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Register a new userConsidering discrepancy when calibrating a mechanistic electrophysiology model
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Uncertainty quantification (UQ) is a vital step in using mathematical models and simulations to take decisions. The field of cardiac simulation has begun to explore and adopt UQ methods to characterise uncertainty in model inputs and how that propagates through to outputs or predictions. In this perspective piece we draw attention to an important and under-addressed source of uncertainty in our predictions -- that of uncertainty in the model structure or the equations themselves. The difference between imperfect models and reality is termed model discrepancy, and we are often uncertain as to the size and consequences of this discrepancy. Here we provide two examples of the consequences of discrepancy when calibrating models at the ion channel and action potential scales. Furthermore, we attempt to account for this discrepancy when calibrating and validating an ion channel model using different methods, based on modelling the discrepancy using Gaussian processes (GPs) and autoregressive-moving-average (ARMA) models, then highlight the advantages and shortcomings of each approach. Finally, suggestions and lines of enquiry for future work are provided.
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Approximate Bayesian computation (ABC) has become an essential tool for the analysis of complex stochastic models when the likelihood function is numerically unavailable. However, the well-established statistical method of empirical likelihood provides another route to such settings that bypasses simulations from the model and the choices of the ABC parameters (summary statistics, distance, tolerance), while being convergent in the number of observations. Furthermore, bypassing model simulations may lead to significant time savings in complex models, for instance those found in population genetics. The BCel algorithm we develop in this paper also provides an evaluation of its own performance through an associated effective sample size. The method is illustrated using several examples, including estimation of standard distributions, time series, and population genetics models.
This is an article submitted to the Ten Simple Rules series of professional development articles published by PLOS Computational Biology.
The lectures were prepared for the {E}cole Th{e}matique sur les Incertitudes en Calcul Scientifique (ETICS) in September 2021.
The central aim in this paper is to address variable selection questions in nonlinear and nonparametric regression. Motivated by statistical genetics, where nonlinear interactions are of particular interest, we introduce a novel and interpretable way to summarize the relative importance of predictor variables. Methodologically, we develop the RelATive cEntrality (RATE) measure to prioritize candidate genetic variants that are not just marginally important, but whose associations also stem from significant covarying relationships with other variants in the data. We illustrate RATE through Bayesian Gaussian process regression, but the methodological innovations apply to other black box methods. It is known that nonlinear models often exhibit greater predictive accuracy than linear models, particularly for phenotypes generated by complex genetic architectures. With detailed simulations and two real data association mapping studies, we show that applying RATE enables an explanation for this improved performance.
Central pattern generators (CPGs) appear to have evolved multiple times throughout the animal kingdom, indicating that their design imparts a significant evolutionary advantage. Insight into how this design is achieved is hindered by the difficulty inherent in examining relationships among electrophysiological properties of the constituent cells of a CPG and their functional connectivity. That is: experimentally it is challenging to estimate the values of more than two or three of these properties simultaneously. We employ a method of statistical data assimilation (D.A.) to estimate the synaptic weights, synaptic reversal potentials, and maximum conductances of ion channels of the constituent neurons in a multi-modal network model. We then use these estimates to predict the functional mode of activity that the network is expressing. The measurements used are the membrane voltage time series of all neurons in the circuit. We find that these measurements provide sufficient information to yield accurate predictions of the networks associated electrical activity. This experiment can apply directly in a real laboratory using intracellular recordings from a known biological CPG whose structural mapping is known, and which can be completely isolated from the animal. The simulated results in this paper suggest that D.A. might provide a tool for simultaneously estimating tens to hundreds of CPG properties, thereby offering the opportunity to seek possible systematic relationships among these properties and the emergent electrical activity.
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