Inference Of Model Parameters Research Articles

Modeling apoptosis resistance in CHO cells with CRISPR-mediated knockouts of Bak1, Bax, and Bok.

Chinese hamster ovary (CHO) cells are the primary platform for the production of biopharmaceuticals. To increase yields, many CHO cell lines have been genetically engineered to resist cell death. However, the kinetics that governs cell fate in bioreactors are confounded by many variables associated with batch processes. Here, we used CRISPR‐Cas9 to create combinatorial knockouts of the three known BCL‐2 family effector proteins: Bak1, Bax, and Bok. To assess the response to apoptotic stimuli, cell lines were cultured in the presence of four cytotoxic compounds with different mechanisms of action. A population‐based model was developed to describe the behavior of the resulting viable cell dynamics as a function of genotype and treatment. Our results validated the synergistic antiapoptotic nature of Bak1 and Bax, while the deletion of Bok had no significant impact. Importantly, the uniform application of apoptotic stresses permitted direct observation and quantification of a delay in the onset of cell death through Bayesian inference of meaningful model parameters. In addition to the classical death rate, a delay function was found to be essential in the accurate modeling of the cell death response. These findings represent an important bridge between cell line engineering strategies and biological modeling in a bioprocess context.

Markov Chains for Horizons MARCH. I. Identifying Biases in Fitting Theoretical Models to Event Horizon Telescope Observations

Abstract We introduce a new Markov Chain Monte Carlo (MCMC) algorithm with parallel tempering for fitting theoretical models of horizon-scale images of black holes to the interferometric data from the Event Horizon Telescope (EHT). The algorithm implements forms of the noise distribution in the data that are accurate for all signal-to-noise ratios. In addition to being trivially parallelizable, the algorithm is optimized for high performance, achieving 1 million MCMC chain steps in under 20 s on a single processor. We use synthetic data for the 2017 EHT coverage of M87 that are generated based on analytic as well as General Relativistic Magnetohydrodynamic (GRMHD) model images to explore several potential sources of biases in fitting models to sparse interferometric data. We demonstrate that a very small number of data points that lie near salient features of the interferometric data exert disproportionate influence on the inferred model parameters. We also show that the preferred orientations of the EHT baselines introduce significant biases in the inference of the orientation of the model images. Finally, we discuss strategies that help identify the presence and severity of such biases in realistic applications.

Invariants in copolar interferometry: An Abelian gauge theory

An $N$-element interferometer measures correlations among pairs of array elements. Closure invariants associated with closed loops among array elements are immune to multiplicative, element-based ("local") corruptions that occur in these measurements. Till recently, it has been unclear how a complete set of independent invariants can be analytically determined. We view the local, element-based corruptions in co-polar correlations as gauge tranformations belonging to the gauge group $\textrm{GL}(1,\mathbb{C})$. Closure quantities are then naturally gauge invariant. We use this to provide a simple and effective formalism, and identify the complete set of independent closure invariants from co-polar interferometric correlations using only quantities defined on $(N-1)(N-2)/2$ elementary and independent triangular loops. The $(N-1)(N-2)/2$ closure phases and $N(N-3)/2$ closure amplitudes (totaling $N^2-3N+1$ real invariants), familiar in astronomical interferometry, naturally emerge from this formalism, which unifies what has required separate treatments until now. We do not require auto-correlations, but can easily include them if reliably measured. This unified view clarifies issues relating to noise and inference of object model parameters. It also allows us to extend the rule of parallel transport associated with Pancharatnam phase in optics to apply to amplitudes as well. The framework presented here extends to $\textrm{GL}(2,\mathbb{C}$) for full polarimetric interferometry as presented in a companion paper, which generalizes and clarifies earlier work. Our findings are relevant to state of the art co-polar and full polarimetric very long baseline interferometry measurements to determine features very near the event horizons of blackholes at the centers of M87, Centaurus~A, and the Milky Way.

On mobility trends analysis of COVID-19 dissemination in Mexico City.

This work presents a tool for forecasting the spread of the new coronavirus in Mexico City, which is based on a mathematical model with a metapopulation structure that uses Bayesian statistics and is inspired by a data-driven approach. The daily mobility of people in Mexico City is mathematically represented by an origin-destination matrix using the open mobility data from Google and the Transportation Mexican Survey. This matrix is incorporated in a compartmental model. We calibrate the model against borough-level incidence data collected between 27 February 2020 and 27 October 2020, while using Bayesian inference to estimate critical epidemiological characteristics associated with the coronavirus spread. Given that working with metapopulation models leads to rather high computational time consumption, and parameter estimation of these models may lead to high memory RAM consumption, we do a clustering analysis that is based on mobility trends to work on these clusters of borough separately instead of taken all of the boroughs together at once. This clustering analysis can be implemented in smaller or larger scales in different parts of the world. In addition, this clustering analysis is divided into the phases that the government of Mexico City has set up to restrict individual movement in the city. We also calculate the reproductive number in Mexico City using the next generation operator method and the inferred model parameters obtaining that this threshold is in the interval (1.2713, 1.3054). Our analysis of mobility trends can be helpful when making public health decisions.

Inferring the effective start dates of non-pharmaceutical interventions during COVID-19 outbreaks

BackgroundDuring Feb-Apr. 2020, many countries implemented non-pharmaceutical interventions (NPIs), such as school closures and lockdowns, to control the COVID-19 pandemic caused by the SARS-CoV-2 virus. Overall, these interventions seem to have reduced the spread of the pandemic. We hypothesized that the official and effective start dates of NPIs can be noticeably different, for example, due to slow adoption by the population, and that these differences can lead to errors in the estimation of the impact of NPIs. MethodsSEIR models were fitted to case data from 12 regions to infer the effective start dates of interventions and compare these with the official dates. The impact of NPIs was estimated from the inferred model parameters. ResultsWe infer mostly late effective start dates of interventions. For example, Italy implemented a lockdown on Mar 11, but we infer the effective start date on Mar 17 (+3.05−2.01 days 95% CI). Moreover, we find that the impact of NPIs can be underestimated if it is assumed they start on their official date. ConclusionsDifferences between the official and effective start of NPIs are likely. Neglecting such differences can lead to underestimation of the impact of NPIs, which could cause decision-makers to escalate interventions and guidelines.

Cluster mean-field theory accurately predicts statistical properties of large-scale DNA methylation patterns.

The accurate establishment and maintenance of DNA methylation patterns is vital for mammalian development and disruption to these processes causes human disease. Our understanding of DNA methylation mechanisms has been facilitated by mathematical modelling, particularly stochastic simulations. Megabase-scale variation in DNA methylation patterns is observed in development, cancer and ageing and the mechanisms generating these patterns are little understood. However, the computational cost of stochastic simulations prevents them from modelling such large genomic regions. Here, we test the utility of three different mean-field models to predict summary statistics associated with large-scale DNA methylation patterns. By comparison to stochastic simulations, we show that a cluster mean-field model accurately predicts the statistical properties of steady-state DNA methylation patterns, including the mean and variance of methylation levels calculated across a system of CpG sites, as well as the covariance and correlation of methylation levels between neighbouring sites. We also demonstrate that a cluster mean-field model can be used within an approximate Bayesian computation framework to accurately infer model parameters from data. As mean-field models can be solved numerically in a few seconds, our work demonstrates their utility for understanding the processes underpinning large-scale DNA methylation patterns.

Estimation of Parameters of Finite Mixture of Rayleigh Distribution by the Expectation‐Maximization Algorithm

In the lifetime process in some systems, most data cannot belong to one single population. In fact, it can represent several subpopulations. In such a case, the known distribution cannot be used to model data. Instead, a mixture of distribution is used to modulate the data and classify them into several subgroups. The mixture of Rayleigh distribution is best to be used with the lifetime process. This paper aims to infer model parameters by the expectation‐maximization (EM) algorithm through the maximum likelihood function. The technique is applied to simulated data by following several scenarios. The accuracy of estimation has been examined by the average mean square error (AMSE) and the average classification success rate (ACSR). The results showed that the method performed well in all simulation scenarios with respect to different sample sizes.

Reconstruction of airflow path parameters in multizone models based on Bayesian inference and measured data

The accurate inference of model parameters is important for predicting contaminant distributions in multizone environments, which is critical for ensuring indoor personnel health and formulating an optimistic ventilation strategy. However, several important airflow path parameters (flow coefficients, flow exponents, etc.) are not directly observed or observable. Therefore, in this study, we proposed a reconstruction method to estimate the parameters for the multizone model based on measured data. MATLAB codes were programmed to call the CONTAM (a multizone simulation program developed by the US National Institute of Standards and Technology (NIST)) engine to simulate the pollutant transport in a multizone scaled building model. The sensitivities of different model parameters were evaluated through a Global Sensitivity Analysis (GSA). Subsequently, a Bayesian inference algorithm was applied to iteratively determine the unknown parameters. Finally, multizone scaled experiments with different forms of pollutant sources were conducted to validate the reconstruction method. The pollutant concentrations predicted using the measured parameters were compared with the those obtained using the reconstructed parameters. The results showed that the concentrations predicted using the reconstructed parameters agreed well with the measured data under constant source (CS) release and most dynamic source (DS) release in different experimental cases. The simulation results based on the reconstructed parameters were more accurate than those based on the directly measured parameters. The proposed reconstruction method can conveniently construct digital models that are equivalent to physical buildings, and these models can be further used to conduct analysis of built environments.

Robust equation discovery considering model discrepancy: A sparse Bayesian and Gaussian process approach

Computational models are widely used to describe engineering systems and to predict their behaviour. However, in many applications, these computational models do not capture the complete physics of the real system, leading to model discrepancy. Model discrepancy causes bias in the inferred model parameters when it is not properly accounted for. This paper proposes a novel approach that seeks to capture the functional form of the model discrepancy and reduce bias in the estimated model parameters through and equation discovery procedure. A sparse Bayesian model is proposed, where sparsity is introduced through a hierarchical prior structure, providing a mechanism for removing erroneous candidate model terms from a series of potential equations as a part of an equation discovery procedure. At the same time, a Gaussian process model is used to account for model discrepancy. These two modelling assumptions are combined in a Bayesian formulation, allowing the system parameters and model discrepancy to be inferred in a probabilistic manner with associated uncertainties quantified based on their posterior distributions. The resulting method is capable of simultaneously providing physical insights into the system behaviour, by selecting the appropriate candidate model components and their respective system parameters, whilst compensating for model discrepancy that may occur due to an incomplete set of candidate terms. In order to efficiently solve the statistical model, an expectation maximisation algorithm is proposed for performing inference, and illustrative examples are presented to validate the proposed method. It is shown that compared to using a conventional sparse Bayesian approach for performing equation discovery, such as the Relevance Vector Machine, the proposed method provides better equation selection and parameter estimation, with less bias in the parameter estimates.

Locally Scaled and Stochastic Volatility Metropolis– Hastings Algorithms

Markov chain Monte Carlo (MCMC) techniques are usually used to infer model parameters when closed-form inference is not feasible, with one of the simplest MCMC methods being the random walk Metropolis–Hastings (MH) algorithm. The MH algorithm suffers from random walk behaviour, which results in inefficient exploration of the target posterior distribution. This method has been improved upon, with algorithms such as Metropolis Adjusted Langevin Monte Carlo (MALA) and Hamiltonian Monte Carlo being examples of popular modifications to MH. In this work, we revisit the MH algorithm to reduce the autocorrelations in the generated samples without adding significant computational time. We present the: (1) Stochastic Volatility Metropolis–Hastings (SVMH) algorithm, which is based on using a random scaling matrix in the MH algorithm, and (2) Locally Scaled Metropolis–Hastings (LSMH) algorithm, in which the scaled matrix depends on the local geometry of the target distribution. For both these algorithms, the proposal distribution is still Gaussian centred at the current state. The empirical results show that these minor additions to the MH algorithm significantly improve the effective sample rates and predictive performance over the vanilla MH method. The SVMH algorithm produces similar effective sample sizes to the LSMH method, with SVMH outperforming LSMH on an execution time normalised effective sample size basis. The performance of the proposed methods is also compared to the MALA and the current state-of-art method being the No-U-Turn sampler (NUTS). The analysis is performed using a simulation study based on Neal’s funnel and multivariate Gaussian distributions and using real world data modeled using jump diffusion processes and Bayesian logistic regression. Although both MALA and NUTS outperform the proposed algorithms on an effective sample size basis, the SVMH algorithm has similar or better predictive performance when compared to MALA and NUTS across the various targets. In addition, the SVMH algorithm outperforms the other MCMC algorithms on a normalised effective sample size basis on the jump diffusion processes datasets. These results indicate the overall usefulness of the proposed algorithms.

Applying Bayesian Markov chain Monte Carlo (MCMC) modeling to predict the melting behavior of phase change materials

A key practical application of PCM-based spherical containers is in packed bed thermal energy storage (TES) devices utilized for air conditioning in large buildings. Proposing high-precision models for the melting characteristics in spherical containers can provide deep insights into the design of TES systems. Herein, a methodology based on Bayesian inference was adopted to provide reliable models that predict the melting rate (f) and surface-averaged Nusselt number (Nu) as two significant factors in PCM melting process in spherical heat storage units. Five proposed models for f and Nu prediction were applied to available datasets. The input of Bayesian-based predictive models included three important dimensionless parameters of the melting problem, namely Ste, Gr, and Fo. Ste (Stefan number) describes the driving force of melting, Gr (Grashof number) reflects the natural convection intensity, and Fo (Fourier number) represents the dimensionless time. For accurate inference of model parameters using the Bayesian Markov chain Monte Carlo (MCMC) technique, an analysis was performed by coding in the WinBUGS language. Several statistical performance criteria (R2, RMSE, and MSE) were utilized to evaluate the efficiency of Bayesian-based predictive models. The results showed that model #4 recorded R2 = 0.980 in the prediction of melting rate. Furthermore, model #5 with R2 = 0.966, had the best performance in predicting the values of surface-averaged Nusselt number. The models recommended in this research yield superior results compared to the previous study, which suggested R2 = 0.975 and R2 = 0. 925 for f and Nu, respectively.

Generative adversarial networks for construction of virtual populations of mechanistic models: simulations to study Omecamtiv Mecarbil action

Biophysical models are increasingly used to gain mechanistic insights by fitting and reproducing experimental and clinical data. The inherent variability in the recorded datasets, however, presents a key challenge. In this study, we present a novel approach, which integrates mechanistic modeling and machine learning to analyze in vitro cardiac mechanics data and solve the inverse problem of model parameter inference. We designed a novel generative adversarial network (GAN) and employed it to construct virtual populations of cardiac ventricular myocyte models in order to study the action of Omecamtiv Mecarbil (OM), a positive cardiac inotrope. Populations of models were calibrated from mechanically unloaded myocyte shortening recordings obtained in experiments on rat myocytes in the presence and absence of OM. The GAN was able to infer model parameters while incorporating prior information about which model parameters OM targets. The generated populations of models reproduced variations in myocyte contraction recorded during in vitro experiments and provided improved understanding of OM’s mechanism of action. Inverse mapping of the experimental data using our approach suggests a novel action of OM, whereby it modifies interactions between myosin and tropomyosin proteins. To validate our approach, the inferred model parameters were used to replicate other in vitro experimental protocols, such as skinned preparations demonstrating an increase in calcium sensitivity and a decrease in the Hill coefficient of the force–calcium (F–Ca) curve under OM action. Our approach thereby facilitated the identification of the mechanistic underpinnings of experimental observations and the exploration of different hypotheses regarding variability in this complex biological system.

Large-Deviation Approach to Random Recurrent Neuronal Networks: Parameter Inference and Fluctuation-Induced Transitions.

We here unify the field-theoretical approach to neuronal networks with large deviations theory. For a prototypical random recurrent network model with continuous-valued units, we show that the effective action is identical to the rate function and derive the latter using field theory. This rate function takes the form of a Kullback-Leibler divergence which enables data-driven inference of model parameters and calculation of fluctuations beyond mean-field theory. Lastly, we expose a regime with fluctuation-induced transitions between mean-field solutions.

Experimental and mathematical insights on the interactions between poliovirus and a defective interfering genome.

During replication, RNA viruses accumulate genome alterations, such as mutations and deletions. The interactions between individual variants can determine the fitness of the virus population and, thus, the outcome of infection. To investigate the effects of defective interfering genomes (DI) on wild-type (WT) poliovirus replication, we developed an ordinary differential equation model, which enables exploring the parameter space of the WT and DI competition. We also experimentally examined virus and DI replication kinetics during co-infection, and used these data to infer model parameters. Our model identifies, and our experimental measurements confirm, that the efficiencies of DI genome replication and encapsidation are two most critical parameters determining the outcome of WT replication. However, an equilibrium can be established which enables WT to replicate, albeit to reduced levels.

Parameter inference for stochastic biochemical models from perturbation experiments parallelised at the single cell level

Parameter inference for stochastic biochemical models from perturbation experiments parallelised at the single cell level

Joint Quantile Regression for Spatial Data

AbstractLinear quantile regression is a powerful tool to investigate how predictors may affect a response heterogeneously across different quantile levels. Unfortunately, existing approaches find it extremely difficult to adjust for any dependency between observation units, largely because such methods are not based upon a fully generative model of the data. For analysing spatially indexed data, we address this difficulty by generalizing the joint quantile regression model of Yang and Tokdar (Journal of the American Statistical Association, 2017, 112(519), 1107–1120) and characterizing spatial dependence via a Gaussian or t-copula process on the underlying quantile levels of the observation units. A Bayesian semiparametric approach is introduced to perform inference of model parameters and carry out spatial quantile smoothing. An effective model comparison criteria is provided, particularly for selecting between different model specifications of tail heaviness and tail dependence. Extensive simulation studies and two real applications to particulate matter concentration and wildfire risk are presented to illustrate substantial gains in inference quality, prediction accuracy and uncertainty quantification over existing alternatives.

Optimal design of experiments for optimization-based model calibration using Fisher information matrix

Statistical model calibration to infer unknown model parameters and model bias has been widely developed through comparison between simulation response and experimental data. Bayesian-based model calibration typically represented as Kennedy and O'Hagan (KOH) framework and optimization-based model calibration have been proposed, but efforts on optimization of experimental design to reduce the epistemic uncertainty minimizing experimental resources are still limited. Furthermore, when an unknown model parameter has natural and uncontrollable variability, the estimation may be much more difficult since both aleatory and epistemic uncertainties exist. In this paper, we have developed a framework to find the optimal design of experiments (DoE) satisfying the target information gain for inference of unknown model parameters based on optimization-based model calibration. The expected Fisher information matrix is approximated to quantify the expected information gain for the maximum likelihood estimation (MLE). Namely, the necessary number of experiments at each experimental design can be obtained to attain desired precision on estimators while minimizing the overall experimental cost. The numerical study verifies the feasibility of the proposed framework, which means that there is certainly a dominant DoE that gives more information to the inference on specific model parameters.

Real-time model calibration with deep reinforcement learning

The real-time, and accurate inference of model parameters is of great importance in many scientific and engineering disciplines that use computational models (such as a digital twin) for the analysis and prediction of complex physical processes. However, fast and accurate inference for processes of complex systems cannot easily be achieved in real-time with state-of-the-art methods under noisy real-world conditions with the requirement of a real-time response. The primary reason is that the inference of model parameters with traditional techniques based on optimization or sampling often suffers from computational and statistical challenges, resulting in a trade-off between accuracy and deployment time. In this paper, we propose a novel framework for inference of model parameters based on reinforcement learning. The proposed methodology is demonstrated and evaluated on two different physics-based models of turbofan engines. The experimental results demonstrate that the proposed methodology outperforms all other tested methods in terms of speed and robustness, with high inference accuracy.

Bayesian inference of root architectural model parameters from synthetic field data

Background and aimsCharacterizing root system architectures of field-grown crops is challenging as root systems are hidden in the soil. We investigate the possibility of estimating root architecture model parameters from soil core data in a Bayesian framework.MethodsIn a synthetic experiment, we simulated wheat root systems in a virtual field plot with the stochastic CRootBox model. We virtually sampled soil cores from this plot to create synthetic measurement data. We used the Markov chain Monte Carlo (MCMC) DREAM(ZS) sampler to estimate the most sensitive root system architecture parameters. To deal with the CRootBox model stochasticity and limited computational resources, we essentially added a stochastic component to the likelihood function, thereby turning the MCMC sampling into a form of approximate Bayesian computation (ABC).ResultsA few zero-order root parameters: maximum length, elongation rate, insertion angles, and numbers of zero-order roots, with narrow posterior distributions centered around true parameter values were identifiable from soil core data. Yet other zero-order and higher-order root parameters were not identifiable showing a sizeable posterior uncertainty.ConclusionsBayesian inference of root architecture parameters from root density profiles is an effective method to extract information about sensitive parameters hidden in these profiles. Equally important, this method also identifies which information about root architecture is lost when root architecture is aggregated in root density profiles.

Analyzing Spatial Panel Data of Cigarette Demand: A Bayesian Hierarchical Modeling Approach

Analysis of spatial panel data is of great importance and inter est in spatial econometrics. Here we consider cigarette demand in a spatial panel of 46 states of the US over a 30-year period. We construct a de mand equation to examine the elasticity of per pack cigarette price and per capita disposable income. The existing spatial panel models account for both spatial autocorrelation and state-wise heterogeneity, but fail to account for temporal autocorrelation. Thus we propose new spatial panel models and adopt a fully Bayesian approach for model parameter inference and predic tion of cigarette demand at future time points using MCMC. We conclude that the spatial panel model that accounts for state-wise heterogeneity, spa tial dependence, and temporal dependence clearly outperforms the existing models. Analysis based on the new model suggests a negative cigarette price elasticity but a positive income elasticity.