Epidemiological inference at the threshold of data availability: an influenza A(H1N2)v spillover event in the United Kingdom

Viruses that infect animals regularly spill over into the human population, but individual events may lead to anything from a single case to a novel pandemic. Rapidly gaining an understanding of a spillover event is critical to calibrating a public health response. We here propose a novel method, using likelihood-free rejection sampling, to evaluate the properties of an outbreak of swine-origin influenza A(H1N2)v in the United Kingdom, detected in November 2023. From the limited data available, we generate historical estimates of the probability that the outbreak had died out in the days following the detection of the first case. Our method suggests that the outbreak could have been said to be over with 95% certainty between 19 and 29 days after the first case was detected, depending upon the probability of a case being detected. We further estimate the number of undetected cases conditional upon the outbreak still being live, the epidemiological parameter R 0, and the date on which the spillover event itself occurred. Our method requires minimal data to be effective. While our calculations were performed after the event, the real-time application of our method has potential value for public health responses to cases of emerging viral infection.

Calibration of agent based models for monophasic and biphasic tumour growth using approximate Bayesian computation

Agent-based models (ABMs) are readily used to capture the stochasticity in tumour evolution; however, these models are often challenging to validate with experimental measurements due to model complexity. The Voronoi cell-based model (VCBM) is an off-lattice agent-based model that captures individual cell shapes using a Voronoi tessellation and mimics the evolution of cancer cell proliferation and movement. Evidence suggests tumours can exhibit biphasic growth in vivo. To account for this phenomena, we extend the VCBM to capture the existence of two distinct growth phases. Prior work primarily focused on point estimation for the parameters without consideration of estimating uncertainty. In this paper, approximate Bayesian computation is employed to calibrate the model to in vivo measurements of breast, ovarian and pancreatic cancer. Our approach involves estimating the distribution of parameters that govern cancer cell proliferation and recovering outputs that match the experimental data. Our results show that the VCBM, and its biphasic extension, provides insight into tumour growth and quantifies uncertainty in the switching time between the two phases of the biphasic growth model. We find this approach enables precise estimates for the time taken for a daughter cell to become a mature cell. This allows us to propose future refinements to the model to improve accuracy, whilst also making conclusions about the differences in cancer cell characteristics.

BayesFlow: Learning Complex Stochastic Models With Invertible Neural Networks

Estimating the parameters of mathematical models is a common problem in almost all branches of science. However, this problem can prove notably difficult when processes and model descriptions become increasingly complex and an explicit likelihood function is not available. With this work, we propose a novel method for globally amortized Bayesian inference based on invertible neural networks that we call BayesFlow. The method uses simulations to learn a global estimator for the probabilistic mapping from observed data to underlying model parameters. A neural network pretrained in this way can then, without additional training or optimization, infer full posteriors on arbitrarily many real data sets involving the same model family. In addition, our method incorporates a summary network trained to embed the observed data into maximally informative summary statistics. Learning summary statistics from data makes the method applicable to modeling scenarios where standard inference techniques with handcrafted summary statistics fail. We demonstrate the utility of BayesFlow on challenging intractable models from population dynamics, epidemiology, cognitive science, and ecology. We argue that BayesFlow provides a general framework for building amortized Bayesian parameter estimation machines for any forward model from which data can be simulated.

A Bayesian brain model of adaptive behavior: an application to the Wisconsin Card Sorting Task

Adaptive behavior emerges through a dynamic interaction between cognitive agents and changing environmental demands. The investigation of information processing underlying adaptive behavior relies on controlled experimental settings in which individuals are asked to accomplish demanding tasks whereby a hidden regularity or an abstract rule has to be learned dynamically. Although performance in such tasks is considered as a proxy for measuring high-level cognitive processes, the standard approach consists in summarizing observed response patterns by simple heuristic scoring measures. With this work, we propose and validate a new computational Bayesian model accounting for individual performance in the Wisconsin Card Sorting Test (WCST), a renowned clinical tool to measure set-shifting and deficient inhibitory processes on the basis of environmental feedback. We formalize the interaction between the task's structure, the received feedback, and the agent's behavior by building a model of the information processing mechanisms used to infer the hidden rules of the task environment. Furthermore, we embed the new model within the mathematical framework of the Bayesian Brain Theory (BBT), according to which beliefs about hidden environmental states are dynamically updated following the logic of Bayesian inference. Our computational model maps distinct cognitive processes into separable, neurobiologically plausible, information-theoretic constructs underlying observed response patterns. We assess model identification and expressiveness in accounting for meaningful human performance through extensive simulation studies. We then validate the model on real behavioral data in order to highlight the utility of the proposed model in recovering cognitive dynamics at an individual level. We highlight the potentials of our model in decomposing adaptive behavior in the WCST into several information-theoretic metrics revealing the trial-by-trial unfolding of information processing by focusing on two exemplary individuals whose behavior is examined in depth. Finally, we focus on the theoretical implications of our computational model by discussing the mapping between BBT constructs and functional neuroanatomical correlates of task performance. We further discuss the empirical benefit of recovering the assumed dynamics of information processing for both clinical and research practices, such as neurological assessment and model-based neuroscience.

POPE: post optimization posterior evaluation of likelihood free models

BACKGROUND

In many domains, scientists build complex simulators of natural phenomena that encode their hypotheses about the underlying processes. These simulators can be deterministic or stochastic, fast or slow, constrained or unconstrained, and so on. Optimizing the simulators with respect to a set of parameter values is common practice, resulting in a single parameter setting that minimizes an objective subject to constraints.

RESULTS

We propose algorithms for post optimization posterior evaluation (POPE) of simulators. The algorithms compute and visualize all simulations that can generate results of the same or better quality than the optimum, subject to constraints. These optimization posteriors are desirable for a number of reasons among which are easy interpretability, automatic parameter sensitivity and correlation analysis, and posterior predictive analysis. Our algorithms are simple extensions to an existing simulation-based inference framework called approximate Bayesian computation. POPE is applied two biological simulators: a fast and stochastic simulator of stem-cell cycling and a slow and deterministic simulator of tumor growth patterns.

CONCLUSIONS

POPE allows the scientist to explore and understand the role that constraints, both on the input and the output, have on the optimization posterior. As a Bayesian inference procedure, POPE provides a rigorous framework for the analysis of the uncertainty of an optimal simulation parameter setting.

Phylodynamic Inference with Kernel ABC and Its Application to HIV Epidemiology

The shapes of phylogenetic trees relating virus populations are determined by the adaptation of viruses within each host, and by the transmission of viruses among hosts. Phylodynamic inference attempts to reverse this flow of information, estimating parameters of these processes from the shape of a virus phylogeny reconstructed from a sample of genetic sequences from the epidemic. A key challenge to phylodynamic inference is quantifying the similarity between two trees in an efficient and comprehensive way. In this study, I demonstrate that a new distance measure, based on a subset tree kernel function from computational linguistics, confers a significant improvement over previous measures of tree shape for classifying trees generated under different epidemiological scenarios. Next, I incorporate this kernel-based distance measure into an approximate Bayesian computation (ABC) framework for phylodynamic inference. ABC bypasses the need for an analytical solution of model likelihood, as it only requires the ability to simulate data from the model. I validate this “kernel-ABC” method for phylodynamic inference by estimating parameters from data simulated under a simple epidemiological model. Results indicate that kernel-ABC attained greater accuracy for parameters associated with virus transmission than leading software on the same data sets. Finally, I apply the kernel-ABC framework to study a recent outbreak of a recombinant HIV subtype in China. Kernel-ABC provides a versatile framework for phylodynamic inference because it can fit a broader range of models than methods that rely on the computation of exact likelihoods.