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Significance of Greenhouse Gas Measurement for Carbon Management Technologies
Published in Subhas K Sikdar, Frank Princiotta, Advances in Carbon Management Technologies, 2020
Bayesian inference methods are applied to estimation of GHG fluxes and their dynamics across global, continental, regional, or urban modeling domains. The observed quantity is the GHG concentration. Statistical optimization methods are based on Bayes’ concept that the probability associated with an event, or initial data set, can be updated by additional information. Stated more formally, Bayesian inference is a method of statistical inference based upon Bayes’ theorem,8 where it is assumed that the probability for a hypothesis can be modified or updated as more evidence or information becomes available. In the case of evidence-based GHG flux estimation, an initial estimate, termed a prior, is updated by additional observations in order to inform or refine the prior estimate with more information and construct a posterior flux estimate. In estimating urban source and sink fluxes, the hypothesis is based upon emissions inventory data for the region of interest. In some cases, an analysis may begin with a so-called “flat prior” that might be derived from a whole-city emission estimate which is then sub-divided equally among the surface grid cells of the NWP applied domain, as illustrated in Figure 4.
Bayesian Inference on General-Order Statistic Models
Published in Mangey Ram, Modeling and Simulation Based Analysis in Reliability Engineering, 2018
Aniket Jain, Biswabrata Pradhan, Debasis Kundu
The choice of prior plays an important role in any Bayesian inference problem. An independent Poisson prior has been assigned to N and for three different lifetime distributions, quite flexible priors to the unknown parameters of the distribution of T have been assumed. Based on the prior distributions and data, posterior distributions are obtained. All the estimates are obtained under the squared error loss (SEL) function. The Bayes estimators under the SEL function cannot be obtained explicitly. Hence, Markov Chain Monte Carlo (MCMC) technique has been used to compute the Bayes estimates and the associated credible intervals. Extensive simulation experiments have been performed to assess the effectiveness of the proposed methods. The performances are quite satisfactory. The analysis of one real data set has been presented to illustrate the proposed methods.
Toward the integration of uncertainty and probabilities in spatial multi-criteria risk analysis
Published in Stein Haugen, Anne Barros, Coen van Gulijk, Trond Kongsvik, Jan Erik Vinnem, Safety and Reliability – Safe Societies in a Changing World, 2018
Bayesian inference is an alternative to the classical statistical inference. In the latter, also known as frequentist inference, only repeatable events have probabilities, while in Bayesian inference probability describes both epistemic and aleatory uncertainty (e.g. O’Hagan, 2003). Indeed, Bayesian analysis combines data representing the entire like-lihood function with prior knowledge about the parameters, which may come from other data sets or the modeler’s experience and physical intuition (e.g. Reis Jr and Stedinger, 2005). The a priori distribution describes what is known before observing any data, while the likelihood reflects the information about the parameters contained in the data. Parameters estimation is made through the posterior distribution, which is computed using Bayes’ Theorem (e.g. O’Hagan, 2003): () p(y|θ)∝L(y;θ)p(θ)
Combination four different ensemble algorithms with the generalized linear model (GLM) for predicting forest fire susceptibility
Published in Geomatics, Natural Hazards and Risk, 2023
Saeid Janizadeh, Sayed M. Bateni, Changhyun Jun, Jungho Im, Hao-Thing Pai, Shahab S. Band, Amir Mosavi
Bayesian inference is a probabilistic approach, which is built on the concept that for each quantity, there is a probability distribution that can be optimized for new data. Bayesian networks (also called belief networks) are probabilistic models that signify information in an unspecified context. Each node in the diagram shows a random variable, and the branches indicate possible dependencies between them (Tran et al. 2020). These conditional dependencies are usually assessed using probabilistic and statistical approaches. Bayesian networks merge statistics, computer science, principles of graph theory, and probability theory. They efficiently represent and calculate probability distributions in a series of random variables (Band et al. 2020). The use of Bayesian methods for the proper modeling and determination of optimal parameters has been undertaken in recent years (Ahmadi et al. 2020). In this study, the Bayesian method was combined with cumulative linear regression to estimate the risk of forest fires.
Bayesian updating methodology for probabilistic model of bridge traffic loads using in-service data of traffic environment
Published in Structure and Infrastructure Engineering, 2022
Thus, this study aims to develop a Bayesian inference methodology to directly update the parameters of the probabilistic model of bridge traffic loads based on new observations regarding the traffic environment. Bayesian inference, a method of statistical inference to quantify the uncertainty of parameters, obtains the posterior probability distribution by combining the existing information represented by a prior model with newly measured data (Ang & Tang, 2007; Box & Tiao, 2011). Bayesian based methods have been widely used to solve a variety of problems in structural engineering (Beck, 2010; Green, Cross, & Worden, 2015; Huang, Beck, & Li, 2017; Leahy et al., 2015; Lee & Song, 2016; Yu & Cai, 2019; Yu et al., 2019). This method enables us to continuously update traffic load effects on bridges by estimating the parameters of the posterior distribution affected by the changes in the surroundings based on WIM data. Besides, it is often impossible to obtain sufficient WIM data in estimating traffic loads on bridges because of challenges in continuous WIM data acquisition. In such cases, by using the indirect information about the traffic around the bridge and the generic probabilistic model of bridge traffic loads as a prior model, Bayesian updating can estimate the traffic load effects on that particular bridge more reasonably and accurately.
Dynamic reliability analysis for residual life assessment of corroded subsea pipelines
Published in Ships and Offshore Structures, 2021
Reza Aulia, Henry Tan, Srinivas Sriramula
Bayesian network modelling is a probabilistic approach representing the relationships between causes and consequences, and their conditional interdependencies through a directed acyclic graph. Whereas Bayesian inference is a statistical method in which Bayes’ theorem is utilised to update the probability for a hypothesis as more evidence or observed data information becomes available. This method is very effective for modelling situations where some information is uncertain or partially unavailable and incoming data is already known. Figure 1 shows a simple Bayesian network consisting of three nodes, i.e. H2S concentration and CO2 partial pressure as the parent nodes and internal corrosion causes as the child node. Each node represents a probability distribution, which may in principle be continuous or discrete, and captures the probability distribution conditional on its direct predecessors (parents), also known as conditional probability table (CPT). The CPT is defined as a set of discrete (not independent) random variables to demonstrate marginal probabilities of each variable with respect to the others. According to Shabarchin and Tesfamariam (2016), the conditional probabilities can be quantified by using information obtained from the field data, expert opinion, analytical model or a combination of all.