891 research outputs found
Markov chain Monte Carlo methods for parameter identification in systems biology models
First, I would like to thank Prof. Dr. Achim Tresch for giving me the opportunity to write this thesis and to work on three fascinating projects. I really appreciate all the fruitful discussions, his constant support and the excellent working atmosphere. I would also like to thank Prof. Dr. Patrick Cramer for being my doctoral supervisor. Furthermore, I would like to thank all the other members of my dissertation committee (Prof. Dr. Rainer Spang
Robust Bayesian target detection algorithm for depth imaging from sparse single-photon data
This paper presents a new Bayesian model and associated algorithm for depth
and intensity profiling using full waveforms from time-correlated single-photon
counting (TCSPC) measurements in the limit of very low photon counts (i.e.,
typically less than 20 photons per pixel). The model represents each Lidar
waveform as an unknown constant background level, which is combined in the
presence of a target, to a known impulse response weighted by the target
intensity and finally corrupted by Poisson noise. The joint target detection
and depth imaging problem is expressed as a pixel-wise model selection and
estimation problem which is solved using Bayesian inference. Prior knowledge
about the problem is embedded in a hierarchical model that describes the
dependence structure between the model parameters while accounting for their
constraints. In particular, Markov random fields (MRFs) are used to model the
joint distribution of the background levels and of the target presence labels,
which are both expected to exhibit significant spatial correlations. An
adaptive Markov chain Monte Carlo algorithm including reversible-jump updates
is then proposed to compute the Bayesian estimates of interest. This algorithm
is equipped with a stochastic optimization adaptation mechanism that
automatically adjusts the parameters of the MRFs by maximum marginal likelihood
estimation. Finally, the benefits of the proposed methodology are demonstrated
through a series of experiments using real data.Comment: arXiv admin note: text overlap with arXiv:1507.0251
Bayesian and Markov chain Monte Carlo methods for identifying nonlinear systems in the presence of uncertainty
In this paper, the authors outline the general principles behind an approach to Bayesian system identification and highlight the benefits of adopting a Bayesian framework when attempting to identify models of nonlinear dynamical systems in the presence of uncertainty. It is then described how, through a summary of some key algorithms, many of the potential difficulties associated with a Bayesian approach can be overcome through the use of Markov chain Monte Carlo (MCMC) methods. The paper concludes with a case study, where an MCMC algorithm is used to facilitate the Bayesian system identification of a nonlinear dynamical system from experimentally observed acceleration time histories
Petri-Net Simulation Model of a Nuclear Component Degradation Process
International audienceMulti physical state modeling (MPSM) is a novel approach being investigated for estimating the reliability of components and systems in the context of probabilistic risk assessment (PRA). The approach integrates multi-state modeling, which describes the degradation process by transitions among discrete states (e.g. initial, micro-crack, rupture, etc) and physical modeling by (physical) equations that govern the degradation process. In practice, the degradation process is non-Markovian and its transition rates are time-dependent and influenced by external factors such as temperature and stress. Under these conditions, it is in general difficult to derive the state probabilities analytically. On the contrary, Petri nets provide a flexible modeling framework for describing degradation processes with arbitrary transition rates. In this paper, we build a Petri net in support of Monte Carlo simulation of the stochastic aging behavior of a nuclear component undergoing stress corrosion cracking. The results are compared with analytical results derived in a previous work of literature
Interacting multiple-models, state augmented Particle Filtering for fault diagnostics
International audienceParticle Filtering (PF) is a model-based, filtering technique, which has drawn the attention of the Prognostic and Health Management (PHM) community due to its applicability to nonlinear models with non-additive and non-Gaussian noise. When multiple physical models can describe the evolution of the degradation of a component, the PF approach can be based on Multiple Swarms (MS) of particles, each one evolving according to a different model, from which to select the most accurate a posteriori distribution. However, MS are highly computational demanding due to the large number of particles to simulate. In this work, to tackle the problem we have developed a PF approach based on the introduction of an augmented discrete state identifying the physical model describing the component evolution, which allows to detect the occurrence of abnormal conditions and identifying the degradation mechanism causing it. A crack growth degradation problem has been considered to prove the effectiveness of the proposed method in the detection of the crack initiation and the identification of the occurring degradation mechanism. The comparison of the obtained results with that of a literature MS method and of an empirical statistical test has shown that the proposed method provides both an early detection of the crack initiation, and an accurate and early identification of the degradation mechanism. A reduction of the computational cost is also achieved.
Real-time forecasting of pesticide concentrations in soil
peer-reviewedForecasting pesticide residues in soils in real time is essential for agronomic purposes, to manage phytotoxic effects, and in catchments to manage surface and ground water quality. This has not been possible in the past due to both modelling and measurement constraints. Here, the analytical transient probability distribution (pdf) of pesticide concentrations is derived. The pdf results from the random ways in which rain events occur after pesticide application. First-order degradation kinetics and linear equilibrium sorption are assumed. The analytical pdfs allow understanding of the relative contributions that climate (mean storm depth and mean rainfall event frequency) and chemical (sorption and degradation) properties have on the variability of soil concentrations into the future. We demonstrated the two uncertain reaction parameters can be constrained using Bayesian methods. An approach to a Bayesian informed forecast is then presented. With the use of new rapid tests capable of providing quantitative measurements of soil concentrations in the field, real-time forecasting of future pesticide concentrations now looks possible for the first time. Such an approach offers new means to manage crops, soils and water quality, and may be extended to other classes of pesticides for ecological risk assessment purposes
A Bayesian approach to robust identification: application to fault detection
In the Control Engineering field, the so-called Robust Identification techniques deal with the problem of obtaining not only a nominal model of the plant, but also an estimate of the uncertainty associated to the nominal model. Such model of uncertainty is typically characterized as a region in the parameter space or as an uncertainty band around the frequency response of the nominal model.
Uncertainty models have been widely used in the design of robust controllers and, recently, their use in model-based fault detection procedures is increasing. In this later case, consistency between new measurements and the uncertainty region is checked. When an inconsistency is found, the existence of a fault is decided.
There exist two main approaches to the modeling of model uncertainty: the deterministic/worst case methods and the stochastic/probabilistic methods. At present, there are a number of different methods, e.g., model error modeling, set-membership identification and non-stationary stochastic embedding. In this dissertation we summarize the main procedures and illustrate their results by means of several examples of the literature.
As contribution we propose a Bayesian methodology to solve the robust identification problem. The approach is highly unifying since many robust identification techniques can be interpreted as particular cases of the Bayesian framework. Also, the methodology can deal with non-linear structures such as the ones derived from the use of observers. The obtained Bayesian uncertainty models are used to detect faults in a quadruple-tank process and in a three-bladed wind turbine
Parameter inference for discretely observed stochastic kinetic models using stochastic gradient descent
Abstract Background Stochastic effects can be important for the behavior of processes involving small population numbers, so the study of stochastic models has become an important topic in the burgeoning field of computational systems biology. However analysis techniques for stochastic models have tended to lag behind their deterministic cousins due to the heavier computational demands of the statistical approaches for fitting the models to experimental data. There is a continuing need for more effective and efficient algorithms. In this article we focus on the parameter inference problem for stochastic kinetic models of biochemical reactions given discrete time-course observations of either some or all of the molecular species. Results We propose an algorithm for inference of kinetic rate parameters based upon maximum likelihood using stochastic gradient descent (SGD). We derive a general formula for the gradient of the likelihood function given discrete time-course observations. The formula applies to any explicit functional form of the kinetic rate laws such as mass-action, Michaelis-Menten, etc. Our algorithm estimates the gradient of the likelihood function by reversible jump Markov chain Monte Carlo sampling (RJMCMC), and then gradient descent method is employed to obtain the maximum likelihood estimation of parameter values. Furthermore, we utilize flux balance analysis and show how to automatically construct reversible jump samplers for arbitrary biochemical reaction models. We provide RJMCMC sampling algorithms for both fully observed and partially observed time-course observation data. Our methods are illustrated with two examples: a birth-death model and an auto-regulatory gene network. We find good agreement of the inferred parameters with the actual parameters in both models. Conclusions The SGD method proposed in the paper presents a general framework of inferring parameters for stochastic kinetic models. The method is computationally efficient and is effective for both partially and fully observed systems. Automatic construction of reversible jump samplers and general formulation of the likelihood gradient function makes our method applicable to a wide range of stochastic models. Furthermore our derivations can be useful for other purposes such as using the gradient information for parametric sensitivity analysis or using the reversible jump samplers for full Bayesian inference. The software implementing the algorithms is publicly available at http://cbcl.ics.uci.edu/sg
Parametric Sensitivity Analysis for Biochemical Reaction Networks based on Pathwise Information Theory
Stochastic modeling and simulation provide powerful predictive methods for
the intrinsic understanding of fundamental mechanisms in complex biochemical
networks. Typically, such mathematical models involve networks of coupled jump
stochastic processes with a large number of parameters that need to be suitably
calibrated against experimental data. In this direction, the parameter
sensitivity analysis of reaction networks is an essential mathematical and
computational tool, yielding information regarding the robustness and the
identifiability of model parameters. However, existing sensitivity analysis
approaches such as variants of the finite difference method can have an
overwhelming computational cost in models with a high-dimensional parameter
space. We develop a sensitivity analysis methodology suitable for complex
stochastic reaction networks with a large number of parameters. The proposed
approach is based on Information Theory methods and relies on the
quantification of information loss due to parameter perturbations between
time-series distributions. For this reason, we need to work on path-space,
i.e., the set consisting of all stochastic trajectories, hence the proposed
approach is referred to as "pathwise". The pathwise sensitivity analysis method
is realized by employing the rigorously-derived Relative Entropy Rate (RER),
which is directly computable from the propensity functions. A key aspect of the
method is that an associated pathwise Fisher Information Matrix (FIM) is
defined, which in turn constitutes a gradient-free approach to quantifying
parameter sensitivities. The structure of the FIM turns out to be
block-diagonal, revealing hidden parameter dependencies and sensitivities in
reaction networks
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