scholarly journals Calibrating models of cancer invasion: parameter estimation using approximate Bayesian computation and gradient matching

2021 ◽  
Vol 8 (6) ◽  
pp. 202237
Author(s):  
Yunchen Xiao ◽  
Len Thomas ◽  
Mark A. J. Chaplain
Keyword(s):  
Measurement Error ◽  
Approximate Bayesian Computation ◽  
Additive Model ◽  
Simulated Data ◽  
Cancer Invasion ◽  
Enzyme Concentration ◽  
Equation Model ◽  
Model Parameters ◽  
Bayesian Computation ◽  
Approximate Bayesian

We present two different methods to estimate parameters within a partial differential equation model of cancer invasion. The model describes the spatio-temporal evolution of three variables—tumour cell density, extracellular matrix density and matrix degrading enzyme concentration—in a one-dimensional tissue domain. The first method is a likelihood-free approach associated with approximate Bayesian computation; the second is a two-stage gradient matching method based on smoothing the data with a generalized additive model (GAM) and matching gradients from the GAM to those from the model. Both methods performed well on simulated data. To increase realism, additionally we tested the gradient matching scheme with simulated measurement error and found that the ability to estimate some model parameters deteriorated rapidly as measurement error increased.

scholarly journals Probabilistic Updating of Structural Models for Damage Assessment Using Approximate Bayesian Computation

Sensors ◽  
2020 ◽  
Vol 20 (11) ◽  
pp. 3197 ◽  
Author(s):  
Zhouquan Feng ◽  
Yang Lin ◽  
Wenzan Wang ◽  
Xugang Hua ◽  
Zhengqing Chen
Keyword(s):  
Damage Assessment ◽  
Approximate Bayesian Computation ◽  
Model Updating ◽  
Likelihood Function ◽  
Probabilistic Approach ◽  
Model Parameters ◽  
Bayesian Computation ◽  
The Novel ◽  
Subset Simulation ◽  
Approximate Bayesian

A novel probabilistic approach for model updating based on approximate Bayesian computation with subset simulation (ABC-SubSim) is proposed for damage assessment of structures using modal data. The ABC-SubSim is a likelihood-free Bayesian approach in which the explicit expression of likelihood function is avoided and the posterior samples of model parameters are obtained using the technique of subset simulation. The novel contributions of this paper are on three fronts: one is the introduction of some new stopping criteria to find an appropriate tolerance level for the metric used in the ABC-SubSim; the second one is the employment of a hybrid optimization scheme to find finer optimal values for the model parameters; and the last one is the adoption of an iterative approach to determine the optimal weighting factors related to the residuals of modal frequency and mode shape in the metric. The effectiveness of this approach is demonstrated using three illustrative examples.

scholarly journals Using approximate Bayesian computation to quantify cell-cell adhesion parameters in a cell migratory process

2016 ◽  
Author(s):  
Robert J. H. Ross ◽  
R. E. Baker ◽  
Andrew Parker ◽  
M. J. Ford ◽  
R. L. Mort ◽  
...  
Keyword(s):  
Cell Adhesion ◽  
Approximate Bayesian Computation ◽  
Cell Interactions ◽  
Model Parameters ◽  
Bayesian Computation ◽  
Accurate Identification ◽  
A Cell ◽  
Approximate Bayesian ◽  
Set Up ◽  
Cell Cell

AbstractIn this work we implement approximate Bayesian computational methods to improve the design of a wound-healing assay used to quantify cell-cell interactions. This is important as cell-cell interactions, such as adhesion and repulsion, have been shown to play an important role in cell migration. Initially, we demonstrate with a model of an ideal experiment that we are able to identify model parameters for agent motility and adhesion, given we choose appropriate summary statistics. Following this, we replace our model of an ideal experiment with a model representative of a practically realisable experiment. We demonstrate that, given the current (and commonly used) experimental set-up, model parameters cannot be accurately identified using approximate Bayesian computation methods. We compare new experimental designs through simulation, and show more accurate identification of model parameters is possible by expanding the size of the domain upon which the experiment is performed, as opposed to increasing the number of experimental repeats. The results presented in this work therefore describe time and cost-saving alterations for a commonly performed experiment for identifying cell motility parameters. Moreover, the results presented in this work will be of interest to those concerned with performing experiments that allow for the accurate identification of parameters governing cell migratory processes, especially cell migratory processes in which cell-cell adhesion or repulsion are known to play a significant role.

scholarly journals A Revised Model of Anatomically Modern Human Expansions Out of Africa through a Machine Learning Approximate Bayesian Computation Approach

Genes ◽  
2020 ◽  
Vol 11 (12) ◽  
pp. 1510
Author(s):  
Maria Teresa Vizzari ◽  
Andrea Benazzo ◽  
Guido Barbujani ◽  
Silvia Ghirotto
Keyword(s):  
Approximate Bayesian Computation ◽  
Simulated Data ◽  
Modern Human ◽  
Genomic Variation ◽  
Population History ◽  
Bayesian Computation ◽  
Dispersal Pattern ◽  
High Coverage ◽  
Out Of Africa ◽  
Approximate Bayesian

There is a wide consensus in considering Africa as the birthplace of anatomically modern humans (AMH), but the dispersal pattern and the main routes followed by our ancestors to colonize the world are still matters of debate. It is still an open question whether AMH left Africa through a single process, dispersing almost simultaneously over Asia and Europe, or in two main waves, first through the Arab Peninsula into southern Asia and Australo-Melanesia, and later through a northern route crossing the Levant. The development of new methodologies for inferring population history and the availability of worldwide high-coverage whole-genome sequences did not resolve this debate. In this work, we test the two main out-of-Africa hypotheses through an Approximate Bayesian Computation approach, based on the Random-Forest algorithm. We evaluated the ability of the method to discriminate between the alternative models of AMH out-of-Africa, using simulated data. Once assessed that the models are distinguishable, we compared simulated data with real genomic variation, from modern and archaic populations. This analysis showed that a model of multiple dispersals is four-fold as likely as the alternative single-dispersal model. According to our estimates, the two dispersal processes may be placed, respectively, around 74,000 and around 46,000 years ago.

scholarly journals ABCDP: Approximate Bayesian Computation with Differential Privacy

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 961
Author(s):  
Mijung Park ◽  
Margarita Vinaroz ◽  
Wittawat Jitkrittum
Keyword(s):  
Approximate Bayesian Computation ◽  
Differential Privacy ◽  
Simulated Data ◽  
Bayesian Computation ◽  
Abc Algorithm ◽  
Quantity Of Interest ◽  
Sparse Vector ◽  
Minimal Modification ◽  
Approximate Bayesian ◽  
Privacy Level

We developed a novel approximate Bayesian computation (ABC) framework, ABCDP, which produces differentially private (DP) and approximate posterior samples. Our framework takes advantage of the sparse vector technique (SVT), widely studied in the differential privacy literature. SVT incurs the privacy cost only when a condition (whether a quantity of interest is above/below a threshold) is met. If the condition is sparsely met during the repeated queries, SVT can drastically reduce the cumulative privacy loss, unlike the usual case where every query incurs the privacy loss. In ABC, the quantity of interest is the distance between observed and simulated data, and only when the distance is below a threshold can we take the corresponding prior sample as a posterior sample. Hence, applying SVT to ABC is an organic way to transform an ABC algorithm to a privacy-preserving variant with minimal modification, but yields the posterior samples with a high privacy level. We theoretically analyzed the interplay between the noise added for privacy and the accuracy of the posterior samples. We apply ABCDP to several data simulators and show the efficacy of the proposed framework.

scholarly journals Incorporating Contact Network Uncertainty in Individual Level Models of Infectious Disease using Approximate Bayesian Computation

2019 ◽  
Vol 16 (1) ◽  
Author(s):  
Waleed Almutiry ◽  
Rob Deardon
Keyword(s):  
Infectious Disease ◽  
Monte Carlo ◽  
Disease Transmission ◽  
Approximate Bayesian Computation ◽  
Disease Model ◽  
Simulated Data ◽  
Computation Time ◽  
Contact Network ◽  
Bayesian Computation ◽  
Approximate Bayesian

AbstractInfectious disease transmission between individuals in a heterogeneous population is often best modelled through a contact network. However, such contact network data are often unobserved. Such missing data can be accounted for in a Bayesian data augmented framework using Markov chain Monte Carlo (MCMC). Unfortunately, fitting models in such a framework can be highly computationally intensive. We investigate the fitting of network-based infectious disease models with completely unknown contact networks using approximate Bayesian computation population Monte Carlo (ABC-PMC) methods. This is done in the context of both simulated data, and data from the UK 2001 foot-and-mouth disease epidemic. We show that ABC-PMC is able to obtain reasonable approximations of the underlying infectious disease model with huge savings in computation time when compared to a full Bayesian MCMC analysis.

scholarly journals Parameter Calibration in Crowd Simulation Models using Approximate Bayesian Computation

2020 ◽  
Vol 5 ◽  
Author(s):  
Nikolai Bode
Keyword(s):  
Model Selection ◽  
Approximate Bayesian Computation ◽  
Model Fitting ◽  
Simulation Models ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Bayesian Computation ◽  
Continuous Space ◽  
Pedestrian Dynamics ◽  
Approximate Bayesian

Simulation models for pedestrian crowds are a ubiquitous tool in research and industry. It is crucial that the parameters of these models are calibrated carefully and ultimately it will be of interest to compare competing models to decide which model is best suited for a particular purpose. In this contribution, I demonstrate how Approximate Bayesian Computation (ABC), which is already a popular tool in other areas of science, can be used for model fitting and model selection in a pedestrian dynamics context. I fit two different models for pedestrian dynamics to data on a crowd passing in one direction through a bottleneck. One model describes movement in continuous-space, the other model is a cellular automaton and thus describes movement in discrete-space. In addition, I compare models to data using two metrics. The first is based on egress times and the second on the velocity of pedestrians in front of the bottleneck. My results show that while model fitting is successful, a substantial degree of uncertainty about the value of some model parameters remains after model fitting. Importantly, the choice of metric in model fitting can influence parameter estimates. Model selection is inconclusive for the egress time metric but supports the continuous-space model for the velocity-based metric. These findings show that ABC is a flexible approach and highlights the difficulties associated with model fitting and model selection for pedestrian dynamics. ABC requires many simulation runs and choosing appropriate metrics for comparing data to simulations requires careful attention. Despite this, I suggest ABC is a promising tool, because it is versatile and easily implemented for the growing number of openly available crowd simulators and data sets.

scholarly journals Distinguishing among complex evolutionary models using unphased whole-genome data through Approximate Bayesian Computation

2018 ◽  
Author(s):  
Silvia Ghirotto ◽  
Maria Teresa Vizzari ◽  
Francesca Tassi ◽  
Guido Barbujani ◽  
Andrea Benazzo
Keyword(s):  
Approximate Bayesian Computation ◽  
Simulated Data ◽  
Computational Effort ◽  
Bayesian Computation ◽  
Experimental Conditions ◽  
Genome Data ◽  
Complete Genomes ◽  
Anatomically Modern Humans ◽  
Demographic Processes ◽  
Approximate Bayesian

AbstractInferring past demographic histories is crucial in population genetics, and the amount of complete genomes now available should in principle facilitate this inference. In practice, however, the available inferential methods suffer from severe limitations. Although hundreds complete genomes can be simultaneously analyzed, complex demographic processes can easily exceed computational constraints, and the procedures to evaluate the reliability of the estimates contribute to increase the computational effort. Here we present an Approximate Bayesian Computation (ABC) framework, based on the Random Forest algorithm, to infer complex past population processes using complete genomes. To do this, we propose to summarize the data by the full genomic distribution of the four mutually exclusive categories of segregating sites (FDSS), a statistic fast to compute from unphased genome data. We constructed an efficient ABC pipeline and tested how accurately it allows one to recognize the true model among models of increasing complexity, using simulated data and taking into account different sampling strategies in terms of number of individuals analyzed, number and size of the genetic loci considered. We tested the power of the FDSS to be informative about even complex evolutionary histories and compared the results with those obtained summarizing the data through the unfolded Site Frequency Spectrum, thus highlighting for both statistics the experimental conditions maximizing the inferential power. Finally, we analyzed two datasets, testing models (a) on the dispersal of anatomically modern humans out of Africa and (b) the evolutionary relationships of the three species of Orangutan inhabiting Borneo and Sumatra.

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