Uncertainty Analysis for Non-identifiable Dynamical Systems: Profile Likelihoods, Bootstrapping and More

Fröhlich, Fabian; Theis, Fabian J.; Hasenauer, Jan

doi:10.1007/978-3-319-12982-2_5

Cited by 53 publications

(87 citation statements)

References 20 publications

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“…PESTO comes with a detailed documentation of all functionalities and the respective methods. For numerical simulation and sensitivity calculation we employed the Advanced MATLAB Interface for CVODES and IDAS (AMICI) [7, 70]. Both toolboxes are developed and available via GitHub and we provide the code used for this study in Additional file 2.…”

Section: Methodsmentioning

confidence: 99%

Comprehensive benchmarking of Markov chain Monte Carlo methods for dynamical systems

et al. 2017

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BackgroundIn quantitative biology, mathematical models are used to describe and analyze biological processes. The parameters of these models are usually unknown and need to be estimated from experimental data using statistical methods. In particular, Markov chain Monte Carlo (MCMC) methods have become increasingly popular as they allow for a rigorous analysis of parameter and prediction uncertainties without the need for assuming parameter identifiability or removing non-identifiable parameters. A broad spectrum of MCMC algorithms have been proposed, including single- and multi-chain approaches. However, selecting and tuning sampling algorithms suited for a given problem remains challenging and a comprehensive comparison of different methods is so far not available.ResultsWe present the results of a thorough benchmarking of state-of-the-art single- and multi-chain sampling methods, including Adaptive Metropolis, Delayed Rejection Adaptive Metropolis, Metropolis adjusted Langevin algorithm, Parallel Tempering and Parallel Hierarchical Sampling. Different initialization and adaptation schemes are considered. To ensure a comprehensive and fair comparison, we consider problems with a range of features such as bifurcations, periodical orbits, multistability of steady-state solutions and chaotic regimes. These problem properties give rise to various posterior distributions including uni- and multi-modal distributions and non-normally distributed mode tails. For an objective comparison, we developed a pipeline for the semi-automatic comparison of sampling results.ConclusionThe comparison of MCMC algorithms, initialization and adaptation schemes revealed that overall multi-chain algorithms perform better than single-chain algorithms. In some cases this performance can be further increased by using a preceding multi-start local optimization scheme. These results can inform the selection of sampling methods and the benchmark collection can serve for the evaluation of new algorithms. Furthermore, our results confirm the need to address exploration quality of MCMC chains before applying the commonly used quality measure of effective sample size to prevent false analysis conclusions.Electronic supplementary materialThe online version of this article (doi:10.1186/s12918-017-0433-1) contains supplementary material, which is available to authorized users.

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Section: Methodsmentioning

confidence: 99%

Comprehensive benchmarking of Markov chain Monte Carlo methods for dynamical systems

et al. 2017

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“…Experience suggests that this latter case is the exception rather than the rule for dynamical systems in cell and molecular biology [54,58]. Some approaches, such as profile-likelihood methods, try to assess the uncertainty for each parameter [59,60], which may hold particular appeal for those interested in inferring specific parameters with accuracy. The likelihood is also used in Bayesian inference where it is combined with the prior p(u)-a probability over the parameter space that reflects the level of existing knowledge (or lack thereof )-to arrive at the posterior distribution…”

Section: Statistical Inferencementioning

confidence: 99%

How to deal with parameters for whole-cell modelling

Babtie¹,

Stumpf²

2017

J. R. Soc. Interface.

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Dynamical systems describing whole cells are on the verge of becoming a reality. But as models of reality, they are only useful if we have realistic parameters for the molecular reaction rates and cell physiological processes. There is currently no suitable framework to reliably estimate hundreds, let alone thousands, of reaction rate parameters. Here, we map out the relative weaknesses and promises of different approaches aimed at redressing this issue. While suitable procedures for estimation or inference of the whole (vast) set of parameters will, in all likelihood, remain elusive, some hope can be drawn from the fact that much of the cellular behaviour may be explained in terms of smaller sets of parameters. Identifying such parameter sets and assessing their behaviour is now becoming possible even for very large systems of equations, and we expect such methods to become central tools in the development and analysis of whole-cell models.

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“…Methods of identifiability analysis [12][13][14][15][16][17][18][19][20] provide more systematic means for helping to determine the appropriate model complexity relative to the data available. In particular, a model is said to be identifiable when it is possible, in principle, to uniquely determine the model parameters using an arbitrary amount of ideal data from a given experiment [23,24].…”

Section: Introductionmentioning

confidence: 99%

“…Instead, identifiability analysis, in general, may be considered as encompassing a set of alternative, precision-based planning (pre-data) and analysis (post-data) tools similar to those advocated by Cox [28], Bland [31] and Rothman and Greenland [30]. Such methods of model identifiability analysis are well-established in the field of systems biology [12][13][14][15][16][17][18][19][20]. In this context experimental data often take the form of time series describing temporal variations of different biochemical molecules in some kind of chemical reaction network or gene regulatory network and these data are modelled using ordinary or stochastic differential equation models [32].…”

Section: Introductionmentioning

confidence: 99%

“…In the present work we focus on apply methods of identifiability analysis to spatiotemporal partial differential equation models, reaction-diffusion equations in particular, which model both spatial and temporal variations in different quantities of interest. We consider both a Bayesian inference framework [15,16] and profile likelihood analysis [17,18].…”

Section: Introductionmentioning

confidence: 99%

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Practical parameter identifiability for spatiotemporal models of cell invasion

Simpson

Baker

Vittadello

et al. 2019

Preprint

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We examine the practical identifiability of parameters in a spatiotemporal reaction-diffusion model of a scratch assay where we have access to a relatively large amount of quantitative experimental data. The experiment involves fluorescent cell cycle labels so that the cell cycle is tracked in real time. This provides spatial information about the position of individual cells as well as temporal information about the cell cycle phase of each cell. Cell cycle labelling is incorporated into the reaction-diffusion model by considering the total population to be composed of two interacting subpopulations. Practical identifiability is examined using a Bayesian Markov Chain Monte Carlo (MCMC) framework, confirming that the parameters are identifiable when we assume that the diffusivities of the two subpopulations are identical, but that the parameters are practically non-identifiable when we allow the diffusivities to be distinct. We also assess identifiability using a profile likelihood approach, and show that this provides similar results to MCMC with the advantage of being an order of magnitude faster to compute. Despite the profile likelihood being relatively underutilised in the mathematical biology literature, we suggest that it ought to be adopted as a screening tool to provide a rapid assessment of practical identifiability before more computationally cumbersome MCMC computations are attempted.

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Uncertainty Analysis for Non-identifiable Dynamical Systems: Profile Likelihoods, Bootstrapping and More

Cited by 53 publications

References 20 publications

Comprehensive benchmarking of Markov chain Monte Carlo methods for dynamical systems

Comprehensive benchmarking of Markov chain Monte Carlo methods for dynamical systems

How to deal with parameters for whole-cell modelling

Practical parameter identifiability for spatiotemporal models of cell invasion

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