Automated parameter estimation for biological models using Bayesian statistical model checking

Abstract

BackgroundProbabilistic models have gained widespread acceptance in the systems biology community as a useful way to represent complex biological systems. Such models are developed using existing knowledge of the structure and dynamics of the system, experimental observations, and inferences drawn from statistical analysis of empirical data. A key bottleneck in building such models is that some system variables cannot be measured experimentally. These variables are incorporated into the model as numerical parameters. Determining values of these parameters that justify existing experiments and provide reliable predictions when model simulations are performed is a key research problem.Domain experts usually estimate the values of these parameters by fitting the model to experimental data. Model fitting is usually expressed as an optimization problem that requires minimizing a cost-function which measures some notion of distance between the model and the data. This optimization problem is often solved by combining local and global search methods that tend to perform well for the specific application domain. When some prior information about parameters is available, methods such as Bayesian inference are commonly used for parameter learning. Choosing the appropriate parameter search technique requires detailed domain knowledge and insight into the underlying system.ResultsUsing an agent-based model of the dynamics of acute inflammation, we demonstrate a novel parameter estimation algorithm by discovering the amount and schedule of doses of bacterial lipopolysaccharide that guarantee a set of observed clinical outcomes with high probability. We synthesized values of twenty-eight unknown parameters such that the parameterized model instantiated with these parameter values satisfies four specifications describing the dynamic behavior of the model.ConclusionsWe have developed a new algorithmic technique for discovering parameters in complex stochastic models of biological systems given behavioral specifications written in a formal mathematical logic. Our algorithm uses Bayesian model checking, sequential hypothesis testing, and stochastic optimization to automatically synthesize parameters of probabilistic biological models.

Towards a Physiological Scale of Vocal Fold Agent-Based Models of Surgical Injury and Repair: Sensitivity Analysis, Calibration and Verification

“…Other existing tools for parameter estimation in ABM include parameter sweeping, Bayesian approaches, greedy algorithms and regressions, hybrid approaches and nonlinear multi-grid/finite difference methods. These methods are often computationally expensive and are not ideal for biological models at large scales [41,43,44,47,48].…”

Comprehensive Review of Models and Methods for Inferences in Bio-Chemical Reaction Networks

“…Inference of state distributions via optimized histograms and statistical fitting is performed in (Atitey et al, 2018b). Formal verification and sequential probability ratio test for parameters estimation are considered in (Hussain, 2016). The moment closure modeling is combined with stochastic simulations for parameter estimation in (Bogomolov et al, 2015).…”

“…Main research problems considered (Dargatz, 2010) Bayesian inference for biochemical models involving diffusion (Mu, 2010) rate and state estimation in S-system and linear fractional model (LFM) (Palmisano, 2010) software tools for modeling and parameter estimation in BRNs (Mazur, 2012) inference via stochastic sampling and Bayesian learning framework (Srivastava, 2012) stochastic simulations of BRNs combined with likelihood based parameter estimation, confidence intervals, sensitivity analysis (Gupta, 2013) parameter estimation in deterministic and stochastic BRNs, inference with model reduction, mostly MCMC methods (Hasenauer, 2013) Bayesian estimation and uncertainty analysis of population heterogeneity and proliferation dynamics (Linder, 2013) penalized LS algorithm and diffusion and linear noise approximations and algebraic statistical models (Flassig, 2014) model identification for large scale gene regulatory networks (Liu, 2014) approximate Bayesian inference methods and sensitivity analysis (Moritz, 2014) structural identification and parameter estimation for modular and layered type of modes (Paul, 2014) analysis of MCMC based methods (Ruess, 2014) optimum estimation and experiment design assuming ML and Bayesian inference and Fisher information (Schenkendorf, 2014) quantification of parameter uncertainty, optimal experiment design for parameter estimation and model selection (Smadbeck, 2014) moment closure methods, model reduction, stability and spectral analysis of BRNs Langevin equation, moment closure approximations, representations of stochastic RDME (Zechner, 2014) inference from heterogeneous snapshot and time-lapse data (Galagali, 2016) Bayesian and non-Bayesian inference in BRNs, adaptive MCMC methods, network-aware inference, inference for approximated BRNs (Hussain, 2016) sequential probability ratio test, Bayesian model checking, automated and formal verification, parameter discovery (Lakatos, 2017) multivariate moment closure and reachability analysis (Liao, 2017) tensor representation and analysis of BRNs of ABC methods can be found in (Drovandi et al, 2016). The basic idea is to find parameter values which generate the same statistics as the observed data.…”

“…Hussain et al (2015);Sun et al (2012);Ashyraliyev et al (2009);Dai and Lai (2010);Chou and Voit (2009);Cedersund et al (2016) Differential evolution(DE) derivative free method, linearly combining randomly selected candidate solutions to obtain iterative improvementsTeijeiro et al (2017); Liu and Wang(2009); Sun et al (2012); Chong et al (2014); Srinivas and Rangaiah (2007); Chong et al (2012) Scatter search (SS) often combined with tabu search, it is local search with temporarily accepting worse solutions and avoiding already visited regions Particle swarm optimiz. (PSO) derivative free method, moving particles (i.e., samples or candidate solutions) towards better solution Nobile et al (2016); Sun et al (2014); Besozzi et al (2009); Cazzaniga et al (2015); Abdullah et al (2013c); Tangherloni et al (2016)…”

Computational modeling of the cell-autonomous mammalian circadian oscillator

“…The models in systems biology are disproportionate in the relatively small amount of available data compared to the relatively large number of parameters in the rate laws [ 74 ]. Therefore, successful and accurate estimation of these parameter values is a critical part of CACO modelling, as the available experimental data tend to be determined with a large uncertainty or under environmental conditions different to the current experiment [ 75 , 76 ]. On practice, this type of measurement is used for determination of biologically “reasonable” range, where the search for optimal estimations of the parameter values is conducted.…”