Post-earthquake assessment of bridges using Bayesian networks with continuous variables

2014 ◽  
pp. 3185-3191
Author(s):  
Y Yue ◽  
D Zonta ◽  
M Pozzi
Keyword(s):  
Bayesian Networks ◽  
Continuous Variables ◽  
Earthquake Assessment

scholarly journals Gaussian Mixture Reduction for Time-Constrained Approximate Inference in Hybrid Bayesian Networks

2019 ◽  
Vol 9 (10) ◽  
pp. 2055 ◽  
Author(s):  
Cheol Young Park ◽  
Kathryn Blackmond Laskey ◽  
Paulo C. G. Costa ◽  
Shou Matsumoto
Keyword(s):  
Bayesian Networks ◽  
Message Passing ◽  
Random Variables ◽  
Computation Time ◽  
Gaussian Mixture ◽  
Image Understanding ◽  
Approximate Inference ◽  
Continuous Variables ◽  
Hybrid Bayesian Networks ◽  
Trade Off

Hybrid Bayesian Networks (HBNs), which contain both discrete and continuous variables, arise naturally in many application areas (e.g., image understanding, data fusion, medical diagnosis, fraud detection). This paper concerns inference in an important subclass of HBNs, the conditional Gaussian (CG) networks, in which all continuous random variables have Gaussian distributions and all children of continuous random variables must be continuous. Inference in CG networks can be NP-hard even for special-case structures, such as poly-trees, where inference in discrete Bayesian networks can be performed in polynomial time. Therefore, approximate inference is required. In approximate inference, it is often necessary to trade off accuracy against solution time. This paper presents an extension to the Hybrid Message Passing inference algorithm for general CG networks and an algorithm for optimizing its accuracy given a bound on computation time. The extended algorithm uses Gaussian mixture reduction to prevent an exponential increase in the number of Gaussian mixture components. The trade-off algorithm performs pre-processing to find optimal run-time settings for the extended algorithm. Experimental results for four CG networks compare performance of the extended algorithm with existing algorithms and show the optimal settings for these CG networks.

scholarly journals The application of Bayesian networks in natural hazard analyses

2013 ◽  
Vol 1 (5) ◽  
pp. 5805-5854
Author(s):  
K. Vogel ◽  
C. Riggelsen ◽  
O. Korup ◽  
F. Scherbaum
Keyword(s):  
Bayesian Networks ◽  
Bayesian Network ◽  
Domain Knowledge ◽  
Natural Hazard ◽  
Hazard Analysis ◽  
Flood Damage ◽  
Continuous Variables ◽  
Real World Data ◽  
Ground Motion Model ◽  
Hazard Assessments

Abstract. In natural hazards we face several uncertainties due to our lack of knowledge and/or the intrinsic randomness of the underlying natural processes. Nevertheless, deterministic analysis approaches are still widely used in natural hazard assessments, with the pitfall of underestimating the hazard with potentially disastrous consequences. In this paper we show that the Bayesian network approach offers a flexible framework for capturing and expressing a broad range of different uncertainties as those encountered in natural hazard assessments. Although well studied in theory, the application of Bayesian networks on real-world data is often not straightforward and requires specific tailoring and adaption of existing algorithms. We demonstrate by way of three case studies (a ground motion model for a seismic hazard analysis, a flood damage assessment, and a landslide susceptibility study) the applicability of Bayesian networks across different domains showcasing various properties and benefits of the Bayesian network framework. We offer suggestions as how to tackle practical problems arising along the way, mainly concentrating on the handling of continuous variables, missing observations, and the interaction of both. We stress that our networks are completely data-driven, although prior domain knowledge can be included if desired.

AN INTRODUCTION TO HIDDEN MARKOV MODELS AND BAYESIAN NETWORKS

2001 ◽  
Vol 15 (01) ◽  
pp. 9-42 ◽  
Author(s):  
ZOUBIN GHAHRAMANI
Keyword(s):  
Bayesian Networks ◽  
Hidden Markov Models ◽  
Markov Models ◽  
Recent Literature ◽  
Hidden Markov ◽  
Continuous Variables ◽  
State Variables ◽  
Exact Inference ◽  
Markov Chain Sampling ◽  
Inference Algorithms

We provide a tutorial on learning and inference in hidden Markov models in the context of the recent literature on Bayesian networks. This perspective makes it possible to consider novel generalizations of hidden Markov models with multiple hidden state variables, multiscale representations, and mixed discrete and continuous variables. Although exact inference in these generalizations is usually intractable, one can use approximate inference algorithms such as Markov chain sampling and variational methods. We describe how such methods are applied to these generalized hidden Markov models. We conclude this review with a discussion of Bayesian methods for model selection in generalized HMMs.

Mixed Bayesian Networks: A Mixture of Gaussian Distributions

1994 ◽  
Vol 33 (05) ◽  
pp. 535-542 ◽  
Author(s):  
J. P. Chevrolat ◽  
F. Rutigliano ◽  
J. L. Golmard
Keyword(s):  
Bayesian Networks ◽  
Probabilistic Models ◽  
Graphical Representation ◽  
Expectation Maximization Algorithm ◽  
Estimation Algorithm ◽  
Continuous Variables ◽  
Gaussian Distributions ◽  
Stochastic Version ◽  
Comprehensive Method ◽  
Mixture Of Gaussian

Abstract:Mixed Bayesian networks are probabilistic models associated with a graphical representation, where the graph is directed and the random variables are discrete or continuous. We propose a comprehensive method for estimating the density functions of continuous variables, using a graph structure and a set of samples. The principle of the method is to learn the shape of densities from a sample of continuous variables. The densities are approximated by a mixture of Gaussian distributions. The estimation algorithm is a stochastic version of the Expectation Maximization algorithm (Stochastic EM algorithm). The inference algorithm corresponding to our model is a variant of junction three method, adapted to our specific case. The approach is illustrated by a simulated example from the domain of pharmacokinetics. Tests show that the true distributions seem sufficiently fitted for practical application.

scholarly journals Learning the Structure of Bayesian Networks: A Quantitative Assessment of the Effect of Different Algorithmic Schemes

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Stefano Beretta ◽  
Mauro Castelli ◽  
Ivo Gonçalves ◽  
Roberto Henriques ◽  
Daniele Ramazzotti
Keyword(s):  
Bayesian Networks ◽  
Quantitative Assessment ◽  
State Of The Art ◽  
Simulated Data ◽  
Detailed Comparison ◽  
Search Space ◽  
Continuous Variables ◽  
Challenging Tasks ◽  
The One ◽  
Algorithmic Approaches

One of the most challenging tasks when adopting Bayesian networks (BNs) is the one of learning their structure from data. This task is complicated by the huge search space of possible solutions and by the fact that the problem is NP-hard. Hence, a full enumeration of all the possible solutions is not always feasible and approximations are often required. However, to the best of our knowledge, a quantitative analysis of the performance and characteristics of the different heuristics to solve this problem has never been done before. For this reason, in this work, we provide a detailed comparison of many different state-of-the-art methods for structural learning on simulated data considering both BNs with discrete and continuous variables and with different rates of noise in the data. In particular, we investigate the performance of different widespread scores and algorithmic approaches proposed for the inference and the statistical pitfalls within them.

scholarly journals Bayesian network learning for natural hazard analyses

2014 ◽  
Vol 14 (9) ◽  
pp. 2605-2626 ◽  
Author(s):  
K. Vogel ◽  
C. Riggelsen ◽  
O. Korup ◽  
F. Scherbaum
Keyword(s):  
Bayesian Networks ◽  
Bayesian Network ◽  
Measurement Errors ◽  
Natural Hazard ◽  
Regional Scale ◽  
Flood Damage ◽  
Continuous Variables ◽  
Real World Data ◽  
Network Learning ◽  
Hazard Assessments

Abstract. Modern natural hazards research requires dealing with several uncertainties that arise from limited process knowledge, measurement errors, censored and incomplete observations, and the intrinsic randomness of the governing processes. Nevertheless, deterministic analyses are still widely used in quantitative hazard assessments despite the pitfall of misestimating the hazard and any ensuing risks. In this paper we show that Bayesian networks offer a flexible framework for capturing and expressing a broad range of uncertainties encountered in natural hazard assessments. Although Bayesian networks are well studied in theory, their application to real-world data is far from straightforward, and requires specific tailoring and adaptation of existing algorithms. We offer suggestions as how to tackle frequently arising problems in this context and mainly concentrate on the handling of continuous variables, incomplete data sets, and the interaction of both. By way of three case studies from earthquake, flood, and landslide research, we demonstrate the method of data-driven Bayesian network learning, and showcase the flexibility, applicability, and benefits of this approach. Our results offer fresh and partly counterintuitive insights into well-studied multivariate problems of earthquake-induced ground motion prediction, accurate flood damage quantification, and spatially explicit landslide prediction at the regional scale. In particular, we highlight how Bayesian networks help to express information flow and independence assumptions between candidate predictors. Such knowledge is pivotal in providing scientists and decision makers with well-informed strategies for selecting adequate predictor variables for quantitative natural hazard assessments.

Sign in / Sign up

Export Citation Format

Share Document