Topological Approximate Bayesian Computation for Parameter Inference of an Angiogenesis Model
Inferring the parameters of models describing biological systems is an important problem in the reverse engineering of the mechanisms underlying these systems. Much work has focused on parameter inference of stochastic and ordinary differential equation models using Approximate Bayesian Computation (ABC). While there is some recent work on inference in spatial models, this remains an open problem. Simultaneously, advances in topological data analysis (TDA), a field of computational mathematics, have enabled spatial patterns in data to be characterised. Here we focus on recent work using topological data analysis to study different regimes of parameter space for a well-studied model of angiogenesis. We propose a method for combining TDA with ABC to infer parameters in the Anderson-Chaplain model of angiogenesis. We demonstrate that this topological approach outperforms ABC approaches that use simpler statistics based on spatial features of the data. This is a first step towards a general framework of spatial parameter inference for biological systems, for which there may be a variety of filtrations, vectorisations, and summary statistics to be considered. All code used to produce our results is available as a Snakemake workflow.
Code (1)
Tasks
Topological Data AnalysisMethods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Topological model selection: a case-study in tumour-induced angiogenesis
Comparing mathematical models offers a means to evaluate competing scientific theories. However, exact methods of model calibration are not applicable to many probabilistic models which simulate high-dimensional spatio-t…
Model SelectionTopological Data AnalysisOn the importance of assessing topological convergence in Bayesian phylogenetic inference
Modern phylogenetics research is often performed within a Bayesian framework, using sampling algorithms such as Markov chain Monte Carlo (MCMC) to approximate the posterior distribution. These algorithms require careful …
DiagnosticObject based Bayesian full-waveform inversion for shear elastography
We develop a computational framework to quantify uncertainty in shear elastography imaging of anomalies in tissues. We adopt a Bayesian inference formulation. Given the observed data, a forward model and their uncertaint…
Bayesian InferenceApproximate Bayesian Computation with Path Signatures
Simulation models often lack tractable likelihood functions, making likelihood-free inference methods indispensable. Approximate Bayesian computation generates likelihood-free posterior samples by comparing simulated and…
Time SeriesTime Series AnalysisAdaptive Gaussian process approximation for Bayesian inference with expensive likelihood functions
We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP) based method to approximate the joint distribution of the unknown parameters and the data. I…
Active LearningBayesian Inference