Delayed Rejection Adaptive Metropolis Research Articles

Parallel multiple-chain DRAM probabilistic model for ultrasonic pulse velocity of concrete performance in the pipe of arch bridge

The existing models for predicting the compaction state of concrete inside steel tubes based on ultrasonic wave velocity have a major limitation in that they cannot comprehensively consider concrete compressive strength, instar, and various sources of uncertainties, both subjective and objective. To overcome this limitation, the study introduced a probability model for ultrasonic wave velocity in the concrete performance inside arch bridge steel tubes, based on the parallel multiple-chain Delayed Rejection Adaptive Metropolis (DRAM) algorithm. Initially, the study considers the influence of concrete compressive strength and instar, establishing a simplified deterministic model for predicting concrete compactness inside the tubes. Building on this, the study incorporates material stochastic uncertainty and cognitive uncertainty, deriving analytical expressions for a probabilistic prediction model of concrete compactness. Furthermore, using parallel processing alongside the DRAM algorithm, the study explores how the number of parallel chains and the order of acceptance probabilities influence the probabilistic model parameters. The study selected and updated the posterior distribution information of the probabilistic model parameters. Finally, the effectiveness of the model was validated using experimental data. As shown in the analysis, with better prediction accuracy and lower dispersion, the model not only selects the optimal Markov chain iteration path in a short time, but also corrects the parameters affecting the prediction accuracy of the existing model, and also provides a probabilistic method for correcting the confidence intervals of the existing model.

A Comparative Study of Single-Chain and Multi-Chain MCMC Algorithms for Bayesian Model Updating-Based Structural Damage Detection

Bayesian model updating has received considerable attention and has been extensively used in structural damage detection. It provides a rigorous statistical framework for realizing structural system identification and characterizing uncertainties associated with modeling and measurements. The Markov Chain Monte Carlo (MCMC) is a promising tool for inferring the posterior distribution of model parameters to avoid the intractable evaluation of multi-dimensional integration. However, the efficacy of most MCMC techniques suffers from the curse of parameter dimension, which restricts the application of Bayesian model updating to the damage detection of large-scale systems. In addition, there are several MCMC techniques that require users to properly choose application-specific models, based on the understanding of algorithm mechanisms and limitations. As seen in the literature, there is a lack of comprehensive work that investigates the performances of various MCMC algorithms in their application of structural damage detection. In this study, the Differential Evolutionary Adaptive Metropolis (DREAM), a multi-chain MCMC, is explored and adapted to Bayesian model updating. This paper illustrates how DREAM is used for model updating with many uncertainty parameters (i.e., 40 parameters). Furthermore, the study provides a tutorial to users who may be less experienced with Bayesian model updating and MCMC. Two advanced single-chain MCMC algorithms, namely, the Delayed Rejection Adaptive Metropolis (DRAM) and Transitional Markov Chain Monte Carlo (TMCMC), and DREAM are elaborately introduced to allow practitioners to understand better the concepts and practical implementations. Their performances in model updating and damage detection are compared through three different engineering applications with increased complexity, e.g., a forty-story shear building, a two-span continuous steel beam, and a large-scale steel pedestrian bridge.

Prediction of bridge structure deformation and strain based on dynamic testing and intelligent algorithms

The field load test is a direct and effective method for evaluating the performance of bridge structures. However, existing bridge field static load tests are costly and inefficient; moreover, they obstruct traffic and cause unavoidable damage to the bridge structure. As an alternative the the static load test, a random model update method based on bridge dynamic load tests and the Bayesian inference is proposed in this paper. The bridge static load test results were predicted with a high accuracy. To speed up the Bayesian method to infer the posterior probability density of the updated parameters, the Gaussian process was used in place of the finite element model, and the Bayesian inference used the Markov chain Monte Carlo method based on the delayed rejection adaptive Metropolis algorithm. First, the parameters to be modified for the bridge structure analysis model were determined based on the global sensitivity analysis method. Second, a uniform design sampling method was used to establish the Gaussian process optimization model to update the random model of the bridge structure. Finally, a reinforced concrete truss arch bridge was used to verify the correctness of the static load results of the bridge predicted by the random model update method based on dynamic load testing and Bayesian inference. The research results reveal that the prediction results of the bridge static load test based on the dynamic load test and Bayesian inference method agree with the actual test results.

Response Surface Model of the Reduced Flexibility Matrix for Bayesian Damage Identification.

The present work is concerned with the use of a Response Surface Model of the reduced flexibility matrix for structural damage identification. A Response Surface Model (RSM) is fitted with the aim at providing a polynomial relationship between nodal cohesion parameters, used to describe the damage field within the structure, and elements of the reduced flexibility matrix. A design of experiment built on combinations of a relatively small number of nodal cohesion parameters is used to fit the RSM. The damage identification problem is formulated within the Bayesian framework and the Delayed Rejection Adaptive Metropolis method is used to sample the posterior probability density function of the uncertain cohesion parameters. Numerical simulations addressing damage identification in plates were carried out in order to assess the proposed approach, which succeeded in the identification of the different damage profiles considered. Besides, the use of a RSM, instead of a FEM of the structure, resulted in reductions of up almost 78% in the required computational cost.

Stochastic inversion for equivalent hydraulic fracture characterization using low-frequency distributed acoustic sensing data

Distributed fiber-optic sensing, a game-changing technology, has been successfully applied in monitoring hydraulic fracturing treatments. The cross-well fiber-optic strain/strain-rate responses are directly related to the fracture-propagation process and dynamic fracture geometry. Extracting the insightful information regarding hydraulic fractures requires robust interpretation workflows. In this paper, we aim to develop a stochastic inversion approach to characterize the dynamic equivalent fracture geometry and quantify the associated uncertainties using cross-well low-frequency distributed acoustic sensing (LF-DAS) measurements. A fast analytical forward solver based on the 3D displacement discontinuity method is developed to model the strain. The objective function is the sum-of-squares error between the modeled strain and the measured strain. We focus on an equivalent fracture geometry with a predefined length centered around the monitoring well, which is a reasonable assumption considering the spatial sensitivity of LF-DAS. Therefore, the model parameters reduce to fracture width and height of the equivalent fracture. We adopted the delayed rejection adaptive metropolis (DRAM) algorithm, an efficient Markov-chain Monte Carlo (MCMC)-based method, to perform the optimization. The efficiency and accuracy of the algorithm are tested using a synthetic case that has three monitoring wells at different locations. The mean values of fracture width and height are both close to the true values with negligible standard deviations for all the three monitoring wells. The algorithm performance is not sensitive to the initial guess and the predefined length needs to be large enough. Then, a field case with a single cluster from the HFTS-2 project is presented. The fracture width increases from about 0.5 mm to about 0.9 mm during the pumping stage and gradually decreases during the shut-in period. The fracture height changes during the pumping stage and stabilizes at about 150 m during the shut-in period, the trend of which is consistent with the LF-DAS signals from the offset vertical monitoring well. To the best of our knowledge, this is the first algorithm that can efficiently quantify the fracture width and height simultaneously. The results could provide novel insights on the characteristics of fracture geometry and significantly improve the understanding of complex fracture propagation processes in subsurface reservoirs.

Bayesian inference for parameter identification in mechanistic models, exemplified using a cow lifetime performance model

Mechanistic models are valuable tools for studying the underlying mechanisms of complex biological phenomena. For example, cow lifespan models can be used to identify differences in resource acquisition and allocation strategies between individuals, which is relevant for decision-making in breeding programs. In such models, differences in simulated traits between individuals are consequences of the parameter set that represents the genetic potential of each animal and its interaction with the environment. This indicates that the identification of these differences is essentially a search for individual parameters. In mechanistic models, this search is generally a non-convex problem that has different local minima because the parameters interact within these models. Due to this and to the simulation time length (e.g. years), there is uncertainty associated with the inference of the parameter values for each individual. This uncertainty can be quantified using Bayesian inference since this approach treats the model parameters as random variables with an underlying probability distribution that describes them. The objective of this work was to employ the Delayed Rejection Adaptive Metropolis (DRAM) algorithm to identify the parameters of a cows’ lifespan model using two datasets of Holstein cows. The datasets contain periodic measurements of Milk Yield (MY), BW, and Body Condition Score (BCS). Additionally, one of the two datasets has information of BW from birth to first calving. The average Mean Absolute Percentage Error (MAPE) minimisation between the simulated and experimental data (MY, BW and BCS) was used as the objective function for parameter search. The Bayesian inference performance was compared with four optimisation metaheuristic approaches: Differential Evolution, Genetic Algorithm, Particle Swarm Optimisation, and Simulated Annealing. Although the results show that all methods are efficient in finding parameter values that reduce the distance between the simulated and experimental data (MAPE < 10%), the DRAM method is more efficient in terms of computational cost, and the parameter distributions obtained with this method offer more information about the statistical properties of each parameter (e.g. median).

Direct inversion for shale brittleness index using a delayed rejection adaptive Metropolis-Markov chain Monte Carlo method

The reservoir brittleness index can characterize the relative brittleness of shale oil and gas reservoirs, which provides guidance for hydraulic fracturing in the later stage of oil and gas exploration and development. It is a significant index to evaluate the sweet spot of oil and gas reservoirs. Most research on the brittleness index involves laboratory measurements and petrophysical quantitative analysis, but few studies directly predict the reservoir brittleness index from prestack seismic data. The Markov chain Monte Carlo (MCMC) probabilistic algorithm incorporating the delayed rejection adaptive Metropolis (DRAM) strategy has been developed to invert the reservoir brittleness index directly. The different brittleness indexes are analyzed and compared by using the constructed rock-physics model of the shale gas exploration area to select the most sensitive one. Based on the chosen brittleness index, the approximate equation of the PP-wave reflection coefficient for the brittleness index is deduced, and the correctness and achievability of the modeling operator are indicated by theoretical analysis. To analyze the uncertainty of the brittleness index and enhance computational efficiency, an improved MCMC probabilistic inversion algorithm is introduced, which aims to optimize the sampling process of the general MCMC algorithm by delayed rejection and adaptive Metropolis strategies. Our study finds that the DRAM strategy improves the efficiency of the algorithm by nearly 30%. Synthetic examples and field seismic data verify the applicability and effectiveness of our inversion method.

Bayesian inversion for anisotropic hydraulic phase-field fracture

In this work, we employ a Bayesian inversion framework to fluid-filled phase-field fracture. We develop a robust and efficient numerical algorithm for hydraulic phase-field fracture toward transversely isotropic and orthotropy anisotropic fracture. In the fluid-driven coupled problem, three primary fields for pressure, displacements, and the crack phase-field are solved while direction-dependent responses (due to the preferred fiber orientation) are enforced via penalty-like parameters. A new crack driving state function is introduced by avoiding the compressible part of anisotropic energy to be degraded. Next, we use a successful extension of the anisotropic hydraulic phase-field fracture as a departure point for Bayesian inversion to estimate material parameters. To this end, we employ the delayed rejection adaptive Metropolis–Hastings (DRAM) algorithm to identify the parameters. The focus is on uncertainties arising from different variables, including elasticity modulus, Biot’s coefficient, Biot’s modulus, dynamic fluid viscosity and Griffith’s energy release rate in the case of the isotopic hydraulic fracture while in the anisotropic setting, we will have additional penalty-like parameters to be identified. Several numerical examples substantiate our algorithmic developments.

Bayesian inversion for unified ductile phase-field fracture

The prediction of crack initiation and propagation in ductile failure processes are challenging tasks for the design and fabrication of metallic materials and structures on a large scale. Numerical aspects of ductile failure dictate a sub-optimal calibration of plasticity- and fracture-related parameters for a large number of material properties. These parameters enter the system of partial differential equations as a forward model. Thus, an accurate estimation of the material parameters enables the precise determination of the material response in different stages, particularly for the post-yielding regime, where crack initiation and propagation take place. In this work, we develop a Bayesian inversion framework for ductile fracture to provide accurate knowledge regarding the effective mechanical parameters. To this end, synthetic and experimental observations are used to estimate the posterior density of the unknowns. To model the ductile failure behavior of solid materials, we rely on the phase-field approach to fracture, for which we present a unified formulation that allows recovering different models on a variational basis. In the variational framework, incremental minimization principles for a class of gradient-type dissipative materials are used to derive the governing equations. The overall formulation is revisited and extended to the case of anisotropic ductile fracture. Three different models are subsequently recovered by certain choices of parameters and constitutive functions, which are later assessed through Bayesian inversion techniques. A step-wise Bayesian inversion method is proposed to determine the posterior density of the material unknowns for a ductile phase-field fracture process. To estimate the posterior density function of ductile material parameters, three common Markov chain Monte Carlo (MCMC) techniques are employed: (i) the Metropolis–Hastings algorithm, (ii) delayed-rejection adaptive Metropolis, and (iii) ensemble Kalman filter combined with MCMC. To examine the computational efficiency of the MCMC methods, we employ the hat{R}{-}convergence tool. The resulting framework is algorithmically described in detail and substantiated with numerical examples.

Application of Markov Chain Monte Carlo Methods for Uncertainty Quantification in Inverse Transport Problems

Determination of the components of a radioactive source/shield system using the system's radiation signature is of great importance in homeland security, material safeguards, and waste management. Although significant progress has been made toward solving this inverse transport problem in recent years, work remains to be done to quantify the uncertainty in reconstructed results. In this article we apply two Markov chain Monte Carlo (MCMC) approaches, the delayed rejection adaptive metropolis (DRAM) and differential evolution adaptive metropolis (DREAM) methods, to solve inverse problems and quantify uncertainty. The DRAM method uses delayed rejection combined with global adaptation of the proposal covariance matrix. The DREAM method hybridizes MCMC sampling with the differential evolution (DE) algorithm. In numerical test cases, the DRAM and DREAM methods are shown to be superior to a first-order inverse Hessian approach for problems with noisy data and multiple unknown quantities, with DREAM converging to the posterior distribution more quickly than DRAM. The DREAM and DRAM results indicate that a full posterior distribution is required to quantify uncertainty in many inverse transport problems.

Bayesian model updating of civil structures with likelihood-free inference approach and response reconstruction technique

Bayesian inference methods typically require a considerable amount of computation time in the calculation of forward models. This limitation restricts the application of Bayesian inference methods for the parameter identification of complex engineering problems. We propose a novel likelihood-free Bayesian inference method for structural parameter identification. An adaptive Gaussian surrogate model (GSM) was integrated with the transitional Markov chain Monte Carlo (MCMC) method for Bayesian inference. The log-likelihood function was approximated with GSM and the transitional MCMC method was used to generate the posterior distribution samples. A response reconstruction technique was combined with the likelihood-free Bayesian inference method for the parameter identification. Both numerical studies and experimental studies were conducted to verify the accuracy and efficiency of the proposed method. The results showed that the proposed method could be used to estimate the posterior probabilities of unknown structural parameters. Additionally, the proposed method was more efficient than the delayed rejection adaptive Metropolis and Gibbs sampling methods.

A new homotopy approach for stochastic static model updating with large uncertain measurement errors

Large measurement errors are a major challenge in structural model updating. Based on the concept of homotopy, a new stochastic static model updating method is proposed to update structural models using uncertain static data with large measurement errors. First, considering the uncertainty of the static measurement, a stochastic model updating equation for element update factors is set up. To solve the stochastic model updating equation, a series of homotopy deformation equations are presented to establish the relationship between the deterministic update factors and the random update factors. Furthermore, the homotopy series expansions of the random update factors can be determined by solving the homotopy deformation equations. Since the measured degrees of freedom of updated structures are usually limited or unavailable, a static condensation technique is used for stochastic model updating. To address the ill-posed problems caused by incomplete measurement information and static measurement errors, the Tikhonov regularization method is used in the process of solving the homotopy deformation equations. Three numerical examples are given to demonstrate the validity of the proposed stochastic model updating method. The numerical results clearly show that unlike the second-order perturbation method, this new method can produce better accuracy in cases with large measurement errors. Compared with the Bayesian method with the Delayed Rejection Adaptive Metropolis sampling technique and even a fast Bayesian method, the proposed method utilizes much less computational time and provides an equivalent accuracy. Finally, static loading experiments on a two-span continuous concrete beam are implemented to validate the proposed model updating method.

Markov Chain Monte Carlo Analysis of the Variable-Volume Exothermic Model for a Continuously Stirred Tank Reactor

In this paper, a variable-volume Continuously Stirred Tank Reactor (CSTR) deterministic exothermic model has been formulated based on the Reynold Transport Theorem. The numerical analysis of the formulated model and the identifiability of its physical parameters are done by using the least squares and the Delayed-Rejection Adaptive Metropolis (DRAM) method. The least square estimates provide the prior information for the DRAM method. The overall numerical results show that the model gives an insight in describing the dynamics of CSTR processes, and 14 parameters of the CSTR are well identified through DRAM convergence diagnostic tests, such as trace, scatter, autocorrelation, histograms, and marginal density plots. Global sensitivity analysis was further performed, by using the partial rank correlation coefficients obtained from the Latin hypercube sampling method, in order to study and quantify the impact of estimated parameters, uncertainties on the model outputs. The results showed that 7 among the 14 estimated model parameters are very sensitive to the model outcomes and so those parameters need to be handled and treated carefully.

Stochastic model updating of rotor support parameters using Bayesian approach

Uncertainties due to assembling, installation, and operational conditions are extensively involved in rotating systems' parameters. Stochastic characteristics of these parameters may seriously affect rotating systems' vibrational characteristics, such as their critical speeds and vibration amplitudes. These effects make the variability of parameters in the modeling of rotary machines inevitable. In rotating machinery, material properties and geometric parameters of the rotor, bearing characteristics and supports stiffness determine the system's dynamic response. Stochastic model updating methods consider model response variability and allocate them to the model parameters; however, they are not commonly employed in rotor dynamics, and deterministic approaches are still prevalent in this field. Due to the cost and efforts needed to set up experiments and obtain outcomes that reflect the machine's actual characteristics, stochastic updating practices of industrial rotating systems are rarely reported in the literature. This paper adopts an appropriate parameter selection procedure and suitable sampling strategy for stochastic model updating to investigate variability in the dynamic behavior of a complex turbo compressor rotor-bearing-support system, leading to successful parameter identification results. The compressor rotor is mounted on hydrodynamic journal bearings with speed-dependent stiffness and damping. Due to the rotating system complex model, a variance-based global sensitivity method is employed for parameter selection to eliminate non-influential parameters in the model updating and to alleviate updating complexity and computational burden. The Bayesian approach in the stochastic model updating is applied to estimate parameter uncertainty in the rotor with speed-dependent characteristics. Advanced Markov chain Monte Carlo sampling method using delayed rejection adaptive Metropolis algorithm is employed in the stochastic model updating. The updating procedure obtains marginal posterior probabilities of parameters, and uncertain parameter distributions are evaluated using the maximum entropy criterion.

Identifying atmospheric pollutant sources using a machine learning dispersion model and Markov chain Monte Carlo methods

Estimating the sources of contaminant or hazard emissions is important for pollution control and safety management. Markov chain Monte Carlo (MCMC), combined with Bayesian inference, was used to identify the source terms of pollutants. However, the efficiency and accuracy of the forward dispersion model greatly impacted the performance of the estimation method. Therefore, a machine learning algorithm (MLA) model with high prediction accuracy and efficiency was proposed and coupled with MCMC method to estimate the source terms. A previously proposed MLA model was used to obtain the expected concentrations in Bayesian estimation. The Delayed Rejection Adaptive Metropolis (DRAM) method was applied to sample particles in order to form Markov chains. To evaluate the performance of the MCMC–MLA method, a Gaussian dispersion model was selected as the forward model. The performances of MCMC–MLA and MCMC–Gaussian models were then compared with release cases in Prairie Grass experiment and the results showed that the MCMC–MLA method converged more rapidly than the MCMC–Gaussian model. Nevertheless, release cases in the Round Hill experiment were also used to test the generalisability of the MCMC–MLA. The results indicated that the performance of MCMC–MLA was better than that of the MCMC–Gaussian model for estimating source terms in estimation accuracy. Hence, the MCMC–MLA method proposed here is potentially a useful tool for identifying emissions source parameters with high accuracy and efficiency, as well as reasonable probability estimates.

Nonlocal viscoelastic Euler-Bernoulli beam model: a Bayesian approach for parameter estimation using the delayed rejection adaptive metropolis algorithm

The present work presents a model for nonlocal and viscoelastic Euler-Bernoulli beams and aspects of its calibration are addressed. The nonlocal feature of the model is described by the nonlocal elasticity theory proposed by Eringen and its viscoelastic behaviour is modelled by means of internal variables. Parametric analyses are performed to determine the impact of the nonlocal and viscoelastic parameters on the modal properties of the system. Inverse analyses are performed under the Bayesian framework and samples of the posterior density function are obtained by means of the Delayed Rejection Adaptive Metropolis (DRAM). The inverse analyses consider a nonlocal viscoelastic beam model with one internal variable and they address three aspects, namely: the impact of a misspecification of the beam diameter, the impact of modelling the beam diameter as an unknown but uninteresting model parameter and the model calibration when synthetic experimental data comes from a model containing two internal variables. The model parameters were chosen such that the system resembles a Single-Walled Carbon Nanotube (SWCNT).

A New Bayesian Methodology for Nonlinear Model Calibration in Computational Systems Biology

Computational modeling is a common tool to quantitatively describe biological processes. However, most model parameters are usually unknown because they cannot be directly measured. Therefore, a key issue in Systems Biology is model calibration, i.e. estimate parameters from experimental data. Existing methodologies for parameter estimation are divided in two classes: frequentist and Bayesian methods. The first ones optimize a cost function while the second ones estimate the parameter posterior distribution through different sampling techniques. Here, we present an innovative Bayesian method, called Conditional Robust Calibration (CRC), for nonlinear model calibration and robustness analysis using omics data. CRC is an iterative algorithm based on the sampling of a proposal distribution and on the definition of multiple objective functions, one for each observable. CRC estimates the probability density function of parameters conditioned to the experimental measures and it performs a robustness analysis, quantifying how much each parameter influences the observables behavior. We apply CRC to three Ordinary Differential Equations (ODE) models to test its performances compared to the other state of the art approaches, namely Profile Likelihood (PL), Approximate Bayesian Computation Sequential Monte Carlo (ABC-SMC) and Delayed Rejection Adaptive Metropolis (DRAM). Compared with these methods, CRC finds a robust solution with a reduced computational cost. CRC is developed as a set of Matlab functions (version R2018), whose fundamental source code is freely available at https://github.com/fortunatobianconi/CRC.

Structural damage detection based on variational Bayesian inference and delayed rejection adaptive Metropolis algorithm

Existing studies on sparse Bayesian learning for structural damage detection usually assume that the posterior probability density functions follow standard distributions which facilitate to circumvent the intractable integration problem of the evidence by means of numerical sampling or analytical derivation. Moreover, the uncertainties of each mode are usually quantified as a common parameter to simplify the calculation. These assumptions may not be realistic in practice. This study proposes a sparse Bayesian method for structural damage detection suitable for standard and nonstandard probability distributions. The uncertainty corresponding to each mode is assumed as different. Variational Bayesian inference is developed and the posterior probability density functions of each unknown are individually derived. The parameters are found to follow the gamma distribution, whereas the distribution of the damage index cannot be directly obtained because of the nonlinear relationship in its posterior probability density function. The delayed rejection adaptive Metropolis algorithm is then adopted to generate numerical samples of the damage index. The coupled damage index and parameters in the variational Bayesian inference are successively calculated via an iterative process. A laboratory-tested frame is utilised to verify the effectiveness of the proposed method. The results indicate that the sparse damage can be accurately detected. The proposed method has the advantage of high accuracy and broad applicability.

Radiation Source Localization Using Surrogate Models Constructed from 3-D Monte Carlo Transport Physics Simulations

Recent research has focused on the development of surrogate models for radiation source localization in a simulated urban domain. We employ the Monte Carlo N-Particle (MCNP) code to provide high-fidelity simulations of radiation transport within an urban domain. The model is constructed to employ a source location () as input and return the estimated count rate for a set of specified detector locations. Because MCNP simulations are computationally expensive, we develop efficient and accurate surrogate models of the detector responses. We construct surrogate models using Gaussian processes and neural networks that we train and verify using the MCNP simulations. The trained surrogate models provide an efficient framework for Bayesian inference and experimental design. We employ Delayed Rejection Adaptive Metropolis (DRAM), a Markov Chain Monte Carlo algorithm, to infer the location and intensity of an unknown source. The DRAM results yield a posterior probability distribution for the source’s location conditioned on the observed detector count rates. The posterior distribution exhibits regions of high and low probability within the simulated environment identifying potential source locations. In this manner, we can quantify the source location to within at least one of these regions of high probability in the considered cases. Employing these methods, we are able to reduce the space of potential source locations by at least 60%.

Bayesian inversion for electrical-impedance tomography in medical imaging using the nonlinear Poisson–Boltzmann equation

We develop an electrical-impedance tomography (EIT) inverse model problem in an infinite-dimensional setting by introducing a nonlinear elliptic PDE as a new EIT forward model. The new model completes the standard linear model by taking the transport of ionic charge into account, which was ignored in the standard equation. We propose Bayesian inversion methods to extract electrical properties of inhomogeneities in the main body, which is essential in medicine to screen the interior body and detect tumors or determine body composition. We also prove well-definedness of the posterior measure and well-posedness of the Bayesian inversion for the presented nonlinear model. The new model is able to distinguish between liquid and tissues and the state-of-the-art delayed-rejection adaptive-Metropolis (DRAM) algorithm is capable of analyzing the statistical variability in the measured data in various EIT experimental designs. This leads to design a reliable device with higher resolution images which is crucial in medicine for diagnostic purposes. We first test the validation of the presented nonlinear model and the proposed inverse method using synthetic data on a simple square computational domain with an inclusion. Then we establish the new model and robustness of the proposed inversion method in solving the ill-posed and nonlinear EIT inverse problem by presenting numerical results of the corresponding forward and inverse problems on a real-world application in medicine and healthcare. The results include the extraction of electrical properties of human leg tissues using measurement data.