Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems

Approximate Bayesian computation methods can be used to evaluate posterior distributions without having to calculate likelihoods. In this paper we discuss and apply an approximate Bayesian computation (ABC) method based on sequential Monte Carlo (SMC) to estimate parameters of dynamical models. We show that ABC SMC gives information about the inferability of parameters and model sensitivity to changes in parameters, and tends to perform better than other ABC approaches. The algorithm is applied to several well known biological systems, for which parameters and their credible intervals are inferred. Moreover, we develop ABC SMC as a tool for model selection; given a range of different mathematical descriptions, ABC SMC is able to choose the best model using the standard Bayesian model selection apparatus.Comment: 26 pages, 9 figure

Choosing summary statistics by least angle regression for approximate Bayesian computation

YesBayesian statistical inference relies on the posterior distribution. Depending on the model, the posterior can be more or less difficult to derive. In recent years, there has been a lot of interest in complex settings where the likelihood is analytically intractable. In such situations, approximate Bayesian computation (ABC) provides an attractive way of carrying out Bayesian inference. For obtaining reliable posterior estimates however, it is important to keep the approximation errors small in ABC. The choice of an appropriate set of summary statistics plays a crucial role in this effort. Here, we report the development of a new algorithm that is based on least angle regression for choosing summary statistics. In two population genetic examples, the performance of the new algorithm is better than a previously proposed approach that uses partial least squares.Higher Education Commission (HEC), College Deanship of Scientific Research, King Saud University, Riyadh Saudi Arabia - research group project RGP-VPP-280

Akt regulates centrosome migration and spindle orientation in the early Drosophila melanogaster embryo

Correct positioning and morphology of the mitotic spindle is achieved through regulating the interaction between microtubules (MTs) and cortical actin. Here we find that, in the Drosophila melanogaster early embryo, reduced levels of the protein kinase Akt result in incomplete centrosome migration around cortical nuclei, bent mitotic spindles, and loss of nuclei into the interior of the embryo. We show that Akt is enriched at the embryonic cortex and is required for phosphorylation of the glycogen synthase kinase-3β homologue Zeste-white 3 kinase (Zw3) and for the cortical localizations of the adenomatosis polyposis coli (APC)–related protein APC2/E-APC and the MT + Tip protein EB1. We also show that reduced levels of Akt result in mislocalization of APC2 in postcellularized embryonic mitoses and misorientation of epithelial mitotic spindles. Together, our results suggest that Akt regulates a complex containing Zw3, Armadillo, APC2, and EB1 and that this complex has a role in stabilizing MT–cortex interactions, facilitating both centrosome separation and mitotic spindle orientation

Computational system identification of continuous-time nonlinear systems using approximate Bayesian computation

In this paper, we derive a system identification framework for continuous-time nonlinear systems, for the first time using a simulation-focused computational Bayesian approach. Simulation approaches to nonlinear system identification have been shown to outperform regression methods under certain conditions, such as non-persistently exciting inputs and fast-sampling. We use the approximate Bayesian computation (ABC) algorithm to perform simulation-based inference of model parameters. The framework has the following main advantages: (1) parameter distributions are intrinsically generated, giving the user a clear description of uncertainty, (2) the simulation approach avoids the difficult problem of estimating signal derivatives as is common with other continuous-time methods, and (3) as noted above, the simulation approach improves identification under conditions of non-persistently exciting inputs and fast-sampling. Term selection is performed by judging parameter significance using parameter distributions that are intrinsically generated as part of the ABC procedure. The results from a numerical example demonstrate that the method performs well in noisy scenarios, especially in comparison to competing techniques that rely on signal derivative estimation

Polymorphisms and promoter overactivity of the p22(phox) gene in vascular smooth muscle cells from spontaneously hypertensive rats

In a previous study, we found that the p22(phox) subunit of the NADH/NADPH oxidase is overexpressed in vascular smooth muscle cells (VSMCs) from spontaneously hypertensive rats (SHRs) with enhanced vascular production of superoxide anion ((.)O(2)(-)). Thus, we have investigated whether changes in the sequence or activity of the promoter region of p22(phox) gene are present in SHRs. To carry out this analysis, first of all, we characterized the rat gene structure and promoter region for the p22(phox) subunit. The p22(phox) gene spans approximately 10 kb and contains 6 exons and 5 introns. Primer extension analysis indicated the transcriptional start site 100 bp upstream from the translational start site. The immediate promoter region of the p22(phox) gene does not contain a TATA box, but there are a CCAC box and putative recognition sites for nuclear factors, such as SP1, gamma-interferon, and nuclear factor-kappaB. Using reporter-gene transfection analysis, we found that this promoter was functional in VSMCs. Furthermore, we observed that p22(phox) promoter activity was significantly higher in VSMCs from SHRs than from normotensive Wistar-Kyoto rats. In addition, we found that there were 5 polymorphisms in the sequence of p22(phox) promoter between Wistar-Kyoto rats and SHRs and that they were functional. The results obtained in this study provide a tool to explore the mechanisms that regulate the expression of p22(phox) gene in rat VSMCs. Furthermore, our findings show that changes in the sequence of p22(phox) gene promoter and in the degree of activation of VSMCs are responsible for upregulated expression of p22(phox) in SHRs

Oxidative Stress in Arterial Hypertension: Role of NAD(P)H Oxidase

Increased vascular reactive oxygen species production, especially superoxide anion, contributes significantly in the functional and structural alterations present in hypertension. An enhanced superoxide production causes a diminished NO bioavailability by an oxidative reaction that inactivates NO. Exaggerated superoxide levels and a low NO bioavailability lead to endothelial dysfunction and hypertrophy of vascular cells. It has been shown that the enzyme NAD(P)H oxidase plays a major role as the most important source of superoxide anion in vascular cells. Several experimental observations have shown an enhanced superoxide generation as a result of the activation of vascular NAD(P)H oxidase in hypertension. Although this enzyme responds to stimuli such as vasoactive factors, growth factors, and cytokines, some recent data suggest the existence of a genetic background modulating the expression of its different components. New polymorphisms have been identified in the promoter of the p22(phox) gene, an essential subunit of NAD(P)H oxidase, influencing the activity of this enzyme. Genetic investigations of these polymorphisms will provide novel markers for determination of genetic susceptibility to oxidative stress in hypertension

Vascular NADH/NADPH oxidase is involved in enhanced superoxide production in spontaneously hypertensive rats

This study was designed to test the hypothesis that stimulation of nicotinamide adenine dinucleotide/nicotinamide adenine dinucleotide phosphate (NADH/NADPH) oxidase is involved in increased vascular superoxide anion (*O(2)(-)) production in spontaneously hypertensive rats (SHR). The study was performed in 16-week-old and 30-week-old normotensive Wistar-Kyoto rats (WKY(16) and WKY(30), respectively) and in 16-week-old and 30-week-old SHR (SHR(16) and SHR(30), respectively). In addition, 16-week-old SHR were treated with oral irbesartan (average dose 20 mg/kg per day) for 14 weeks (SHR(30)-I). Aortic NADH/NADPH oxidase activity was determined by use of chemiluminescence with lucigenin. The expression of p22phox messenger RNA was assessed by competitive reverse transcription-polymerase chain reaction. Vascular responses to acetylcholine were determined by isometric tension studies. Aortic wall structure was studied, determining the media thickness and the cross-sectional area by morphometric analysis. Whereas systolic blood pressure was significantly increased in the 2 groups of hypertensive animals compared with their normotensive controls, no differences were observed in systolic blood pressure between SHR(30) and SHR(16). No other differences in the parameters measured were found between WKY(16) and SHR(16). In SHR(30) compared with WKY(30), we found significantly greater p22phox mRNA level, NADH/NADPH-driven *O(2)(-) production, media thickness, and cross-sectional area and an impaired vasodilation in response to acetylcholine. Treated SHR had similar NADH/NADPH oxidase activity and p22phox expression as the WKY(30) group. The vascular functional and morphological parameters were improved in SHR(30)-I. These findings suggest that an association exists between p22phox gene overexpression and NADH/NADPH overactivity in the aortas of adult SHR. Enhanced NADH/NADPH oxidase-dependent *O(2)(-) production may contribute to endothelial dysfunction and vascular hypertrophy in this genetic model of hypertension

Forward-in-Time, Spatially Explicit Modeling Software to Simulate Genetic Lineages Under Selection

SELECTOR is a software package for studying the evolution of multiallelic genes under balancing or positive selection while simulating complex evolutionary scenarios that integrate demographic growth and migration in a spatially explicit population framework. Parameters can be varied both in space and time to account for geographical, environmental, and cultural heterogeneity. SELECTOR can be used within an approximate Bayesian computation estimation framework. We first describe the principles of SELECTOR and validate the algorithms by comparing its outputs for simple models with theoretical expectations. Then, we show how it can be used to investigate genetic differentiation of loci under balancing selection in interconnected demes with spatially heterogeneous gene flow. We identify situations in which balancing selection reduces genetic differentiation between population groups compared with neutrality and explain conflicting outcomes observed for human leukocyte antigen loci. These results and three previously published applications demonstrate that SELECTOR is efficient and robust for building insight into human settlement history and evolution

Non-linear regression models for Approximate Bayesian Computation

Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the curse of dimensionality when the number of summary statistics is increased. Here we propose a machine-learning approach to the estimation of the posterior density by introducing two innovations. The new method fits a nonlinear conditional heteroscedastic regression of the parameter on the summary statistics, and then adaptively improves estimation using importance sampling. The new algorithm is compared to the state-of-the-art approximate Bayesian methods, and achieves considerable reduction of the computational burden in two examples of inference in statistical genetics and in a queueing model.Comment: 4 figures; version 3 minor changes; to appear in Statistics and Computin

Piecewise Approximate Bayesian Computation: fast inference for discretely observed Markov models using a factorised posterior distribution

Many modern statistical applications involve inference for complicated stochastic models for which the likelihood function is difficult or even impossible to calculate, and hence conventional likelihood-based inferential techniques cannot be used. In such settings, Bayesian inference can be performed using Approximate Bayesian Computation (ABC). However, in spite of many recent developments to ABC methodology, in many applications the computational cost of ABC necessitates the choice of summary statistics and tolerances that can potentially severely bias the estimate of the posterior. We propose a new “piecewise” ABC approach suitable for discretely observed Markov models that involves writing the posterior density of the parameters as a product of factors, each a function of only a subset of the data, and then using ABC within each factor. The approach has the advantage of side-stepping the need to choose a summary statistic and it enables a stringent tolerance to be set, making the posterior “less approximate”. We investigate two methods for estimating the posterior density based on ABC samples for each of the factors: the first is to use a Gaussian approximation for each factor, and the second is to use a kernel density estimate. Both methods have their merits. The Gaussian approximation is simple, fast, and probably adequate for many applications. On the other hand, using instead a kernel density estimate has the benefit of consistently estimating the true piecewise ABC posterior as the number of ABC samples tends to infinity. We illustrate the piecewise ABC approach with four examples; in each case, the approach offers fast and accurate inference