Implicitly localized MCMC sampler to cope with nonlocal/nonlinear data constraints in large-size inverse problems

2020 ◽  
Author(s):  
Jean-Michel Brankart
Keyword(s):  
Probability Distribution ◽  
Inverse Problems ◽  
Large Scale ◽  
Prior Probability ◽  
Practical Applications ◽  
Posterior Probability Distribution ◽  
Prior Probability Distribution ◽  
Large Size ◽  
Non Gaussian ◽  
Nonlocal Nonlinear

<p>Many practical applications involve the resolution of large-size inverse problems, without providing more than a moderate-size sample to describe the prior probability distribution. In this situation, additional information must be supplied to augment the effective dimension of the available sample, for instance using a covariance localization approach. In this study, it is suggested that covariance localization can be efficiently applied to an approximate variant of the Metropolis/Hastings algorithm, by modulating the ensemble members by the large-scale patterns of other members. Modulation is used to design a (global) proposal probability distribution (i) that can be sampled at a very low cost, (ii) that automatically accounts for a localized prior covariance, and (iii) that leads to an efficient sampler for the augmented prior probability distribution or for the posterior probability distribution. The resulting algorithm is applied to an academic example, illustrating (i) the effectiveness of covariance localization, (ii) the ability of the method to deal with nonlocal/nonlinear observation operators and non-Gaussian observation errors, (iii) the reliability, resolution and optimality of the updated ensemble, using probabilistic scores appropriate to a non-Gaussian posterior distribution, and (iv) the scalability of the algorithm as a function of the size of the problem. The codes are openly available from github.com/brankart/ensdam.</p>

scholarly journals Bayesian estimation of the seroprevalence of antibodies to SARS-CoV-2

JAMIA Open ◽  
2020 ◽  
Author(s):  
Qunfeng Dong ◽  
Xiang Gao
Keyword(s):  
Probability Distribution ◽  
Large Scale ◽  
Prior Probability ◽  
Probability Distributions ◽  
Single Point ◽  
Point Estimates ◽  
Specificity And Sensitivity ◽  
Large Scale Dataset ◽  
The Us ◽  
Antibody Tests

Abstract Accurate estimations of the seroprevalence of antibodies to severe acute respiratory syndrome coronavirus 2 need to properly consider the specificity and sensitivity of the antibody tests. In addition, prior knowledge of the extent of viral infection in a population may also be important for adjusting the estimation of seroprevalence. For this purpose, we have developed a Bayesian approach that can incorporate the variabilities of specificity and sensitivity of the antibody tests, as well as the prior probability distribution of seroprevalence. We have demonstrated the utility of our approach by applying it to a recently published large-scale dataset from the US CDC, with our results providing entire probability distributions of seroprevalence instead of single-point estimates. Our Bayesian code is freely available at https://github.com/qunfengdong/AntibodyTest.

scholarly journals A Bayesian Inference Method Using Monte Carlo Sampling for Estimating the Number of Communities in Bipartite Networks

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Guo-Zheng Wang ◽  
Li Xiong ◽  
Hu-Chen Liu
Keyword(s):  
Monte Carlo ◽  
Bayesian Inference ◽  
Probability Distribution ◽  
Community Detection ◽  
Degree Distribution ◽  
Prior Probability ◽  
Bipartite Networks ◽  
Inference Method ◽  
Prior Probability Distribution ◽  
Bayesian Inference Method

Community detection is an important analysis task for complex networks, including bipartite networks, which consist of nodes of two types and edges connecting only nodes of different types. Many community detection methods take the number of communities in the networks as a fixed known quantity; however, it is impossible to give such information in advance in real-world networks. In our paper, we propose a projection-free Bayesian inference method to determine the number of pure-type communities in bipartite networks. This paper makes the following contributions: (1) we present the first principle derivation of a practical method, using the degree-corrected bipartite stochastic block model that is able to deal with networks with broad degree distributions, for estimating the number of pure-type communities of bipartite networks; (2) a prior probability distribution is proposed over the partition of a bipartite network; (3) we design a Monte Carlo algorithm incorporated with our proposed method and prior probability distribution. We give a demonstration of our algorithm on synthetic bipartite networks including an easy case with a homogeneous degree distribution and a difficult case with a heterogeneous degree distribution. The results show that the algorithm gives the correct number of communities of synthetic networks in most cases and outperforms the projection method especially in the networks with heterogeneous degree distributions.

scholarly journals Towards a better understanding of galaxy clusters

2014 ◽  
Vol 10 (S306) ◽  
pp. 273-275
Author(s):  
Pedro T. P. Viana
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Probability Distribution Function ◽  
Large Scale ◽  
Posterior Probability ◽  
Galaxy Cluster ◽  
Relevant Information ◽  
Posterior Probability Distribution ◽  
Cluster Properties ◽  
The Universe

AbstractObservational data on clusters of galaxies holds relevant information that can be used to determine the relative plausibility of different models for the large-scale evolution of the Universe, or estimate the joint posterior probability distribution function of the parameters that pertain to each model. Within the next few years, several surveys of the sky will yield large galaxy cluster catalogues. In order to make use of the vast amount of information they will contain, their selection functions will have to be properly understood. We argue this, as well as the estimation of the full joint posterior probability distribution function of the most relevant cluster properties, can be best achieved in the framework of bayesian statistics.

scholarly journals Bayesian Update with Information Quality under the Framework of Evidence Theory

Entropy ◽  
2018 ◽  
Vol 21 (1) ◽  
pp. 5 ◽  
Author(s):  
Yuting Li ◽  
Fuyuan Xiao
Keyword(s):  
Probability Distribution ◽  
Posterior Probability ◽  
Information Quality ◽  
Prior Probability ◽  
Evidence Theory ◽  
Combination Rule ◽  
Posterior Probability Distribution ◽  
Basic Probability ◽  
Bayesian Update ◽  
Different Sources

Bayesian update is widely used in data fusion. However, the information quality is not taken into consideration in classical Bayesian update method. In this paper, a new Bayesian update with information quality under the framework of evidence theory is proposed. First, the discounting coefficient is determined by information quality. Second, the prior probability distribution is discounted as basic probability assignment. Third, the basic probability assignments from different sources can be combined with Dempster’s combination rule to obtain the fusion result. Finally, with the aid of pignistic probability transformation, the combination result is converted to posterior probability distribution. A numerical example and a real application in target recognition show the efficiency of the proposed method. The proposed method can be seen as the generalized Bayesian update. If the information quality is not considered, the proposed method degenerates to the classical Bayesian update.

Prior probabilities and thermal characteristics of heat engines

Open Physics ◽  
2012 ◽  
Vol 10 (3) ◽  
Author(s):  
Preety Aneja ◽  
Ramandeep Johal
Keyword(s):  
Probability Distribution ◽  
Bayesian Approach ◽  
Prior Information ◽  
Prior Probability ◽  
Thermal Characteristics ◽  
Complete Information ◽  
Otto Cycle ◽  
Prior Probabilities ◽  
Prior Probability Distribution ◽  
Heat Engines

AbstractThe thermal characteristics of a heat cycle are studied from a Bayesian approach. In this approach, we assign a certain prior probability distribution to an uncertain parameter of the system. Based on that prior, we study the expected behaviour of the system and it has been found that even in the absence of complete information, we obtain thermodynamic-like behaviour of the system. Two models of heat cycles, the quantum Otto cycle and the classical Otto cycle are studied from this perspective. Various expressions for thermal efficiences can be obtained with a generalised prior of the form Π(x) ∝ 1/x b. The predicted thermodynamic behaviour suggests a connection between prior information about the system and thermodynamic features of the system.

scholarly journals Multi-View-Based Pose Estimation and Its Applications on Intelligent Manufacturing

Sensors ◽  
2020 ◽  
Vol 20 (18) ◽  
pp. 5072
Author(s):  
Haiwei Yang ◽  
Peilin Jiang ◽  
Fei Wang
Keyword(s):  
Pose Estimation ◽  
Large Scale ◽  
Estimation Method ◽  
Intelligent Manufacturing ◽  
Degree Of Freedom ◽  
Guidance System ◽  
Visual Guidance ◽  
Practical Applications ◽  
Large Size ◽  
Six Degree Of Freedom

Pose estimation is a typical problem in the field of image processing, the purpose of which is to compare or fuse images acquired under different conditions. In recent years, many studies have focused on pose estimation algorithms, but so far there are still many challenges, such as efficiency, complexity and accuracy for various targets and conditions, in the field of algorithm research and practical applications. In this paper, a multi-view-based pose estimation method is proposed. This method can solve the pose estimation problem effectively for large-scale targets and achieve good performance accuracy and stability. Compared with existing methods, this method uses different views (positions and angles), each of which only observes some features of large-size parts, to estimate the six-degree-of-freedom pose of the entire large-size parts. Experimental results demonstrate that the accurate six-degree-of-freedom pose for different targets can be obtained by the proposed method which plays an important role in many actual production lines. What is more, a new visual guidance system, applied into intelligent manufacturing, is presented based on this method. The new visual guidance system has been widely used in automobile manufacturing with high accuracy and efficiency but low cost.

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