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bayesian inference for controlled branching processes through MCMC and ABC methodologies

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS 2013年第2期107卷 459-473页

作者： Gonzalez, Miguel Gutierrez, Cristina Martinez, Rodrigo del Puerto, Ines M. Univ Extremadura Dept Math Badajoz Spain

The controlled branching process (CBP) is a generalization of the classical Bienaym,-Galton-Watson branching process, and, in the terminology of population dynamics, is used to describe the evolution of populations in which a control of the population size at each generation is needed. In this work, we deal with the problem of estimating the offspring distribution and its main parameters for a CBP with a deterministic control function assuming that the only observable data are the total number of individuals in each generation. We tackle the problem from a bayesian perspective in a non parametric context. We consider a Markov chain Monte Carlo (MCMC) method, in particular the Gibbs sampler and approximate bayesian computation (ABC) methodology. The first is a data imputation method and the second relies on numerical simulations. Through a simulated experiment we evaluate the accuracy of the MCMC and ABC techniques and compare their performances.

关键词： Controlled branching process bayesian inference Gibbs sampler Approximate bayesian computation Non-parametric

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bayesian inference of constitutive model parameters from uncertain uniaxial experiments on murine tendons

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JOURNAL OF THE MECHANICAL BEHAVIOR OF BIOMEDICAL MATERIALS 2019年 96卷 285-300页

作者： Akintunde, Akinjide R. Miller, Kristin S. Schiavazzi, Daniele E. Tulane Univ Dept Biomed Engn New Orleans LA 70118 USA Univ Notre Dame Dept Appl & Computat Math & Stat Notre Dame IN 46556 USA

Constitutive models for biological tissue are typically formulated as a mixture of constituents and the overall response is then assembled by superposition or compatibility. This ensures the stress response of the biological tissue to be in the range of a given constitutive relationship, guaranteeing that at least one parameter combination exists so that an experimental response can be sufficiently well captured. Another, perhaps more challenging, problem is to use constitutive models as a proxy to infer the structure/function of a biological tissue from experiments. In other words, we determine the optimal set of parameters by solving an inverse problem and use these parameters to infer the integrity of the tissue constituents. In previous studies, we focused on the mechanical stress-stretch response of the murine patellar tendon at various age and healing timepoints and solved the inverse problem using three constitutive models, i.e., the Freed-Rajagopal, Gasser-Ogden-Holzapfel and Shearer in order of increasing microstructural detail. Herein, we extend this work by adopting a bayesian perspective on parameter estimation and implement the constitutive relations in the tulip library for uncertainty analysis, critically analyzing parameter marginals, correlations, identifiability and sensitivity. Our results show the importance of investigating the variability of parameter estimates and that results from optimization may be misleading, particularly for models with many parameters inferred from limited experimental evidence. In our study, we show that different age and healing conditions do not correspond to statistically significant separation among the Gasser-Ogden-Holzapfel and Shearer model parameters, while the phenomenological Freed-Rajagopal model is instead characterized by better indentifiability and parameter learning. Use of the complete experimental observations rather than averaged stress-stretch responses appears to positively constrain inference and re

关键词： Uncertainty quantification bayesian inference Constitutive models for murine patellar tendons Parameter sensitivity and identifiability

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bayesian inference as a tool for improving estimates of effective elastic parameters of wood

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COMPUTERS & STRUCTURES 2019年 218卷 94-107页

作者： Sejnoha, Michal Janda, Tomas Vorel, Jan Kucikova, Lucie Padevet, Pavel Hrbek, Vladimir Czech Tech Univ Fac Civil Engn Dept Mech Thakurova 7 Prague 16629 6 Czech Republic

A simple approach to the identification of geometrical and material uncertainties of wood is presented. This stochastic mechanics problem combines classical micromechanics, computational homogenization and experimental measurements with bayesian inference to estimate the model parameters including the characteristics of errors in macroscopic elastic properties of wood caused by randomness of microstructural details on the one hand and the experimental errors on the other hand. The former source of uncertainty includes, for example, variability in microfibril angle and growth ring density. Even such limiting consideration of random input illustrates the need for combined computational and experimental approach in a reliable prediction of the desired material properties. Tying the two approaches in the framework of bayesian statistical method proves useful when addressing their limitations and as such giving better notion on the credibility of the prediction. This is demonstrated here on one particular example of spruce wood. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Spruce wood bayesian inference Homogenization Nanoindentation Digital image correlation Microfibril angle

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bayesian inference of multi-valued information symbol by a CDMA demodulator using multi-valued spreading code sequence

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PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 2006年第2期361卷 543-568页

作者： Katayama, K Muroran Inst Technol Fac Engn Dept Comp Sci & Syst Engn Muroran Hokkaido 0508585 Japan

We make an estimation of a maximizer of posterior marginals (MPM) as for a multi-valued information symbol by a code-division Multiple access (CDMA) demodulator using a multivalued spreading code sequence within a framework of a bayesian inference. We calculate an estimation error of the CDMA demodulator and the information capacity of the CDMA channel by using a replica method. We clarify that because of redundancy for degree of the multi-values, the multi-valued information symbol and the multi-valued spreading code sequence are useful as for improvement of information transmission by comparing performance for various degrees of the multi-values. (c) 2005 Elsevier B.V. All rights reserved.

关键词： CDMA demodulator multi-valued information symbol multi-valued spreading code sequence bayesian inference replica method

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bayesian inference in Action in EMC-Fundamentals and Applications

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IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY 2017年第4期59卷 1114-1124页

作者： Carobbi, Carlo F. M. Univ Florence Dept Informat Engn I-50139 Florence Italy

The scope of this study is to introduce the reader to bayesian inference applied to the evaluation of measurement uncertainty and conformity assessment in the field of radiofrequency (RF) and electromagnetic compatibility (EMC) measurements and testing. The advantages stemming from the use of bayesian inference with respect to the consolidated theoretical framework provided by the Guide to the Expression of Uncertainty in Measurement (widely known as the "GUM") are emphasized, also in order to appreciate the reasons behind the ongoing revision of the same GUM. An important result of bayesian inference has been already implemented in two guides to the evaluation of EMCmeasurement uncertainty, namely, the IEC TR 61000-1-6 and the standard ANSI C63.23. Further, it is here shown that through bayesian inference mathematical tools can be derived for the assessment of conformity of distribution of values, such as the electric field over a surface, taking into proper account both the intrinsic variability among the values of the distribution and the measurement uncertainty of each value. The theoretical background is first introduced and then two applications of bayesian inference to measurement uncertainty and conformity assessment in the field of RF and EMC measurements and testing are thoroughly described.

关键词： bayesian inference conformity assessment electromagnetic compatibility (EMC) evaluation of measurement uncertainty radiofrequency (RF) measurements

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bayesian inference in the space of topological maps

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IEEE TRANSACTIONS ON ROBOTICS 2006年第1期22卷 92-107页

作者： Ranganathan, A Menegatti, E Dellaert, F Georgia Inst Technol GVU Ctr Atlanta GA 30332 USA Univ Padua Dept Informat Engn Intelligent Autonomous Syst Lab I-35131 Padua Italy

While probabilistic techniques have previously been investigated extensively for performing inference over the space of metric maps, no corresponding general-purpose methods exist for topological maps. We present the concept of probabilistic topological maps (PTMs), a sample-based representation that approximates the posterior distribution over topologies, given available sensor measurements. We show that the space of topologies is equivalent to the intractably large space of set partitions on the set of available measurements. The combinatorial nature of the problem is overcome by computing an approximate, sample-based representation of the posterior. The PTM is obtained by performing bayesian inference over the space of all possible topologies, and provides a systematic solution to the problem of perceptual aliasing in the domain of topological mapping. In this paper, we describe a general framework for modeling measurements, and the use of a Markov-chain Monte Carlo algorithm that uses specific instances of these models for odometry and appearance measurements to estimate the posterior distribution. We present experimental results that validate our technique and generate good maps when using odometry and appearance, derived from panoramic images, as sensor measurements.

关键词： bayesian inference Markov-chain Monte Carlo (MCMC) mobile robots perceptual aliasing probability distributions sample-based representations topological maps

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bayesian inference for thermal response test parameter estimation and uncertainty assessment

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APPLIED ENERGY 2018年 209卷 306-321页

作者： Choi, Wonjun Kikumoto, Hideki Choudhary, Ruchi Ooka, Ryozo Univ Tokyo Inst Ind Sci Meguro Ku 4-6-1 Komaba Tokyo 1538505 Japan Univ Cambridge Dept Engn Energy Efficient Cities Initiat Trumpington St Cambridge CE2 1PZ England

The effective ground thermal conductivity and borehole thermal resistance constitute information needed to design a ground-source heat pump (GSHP). In situ thermal response tests (TRTs) are considered reliable to obtain these parameters, but interpreting TRT data by a deterministic approach may result in significant uncertainties in the estimates. In light of the impact of the two parameters on GSHP applications, the quantification of uncertainties is necessary. For this purpose, in this study, we develop a stochastic method based on bayesian inference to estimate the two parameters and associated uncertainties. Numerically generated noisy TRT data and reference sandbox TRT data were used to verify the proposed method. The posterior probability density functions obtained were used to extract the point estimates of the parameters and their credible intervals. Following its verification, the proposed method was applied to in situ TRT data, and the relationship between test time and estimation accuracy was examined. The minimum TRT time of 36 h recommended by ASHRAE produced an uncertainty of similar to +/- 21% for effective thermal conductivity. However, the uncertainty of estimation decreased exponentially with increasing TRT time, and was +/- 8.3% after a TRT time of 54 h, lower than the generally acceptable range of uncertainty of +/- 10%. Based on the obtained results, a minimum TRT time of 50 h is suggested and that of 72 h is expected to produce sufficiently accurate estimates for most cases.

关键词： Ground-source heat pump (GSHP) Thermal response test (TRT) Minimum TRT time bayesian inference Uncertainty assessment Parameter estimation

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bayesian inference-Based Behavioral Modeling Technique for GaN HEMTs

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES 2019年第6期67卷 2291-2301页

作者： Cai, Jialin King, Justin B. Su, Jiangtao Yu, Chao Chen, Shichang Sun, Lingling Wang, Haiqi Liu, Jun Hangzhou Dianzi Univ Coll Elect & Informat Minist Educ Key Lab RF Circuit & Syst Hangzhou 310018 Peoples R China Trinity Coll Dublin RF Grp Dublin D02 PN40 Ireland Southeast Univ Sch Informat Sci & Engn State Key Lab Millimeter Waves Nanjing Jiangsu Peoples R China Environm Protect Inst Hangzhou 311251 Zhejiang Peoples R China

A new, frequency-domain, behavioral modeling methodology for gallium nitride (GaN) high-electron-mobility transistors (HEMTs), based on the bayesian inference theory, is presented in this paper. Several different probability distribution (kernel) functions are examined for the bayesian-based modeling architecture, with the optimal kernel function identified through experimental testing. These results are compared to an alternative approach based on the artificial neural networks (ANNs), with the data showing that the proposed approach demonstrates improved accuracy, while at the same time, alleviating the well-known ANN overfitting issue. Model verification is performed at the fundamental and harmonic frequencies using the identified optimal kernel, through comparisons with simulated data from a reference nonlinear circuit model, and with experimental data from separate 2- and 10-W GaN HEMT devices, over a wide range of load conditions. The models can predict accurately the optimal area of the fundamental output power on the Smith chart and the area of optimal power efficiency. Furthermore, the ability of the model to interpolate across input power levels and input frequencies is also tested, with excellent fidelity to the simulated and measured data obtained.

关键词： bayesian inference black box model gallium nitride (GaN) high-electron-mobility transistor (HEMT) nonlinear behavioral modeling power transistor

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bayesian inference and uncertainty quantification for hydrogen-enriched and lean-premixed combustion systems

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INTERNATIONAL JOURNAL OF HYDROGEN ENERGY 2021年第46期46卷 23927-23942页

作者： Yousefian, Sajjad Bourque, Gilles Monaghan, Rory F. D. Natl Univ Ireland Galway Sch Engn Galway Ireland Natl Univ Ireland Galway Combust Chem Ctr Galway Ireland SFI Res Ctr Energy Climate & Marine MaREI Galway Ireland Siemens Energy Canada Ltd 9545 Cote Liesse Rd Montreal PQ Canada McGill Univ Dept Mech Engn Montreal PQ Canada

Development of probabilistic modelling tools to perform bayesian inference and uncertainty quantification (UQ) is a challenging task for practical hydrogen-enriched and low emission combustion systems due to the need to take into account simultaneously simulated fluid dynamics and detailed combustion chemistry. A large number of evaluations is required to calibrate models and estimate parameters using experimental data within the framework of bayesian inference. This task is computationally prohibitive in high-fidelity and deterministic approaches such as large eddy simulation (LES) to design and optimize combustion systems. Therefore, there is a need to develop methods that: (a) are suitable for bayesian inference studies and (b) characterize a range of solutions based on the uncertainty of modelling parameters and input conditions. This paper aims to develop a computationally-efficient toolchain to address these issues for probabilistic modelling of NOx emission in hydrogen-enriched and lean-premixed combustion systems. A novel method is implemented into the toolchain using a chemical reactor network (CRN) model, non-intrusive polynomial chaos expansion based on the point collocation method (NIPCE-PCM), and the Markov Chain Monte Carlo (MCMC) method. First, a CRN model is generated for a combustion system burning hydrogen-enriched methane/air mixtures at high-pressure lean-premixed conditions to compute NOx emission. A set of metamodels is then developed using NIPCE-PCM as a computationally efficient alternative to the physics based CRN model. These surrogate models and experimental data are then implemented in the MCMC method to perform a two-step bayesian calibration to maximize the agreement between model predictions and measurements. The average standard deviations for the prediction of exit temperature and NOx emission are reduced by almost 90% using this method. The calibrated model then used with confidence for global sensitivity and reli-ability analysis s

关键词： Probabilistic modelling Uncertainty quantification bayesian inference Combustion systems Chemical reactor network Markov Chain Monte Carlo

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bayesian inference With Nonlinear Generative Models: Comments on Secure Learning

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IEEE TRANSACTIONS ON INFORMATION THEORY 2023年第12期69卷 7998-8028页

作者： Bereyhi, Ali Loureiro, Bruno Krzakala, Florent Mueller, Ralf R. Schulz-Baldes, Hermann Friedrich Alexander Univ FAU Erlangen Nurnberg Inst Digital Commun IDC D-91058 Erlangen Germany Univ Toronto Wireless Comp Lab WCL Toronto ON M5S 2E4 Canada Ecole Polytech Fed Lausanne EPFL Informat Learning & Phys Lab IdePHICS CH-1015 Lausanne Switzerland Ecole Normale Super Ctr Data Sci F-75230 Paris France Friedrich Alexander Univ FAU Erlangen Nurnberg Dept Math D-91058 Erlangen Germany

Unlike the classical linear model, nonlinear generative models have been addressed sparsely in the literature of statistical learning. This work aims to shed light on these models and their secrecy potential. To this end, we invoke the replica method to derive the asymptotic normalized cross entropy in an inverse probability problem whose generative model is described by a Gaussian random field with a generic covariance function. Our derivations further demonstrate the asymptotic statistical decoupling of the bayesian estimator and specify the decoupled setting for a given nonlinear model. The replica solution depicts that strictly nonlinear models establish an all-or-nothing phase transition: there exists a critical load at which the optimal bayesian inference changes from perfect to an uncorrelated learning. Based on this finding, we design a new secure coding scheme which achieves the secrecy capacity of the wiretap channel. This interesting result implies that strictly nonlinear generative models are perfectly secured without any secure coding. We justify this latter statement through the analysis of an illustrative model for perfectly secure and reliable inference.

关键词： Bayes methods Nonlinear optics Information theory Glass Encoding Statistical learning Load modeling Nonlinear generative models bayesian inference Gaussian random fields information-theoretically secure learning replica method decoupling principle

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