Comparing two sequential Monte Carlo samplers for exact and approximate Bayesian inference on biological models

Bayesian methods are advantageous for biological modelling studies due to their ability to quantify and characterize posterior variability in model parameters. When Bayesian methods cannot be applied, due either to non-determinism in the model or limitations on system observability, approximate Bayesian computation (ABC) methods can be used to similar effect, despite producing inflated estimates of the true posterior variance. Owing to generally differing application domains, there are few studies comparing Bayesian and ABC methods, and thus there is little understanding of the properties and magnitude of this uncertainty inflation. To address this problem, we present two popular strategies for ABC sampling that we have adapted to perform exact Bayesian inference, and compare them on several model problems. We find that one sampler was impractical for exact inference due to its sensitivity to a key normalizing constant, and additionally highlight sensitivities of both samplers to various algorithmic parameters and model conditions. We conclude with a study of the O'Hara–Rudy cardiac action potential model to quantify the uncertainty amplification resulting from employing ABC using a set of clinically relevant biomarkers. We hope that this work serves to guide the implementation and comparative assessment of Bayesian and ABC sampling techniques in biological models.

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Approximate Bayesian inference of seismic velocity and pore-pressure uncertainty with basin modeling, rock physics, and imaging constraints

Geophysics ◽

10.1190/geo2019-0767.1 ◽

2020 ◽

Vol 85 (5) ◽

pp. ID19-ID34

Author(s):

Anshuman Pradhan ◽

Nader C. Dutta ◽

Huy Q. Le ◽

Biondo Biondi ◽

Tapan Mukerji

Keyword(s):

Bayesian Inference ◽

Pore Pressure ◽

Seismic Velocity ◽

Rock Physics ◽

Real Field ◽

Model Parameters ◽

Basin Modeling ◽

Approximate Bayesian ◽

Well Data ◽

Approximate Bayesian Inference

We have introduced a methodology for quantifying seismic velocity and pore-pressure uncertainty that incorporates information regarding the geologic history of a basin, rock physics, well log, drilling, and seismic data. In particular, our approach relies on linking velocity models to the basin modeling outputs of porosity, mineral volume fractions, and pore pressure through rock-physics models. We account for geologic uncertainty by defining prior probability distributions on lithology-specific porosity compaction model parameters, permeability-porosity model parameters, and heat-flow boundary condition. Monte Carlo basin simulations are performed by sampling the prior uncertainty space. We perform probabilistic calibration of the basin model outputs by defining data likelihood distributions to represent well data uncertainty. Rock physics modeling transforms the basin modeling outputs to give us multiple velocity realizations used to perform multiple depth migrations. We have developed an approximate Bayesian inference framework that uses migration velocity analysis in conjunction with well data for updating velocity and basin modeling uncertainty. We apply our methodology in 2D to a real field case from the Gulf of Mexico; our methodology allows for building a geologic and physical model space for velocity and pore-pressure prediction with reduced uncertainty.

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Approximate Bayesian Inference for a Mechanistic Model of Vesicle Release at a Ribbon Synapse

10.1101/669218 ◽

2019 ◽

Cited By ~ 5

Author(s):

Cornelius Schröder ◽

Ben James ◽

Leon Lagnado ◽

Philipp Berens

Keyword(s):

Bayesian Inference ◽

Neural Activity ◽

Mechanistic Model ◽

Glutamate Release ◽

Model Parameters ◽

Ribbon Synapse ◽

Mechanistic Models ◽

Coupled Equations ◽

Approximate Bayesian ◽

Approximate Bayesian Inference

AbstractThe inherent noise of neural systems makes it difficult to construct models which accurately capture experimental measurements of their activity. While much research has been done on how to efficiently model neural activity with descriptive models such as linear-nonlinear-models (LN), Bayesian inference for mechanistic models has received considerably less attention. One reason for this is that these models typically lead to intractable likelihoods and thus make parameter inference difficult. Here, we develop an approximate Bayesian inference scheme for a fully stochastic, biophysically inspired model of glutamate release at the ribbon synapse, a highly specialized synapse found in different sensory systems. The model translates known structural features of the ribbon synapse into a set of stochastically coupled equations. We approximate the posterior distributions by updating a parametric prior distribution via Bayesian updating rules and show that model parameters can be efficiently estimated for synthetic and experimental data from in vivo two-photon experiments in the zebrafish retina. Also, we find that the model captures complex properties of the synaptic release such as the temporal precision and outperforms a standard GLM. Our framework provides a viable path forward for linking mechanistic models of neural activity to measured data.

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