Broadwick: a framework for computational epidemiology

Analytically or computationally intractable likelihood functions can arise in complex statistical inferential problems making them inaccessible to standard Bayesian inferential methods. Approximate Bayesian computation (ABC) methods address such inferential problems by replacing direct likelihood evaluations with repeated sampling from the model. ABC methods have been predominantly applied to parameter estimation problems and less to model choice problems due to the added difficulty of handling multiple model spaces. The ABC algorithm proposed here addresses model choice problems by extending Fearnhead and Prangle (2012, Journal of the Royal Statistical Society, Series B 74, 1-28) where the posterior mean of the model parameters estimated through regression formed the summary statistics used in the discrepancy measure. An additional stepwise multinomial logistic regression is performed on the model indicator variable in the regression step and the estimated model probabilities are incorporated into the set of summary statistics for model choice purposes. A reversible jump Markov chain Monte Carlo step is also included in the algorithm to increase model diversity for thorough exploration of the model space. This algorithm was applied to a validating example to demonstrate the robustness of the algorithm across a wide range of true model probabilities. Its subsequent use in three pathogen transmission examples of varying complexity illustrates the utility of the algorithm in inferring preference of particular transmission models for the pathogens.

Event Abstract Back to Event Statistical uncertainty and sensitivity analysis of intracellular signaling models - through approximate Bayesian computation and variance based global sensitivity analysis Olivia Eriksson1, 2*, Alexandra Jauhiainen1, 3, Sara Maad Sasane4, Anu G Nair5, Carolina Sartorius4 and Jeanette Hellgren Kotaleski2, 5, 6 1 Contributed equally to this work, Sweden 2 Stockholm University, Department of Numerical Analysis and Computer Science, Sweden 3 AstraZeneca AB R&D, Early Clinical Biometrics, Sweden 4 Lund University, Centre for Mathematical Sciences, Sweden 5 KTH Royal Institute of Technology, School of Computer Science and Communication, Sweden 6 Karolinska Institute, Department of Neuroscience, Sweden Computational dynamical models describing intracellular signaling pathways of nerve cells are increasing in size and complexity as more information is obtained from experiments. Models describing protein interactions within neurons can contain over hundred protein reactions [1, 2]. These models are built from knowledge about the interaction topology, inferred from e.g. gene knock-out experiments, as well as from experimental quantitative data describing the input-output relationship of the observed system. The quantitative data are often sparse as compared to the size of the system, and translating the experimental information into dynamical models often results in large uncertainties in the parameter (e.g reaction rates) values. This uncertainty is partly due to the sparseness in experimental time series data (practical unidentifiability), but it is also an intrinsic feature of the modeled system (structural unidentifiability) and could reflect the possibility for biological variation [3]; in many biological systems the same function can be achieved in partly different ways due to degeneracy and redundancy. Here we investigate the extent of this parameter uncertainty, in a model describing calcium (Ca)-dependent activation of Calmodulin (CaM), Protein phosphatase 2B (PP2B) and Ca/CaM-dependent protein kinase II (CamKII) [4], which is an intracellular pathway of importance to synaptic plasticity. We presume that the structure of the model is correct and then characterize the uncertainty in the parameters based on data. This is done by sampling the subspace of parameter values which has an equally good fit to data (corresponding to the “viable space” in [5]), through a statistical approach known as Approximate Bayesian Computation (ABC) with Markov Chain Monte Carlo (MCMC) [6]. ABC has been proposed for parameter estimation in system biology models previously, albeit in slightly different settings, e.g. [7, 8], and can be applied to a wide range of problems. In order to characterize the viable space efficiently with several experimental datasets, we employ multivariate probability distributions called copulas as a part of the ABC sampling. The result is a multivariate posterior distribution for the parameters, which represents how much they are constrained by the data (i.e. the uncertainty) as illustrated in Figure 1 (pairwise plots of viable space for four parameters indicating constraints and dependencies before and after calibration to data). The next step is to look into how the parameter uncertainty is translated to uncertainty of the predictions made from the model. We also investigate the role and importance of different parameters, with respect to different model outputs including the predictions, by means of global sensitivity analysis [9]. Figure 2 illustrates the sensitivity of one of the outputs calculated by a method based on the decomposition of the variance [10, 11, 12], showing different types of sensitivity measures. Finally, we explore how the sensitivity of different subsets of parameters change as different parts of the viable space are investigated, which is shown in Figure 3, where sensitivity profiles are clustered into groups with different sensitivity characteristics. Figure 1 Figure 2 Figure 3 Acknowledgements This research was supported by funding from the Swedish e-Science Research Centre and the Human Brain Project References [1] Gutierrez-Arenas O, Eriksson O, Hellgren Kotaleski J (2014) Segregation and Crosstalk of D1 Receptor-Mediated Activation of ERK in Striatal Medium Spiny Neurons upon Acute Administration of Psychostimulants. PLoS Comput Biol 10, e1003445. [2] Nair AG, Gutierrez-Arenas O, Eriksson O, Vincent P, and Hellgren Kotaleski J (2015) Sensing Positive versus Negative Reward Signals through Adenylyl Cyclase-Coupled GPCRs in Direct and Indirect Pathway Striatal Medium Spiny Neurons. J. Neuroscience 35, 14017-14030. [3] Marder E, Goeritz ML, Otopalik AG (2015) Robust circuit rhythms in small circuits arise from variable circuit components and mechanisms. Curr Opin Neurobiol 31, 156-163. [4] Nair AG, Gutierrez-Arenas O, Eriksson O, Jauhiainen A, Blackwell KT and Kotaleski, JH (2014). Modeling intracellular signaling underlying striatal function in health and disease. Progress in molecular biology and translational science, 123, 277 [5] Zamora-Sillero E, Hafner M, Ibig A, Stelling J, and Wagner, A. (2011). Efficient characterization of high-dimensional parameter spaces for systems biology. BMC systems biology 5, 142. [6] Marjoram P, Molitor J, Plagnol V, and Tavare S (2003) Markov chain Monte Carlo without likelihoods. Proc. Natl. Acad. Sci. U.S.A. 100, 15324–15328. [7] Toni T, Welch D, Strelkowa N, Ipsen A, and Stumpf MP. Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems. J R Soc Interface, 6, 187–202. [8] Liepe J, Kirk P, Filippi S, Toni T, Barnes CP, and Stumpf MP. A framework for parameter estimation and model selection from experimental data in systems biology using approximate Bayesian computation. Nat Protoc, 9, 439–456. [9] Saltelli A, Ratto M, Andres T, Campolongo F, Cariboni J, Gatelli D, Saisana M, Tarantola S Global sensitivity analysis: the primer. In Wiley 2008 New York, NY:Wiley. [10] Sobol IM (2001) Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates, Math. Comput. Simul. 55, 271–280. [11] Saltelli A (2002) Making best use of model evaluations to compute sensitivity indices. Comp Phys Comm 145, 280 – 297. [12] Halnes G, Ulfhielm E Ljunggren EE, Kotaleski JH and Rospars JP (2009) Modelling and sensitivity analysis of the reactions involving receptor, G-protein and effector in vertebrate olfactory receptor neurons. Journal of computational neuroscience 27, 471-491. Keywords: sensitivity analysis, Approximate Bayesian Computation, copulas, intracellular signalling, Dynamical Modeling, global sensitivity analysis, Markov chain Monte Carlo, variance decomposition Conference: Neuroinformatics 2016, Reading, United Kingdom, 3 Sep - 4 Sep, 2016. Presentation Type: Investigator presentations Topic: Computational neuroscience Citation: Eriksson O, Jauhiainen A, Maad Sasane S, Nair A, Sartorius C and Hellgren Kotaleski J (2016). Statistical uncertainty and sensitivity analysis of intracellular signaling models - through approximate Bayesian computation and variance based global sensitivity analysis. Front. Neuroinform. Conference Abstract: Neuroinformatics 2016. doi: 10.3389/conf.fninf.2016.20.00014 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 31 May 2016; Published Online: 18 Jul 2016. * Correspondence: PhD. Olivia Eriksson, Contributed equally to this work, Stockholm, Sweden, olivia@kth.se Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Olivia Eriksson Alexandra Jauhiainen Sara Maad Sasane Anu G Nair Carolina Sartorius Jeanette Hellgren Kotaleski Google Olivia Eriksson Alexandra Jauhiainen Sara Maad Sasane Anu G Nair Carolina Sartorius Jeanette Hellgren Kotaleski Google Scholar Olivia Eriksson Alexandra Jauhiainen Sara Maad Sasane Anu G Nair Carolina Sartorius Jeanette Hellgren Kotaleski PubMed Olivia Eriksson Alexandra Jauhiainen Sara Maad Sasane Anu G Nair Carolina Sartorius Jeanette Hellgren Kotaleski Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

<strong class="journal-contentHeaderColor">Abstract.</strong> The Approximate Bayesian computation (ABC) methods provide a powerful tool for sampling from Bayesian posteriors for cases where we can simulate samples, but we have no access to an explicit expression of the likelihood function. The Simulated Annealing ABC (SABC) algorithm has been proposed to achieve a fast convergence to an unbiased approximation to the posterior by adaptively decreasing an initially coarse tolerance value. However, this algorithm uses a rather simplistic random walk Metropolis (RWM) sampler to generate trial moves in a Markov chain and always requires an excessive number of model evaluations for approximating the posterior, which inevitably lowers the sampling efficiency and limits its applications in more complex hydrologic modelling practices. Inspired by the advances made in Markov Chain Monte Carlo (MCMC) methods, we incorporated an adaptive Differential Evolution scheme to enhance the efficiency of SABC sampling. This scheme has its roots within Differential Evolution Markov Chains (DE-MC), and additionally utilizes a self-adaptive randomized subspace sampling strategy to optimally select the dimensions of parameters to be updated each time a proposal is generated. The superiority of the modified SABC (mSABC) over the original SABC algorithm was demonstrated through a SAC-SMA application to the Danjiangkou Reservoir region (DRR). The case study results showed that mSABC was far more efficient with lower computation costs and higher acceptance rates, and achieved higher numerical accuracy than the original SABC algorithm. mSABC also resulted in a better overall prediction of streamflow time series and signatures. The introduction of more advanced MCMC sampler into SABC helps to speed up convergence to the approximate posterior while achieving better model performance, which significantly widens the applicability of SABC to complex posterior exploration problems.

Wastewater production, like many other engineered and environmental processes, is inherent stochastic in nature and requires the use of complex stochastic models, for example, to predict realistic patterns of down-the-drain chemicals or pharmaceuticals and personal care products. Up until now, a formal method of statistical inference has been lacking for many of those models, where explicit likelihood functions were intractable. In this Article, we investigate Approximate Bayesian Computation (ABC) methods to infer important parameters of stochastic environmental models. ABC methods have been recently suggested to perform model-based inference in a Bayesian setting when model likelihoods are analytically or computationally intractable and have not been applied to environmental systems analysis or water quality modeling before. In a case study, we investigate the performance of three different algorithms to infer the number of wastewater pulses contained in three high-resolution data series of benzotriazole and total nitrogen loads in sewers. We find that all algorithms perform well and that the uncertainty in the inferred number of corresponding wastewater pulses varies between 6% and 28%. In our case, the results are more sensitive to substance characteristics than to catchment properties. Although the application of ABC methods requires careful tuning and attention to detail, they have a great general potential to update stochastic model parameters with monitoring data and improve their predictive capabilities.

We illustrate the process undertaken to inform surveillance for cassava brown streak disease (CBSD). CBSD is currently the most devastating cassava pathogen in East, central and southern Africa affecting a staple crop for over 700 million people on the continent and posing a major threat to West Africa. The process involved the following steps: firstly collating and digitising historic surveillance data from historic paper and electronic records from Uganda. Secondly, constructing a cassava production density map based on historic cassava production statistics standardised to 2014 levels. Thirdly, construction of a stochastic spatiotemporal CBSD spread model and the estimation of model parameters using historic surveillance data and Approximate Bayesian Computation (ABC) methods. Subsequently, the model is validated against a subset of the data which has not been used for parameter estimation. Finally, model predictions are used to inform risk-driven CBSD surveillance and control programmes.

Parameter inference in small world network disease models with approximate Bayesian Computational methods

Probabilistic logic programming formalisms permit the definition of potentially very complex probability distributions. This complexity can often make learning hard, even when structure is fixed and learning reduces to parameter estimation. In this paper an approximate Bayesian computation (ABC) method is presented which computes approximations to the posterior distribution over PRISM parameters. The key to ABC approaches is that the likelihood function need not be computed, instead a 'distance' between the observed data and synthetic data generated by candidate parameter values is used to drive the learning. This makes ABC highly appropriate for PRISMprograms which can have an intractable likelihood function, but from which synthetic data can be readily generated. The algorithm is experimentally shown to work well on an easy problem but further work is required to produce acceptable results on harder ones.

Approximate Bayesian computation (ABC) is used to estimate unknown parameter values, as well as their uncertainties, in Reynolds-averaged Navier–Stokes (RANS) simulations of turbulent flows. The ABC method approximates posterior distributions of model parameters, but does not require the direct computation, or estimation, of a likelihood function. This method thus enables relatively simple and flexible parameter estimation for complex models and a wide range of reference data. This paper describes the ABC approach, including the use of a calibration step, adaptive proposal, and Markov chain Monte Carlo (MCMC) technique to accelerate the parameter estimation, resulting in an ABC approach with improved MCMC, denoted ABC-IMCMC. As a test of the classic ABC rejection algorithm and ABC-IMCMC, parameters are estimated in a nonequilibrium RANS model using reference data from direct numerical simulations of periodically sheared homogeneous turbulence. The use of ABC-IMCMC is then demonstrated to estimate parameters in the Menter shear-stress-transport (SST) model using experimental reference data for an axisymmetric transonic bump. This paper shows that the accuracy of the SST model for this test case can be improved using ABC-IMCMC, indicating that ABC-IMCMC is a promising method for the calibration of RANS models using a wide range of reference data.

Approximate Bayesian computation (ABC) constitutes a class of computational methods rooted in Bayesian statistics. In all model-based statistical inference, the likelihood function is of central importance, since it expresses the probability of the observed data under a particular statistical model, and thus quantifies the support data lend to particular values of parameters and to choices among different models. For simple models, an analytical formula for the likelihood function can typically be derived. However, for more complex models, an analytical formula might be elusive or the likelihood function might be computationally very costly to evaluate. ABC methods bypass the evaluation of the likelihood function. In this way, ABC methods widen the realm of models for which statistical inference can be considered. ABC methods are mathematically well-founded, but they inevitably make assumptions and approximations whose impact needs to be carefully assessed. Furthermore, the wider application domain of ABC exacerbates the challenges of parameter estimation and model selection. ABC has rapidly gained popularity over the last years and in particular for the analysis of complex problems arising in biological sciences (e.g., in population genetics, ecology, epidemiology, and systems biology).

Understanding the processes by which new diseases are introduced in previously healthy areas is of major interest in elaborating prevention and management policies, as well as in understanding the dynamics of pathogen diversity at large spatial scale. In this study, we aimed to decipher the dispersal processes that have led to the emergence of the plant pathogenic fungus Microcyclus ulei, which is responsible for the South American Leaf Blight (SALB). This fungus has devastated rubber tree plantations across Latin America since the beginning of the twentieth century. As only imprecise historical information is available, the study of population evolutionary history based on population genetics appeared most appropriate. The distribution of genetic diversity in a continental sampling of four countries (Brazil, Ecuador, Guatemala and French Guiana) was studied using a set of 16 microsatellite markers developed specifically for this purpose. A very strong genetic structure was found (F(st)=0.70), demonstrating that there has been no regular gene flow between Latin American M. ulei populations. Strong bottlenecks probably occurred at the foundation of each population. The most likely scenario of colonization identified by the Approximate Bayesian Computation (ABC) method implemented in DIYABC suggested two independent sources from the Amazonian endemic area. The Brazilian, Ecuadorian and Guatemalan populations might stem from serial introductions through human-mediated movement of infected plant material from an unsampled source population, whereas the French Guiana population seems to have arisen from an independent colonization event through spore dispersal.

In time-series analysis, state-space models (SSMs) have been widely used to estimate the conditional probability distributions of hidden variables and parameter values, as well as to understand structures that can generate the data. For example, the Kalman filter is used to analytically calculate the conditional probability distribution on linear SSMs in terms of minimizing the variance, and several extensions, such as the unscented Kalman filter and particle filter, have been applied to calculate the approximate distribution on nonlinear SSMs. Recently, the approximate Bayesian computation (ABC) has been applied to such time-series filtering to handle intractable likelihoods; however, it remains problematic with respect to consistently achieving a reduction of the estimation bias, evaluating the validity of the models, and dealing with replicated observations. To address these problems, in this paper, we propose a novel method combined with the kernel ABC to perform filtering, parameter estimation, and the model evaluation in SSMs. Simulation studies show that the proposed method produces inference that is comparable to other ABC methods, with the advantage of not requiring a careful calibration of the ABC threshold. In addition, we evaluate the performance of the model-selection capability using true and competitive models on synthetic data from nonlinear SSMs. Finally, we apply the proposed method to real data in rat circadian oscillations, and demonstrated the usefulness in practical situations.

The development of mathematical models for studying newly emerging and re-emerging infectious diseases has gained momentum due to global events. The gyrodactylid-fish system, like many host-parasite systems, serves as a valuable resource for ecological, evolutionary, and epidemiological investigations owing to its ease of experimental manipulation and long-term monitoring. Although this system has an existing individual-based model, it falls short in capturing information about species-specific microhabitat preferences and other biological details for different Gyrodactylus strains across diverse fish populations. This current study introduces a new individual-based stochastic simulation model that uses a hybrid τ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au $$\\end{document}-leaping algorithm to incorporate this essential data, enhancing our understanding of the complexity of the gyrodactylid-fish system. We compare the infection dynamics of three gyrodactylid strains across three host populations. A modified sequential-type approximate Bayesian computation (ABC) method, based on sequential Monte Carlo and sequential importance sampling, is developed. Additionally, we establish two penalised local-linear regression methods (based on L1 and L2 regularisations) for ABC post-processing analysis to fit our model using existing empirical data. With the support of experimental data and the fitted mathematical model, we address open biological questions for the first time and propose directions for future studies on the gyrodactylid-fish system. The adaptability of the mathematical model extends beyond the gyrodactylid-fish system to other host-parasite systems. Furthermore, the modified ABC methodologies provide efficient calibration for other multi-parameter models characterised by a large set of correlated or independent summary statistics.

Next-generation sequencing of pooled samples (Pool-seq) is a popular method to assess genome-wide diversity patterns in natural and experimental populations. However, Pool-seq is associated with specific sources of noise, such as unequal individual contributions. Consequently, using Pool-seq for the reconstruction of evolutionary history has remained underexplored. Here we describe a novel Approximate Bayesian Computation (ABC) method to infer demographic history, explicitly modelling Pool-seq sources of error. By jointly modelling Pool-seq data, demographic history and the effects of selection due to barrier loci, we obtain estimates of demographic history parameters accounting for technical errors associated with Pool-seq. Our ABC approach is computationally efficient as it relies on simulating subsets of loci (rather than the whole-genome) and on using relative summary statistics and relative model parameters. Our simulation study results indicate Pool-seq data allows distinction between general scenarios of ecotype formation (single versus parallel origin) and to infer relevant demographic parameters (e.g. effective sizes and split times). We exemplify the application of our method to Pool-seq data from the rocky-shore gastropod Littorina saxatilis, sampled on a narrow geographical scale at two Swedish locations where two ecotypes (Wave and Crab) are found. Our model choice and parameter estimates show that ecotypes formed before colonization of the two locations (i.e. single origin) and are maintained despite gene flow. These results indicate that demographic modelling and inference can be successful based on pool-sequencing using ABC, contributing to the development of suitable null models that allow for a better understanding of the genetic basis of divergent adaptation.

Approximate Bayesian Computation (ABC) methods have a lot of success to accomplish Bayesian inference on the parameters of models for which the calculation of the likelihood is intractable. These algorithms consists in comparing the observed dataset to many simulated datasets. These ones can be generated in different ways. Typically, the rejection ABC scheme consists first of simulating parameters using independent calls to the prior distribution and then, given these values, generating the datasets using independent calls to the model. For such a method, the computation time needed to get a suitable approximation of the posterior distribution can be very long. Also, there exist some sequential Monte Carlo methods replacing simulations from the prior by using successive approximations to the posterior distribution. Here, we recall a sequential simulation algorithm and we compare different parallelization strategies. We notably shown that the parallelization of the sequential ABC sampler is useless when using more than four threads per instance of the program and that the standard rejection ABC sampler has to be used when facing a large number of cores. Indeed, in such a case, the cost of the sequential ABC sampler's parallelization prohibits its use.

Identification of contaminant sources in rivers is crucial for river protection and emergency response. This study presents an innovative approach for identifying river pollution sources by using Bayesian inference and cellular automata (CA) modeling. A general Bayesian framework is proposed that combines the CA model with observed data to identify unknown sources of river pollution. To reduce the computational burden of the Bayesian inference, a CA contaminant transport model is developed to efficiently simulate pollutant concentration values in the river. These simulated concentration values are then used to calculate the likelihood function of available measurements. The Markov chain Monte Carlo (MCMC) method is used to produce the posterior distribution of contaminant source parameters, which is a sampling-based method that enables the estimation of complex posterior distributions. The suggested methodology is applied to a real case study of the Fen River in Yuncheng City, Shanxi Province, Northern China, and it estimates the release time, release mass, and source location with relative errors below 19%. The research indicates that the proposed methodology is an effective and flexible way to identify the location and concentrations of river contaminant sources.