABC-SMC. The C++ code of the proposed methods, together with test data, is available at the github web page https://github.com/Mijan/LFNS_paper.

The behaviour of mathematical models of biochemical reactions is governed by model parameters encoding for various reaction rates, molecule concentrations and other biochemical quantities. As the general purpose of these models is to reproduce and predict the true biological response to different stimuli, the inference of these parameters, given experimental observations, is a crucial part of Systems Biology. While plenty of methods have been published for the inference of model parameters, most of them require the availability of the likelihood function and thus cannot be applied to models that do not allow for the computation of the likelihood. Further, most established methods do not provide an estimate of the variance of the obtained estimator. In this paper, we present a novel inference method that accurately approximates the posterior distribution of parameters and does not require the evaluation of the likelihood function. Our method is based on the nested sampling algorithm and approximates the likelihood with a particle filter. We show that the resulting posterior estimates are unbiased and provide a way to estimate not just the posterior distribution, but also an error estimate of the final estimator. We illustrate our method on several stochastic models with simulated data as well as one model of transcription with real biological data.

Incorporating prior knowledge improves detection of differences in bacterial growth rate

Background

Robust statistical detection of differences in the bacterial growth rate can be challenging, particularly when dealing with small differences or noisy data. The Bayesian approach provides a consistent framework for inferring model parameters and comparing hypotheses. The method captures the full uncertainty of parameter values, whilst making effective use of prior knowledge about a given system to improve estimation.

Results

We demonstrated the application of Bayesian analysis to bacterial growth curve comparison. Following extensive testing of the method, the analysis was applied to the large dataset of bacterial responses which are freely available at the web-resource, ComBase. Detection was found to be improved by using prior knowledge from clusters of previously analysed experimental results at similar environmental conditions. A comparison was also made to a more traditional statistical testing method, the F-test, and Bayesian analysis was found to perform more conclusively and to be capable of attributing significance to more subtle differences in growth rate.

Conclusions

We have demonstrated that by making use of existing experimental knowledge, it is possible to significantly improve detection of differences in bacterial growth rate.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-015-0204-9) contains supplementary material, which is available to authorized users.

Tipping point analysis of atmospheric oxygen concentration

We apply tipping point analysis to nine observational oxygen concentration records around the globe, analyse their dynamics and perform projections under possible future scenarios, leading to oxygen deficiency in the atmosphere. The analysis is based on statistical physics framework with stochastic modelling, where we represent the observed data as a composition of deterministic and stochastic components estimated from the observed data using Bayesian and wavelet techniques.

SYSBIONS: nested sampling for systems biology

MOTIVATION

Model selection is a fundamental part of the scientific process in systems biology. Given a set of competing hypotheses, we routinely wish to choose the one that best explains the observed data. In the Bayesian framework, models are compared via Bayes factors (the ratio of evidences), where a model's evidence is the support given to the model by the data. A parallel interest is inferring the distribution of the parameters that define a model. Nested sampling is a method for the computation of a model's evidence and the generation of samples from the posterior parameter distribution.

RESULTS

We present a C-based, GPU-accelerated implementation of nested sampling that is designed for biological applications. The algorithm follows a standard routine with optional extensions and additional features. We provide a number of methods for sampling from the prior subject to a likelihood constraint.

AVAILABILITY AND IMPLEMENTATION

The software SYSBIONS is available from http://www.theosysbio.bio.ic.ac.uk/resources/sysbions/

CONTACT

m.stumpf@imperial.ac.uk, robert.johnson11@imperial.ac.uk.