scholarly journals Construction of marginal probability density function of model parameters of cell population

2012 ◽  
Vol 12 (12) ◽  
Author(s):  
Marina Vinogradova
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Cell Population ◽  
Model Parameters ◽  
Marginal Probability

Improved MCMC Method for Parameter Estimation Based on Marginal Probability Density Function

2011 ◽  
Author(s):  
Dawn An ◽  
Joo-Ho Choi
Keyword(s):  
Monte Carlo ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Uncertain Parameters ◽  
Marginal Probability ◽  
Mcmc Method ◽  
Proposal Distribution ◽  
Engineering Problems ◽  
Probability Density Function Pdf

In many engineering problems, sampling is often used to estimate and quantify the probability distribution of uncertain parameters during the course of Bayesian framework, which is to draw proper samples that follow the probabilistic feature of the parameters. Among numerous approaches, Markov Chain Monte Carlo (MCMC) has gained the most popularity due to its efficiency and wide applicability. The MCMC, however, does not work well in the case of increased parameters and/or high correlations due to the difficulty of finding proper proposal distribution. In this paper, a method employing marginal probability density function (PDF) as a proposal distribution is proposed to overcome these problems. Several engineering problems which are formulated by Bayesian approach are addressed to demonstrate the effectiveness of proposed method.

Uncertainty quantification of nonlinear distributed parameter systems using generalized polynomial chaos

2019 ◽  
Vol 67 (4) ◽  
pp. 283-303
Author(s):  
Chettapong Janya-anurak ◽  
Thomas Bernard ◽  
Jürgen Beyerer
Keyword(s):  
Probability Density Function ◽  
Uncertainty Quantification ◽  
Probability Density ◽  
Density Function ◽  
Polynomial Chaos ◽  
Distributed Parameter Systems ◽  
Computational Effort ◽  
Distributed Parameter ◽  
Model Parameters ◽  
Generalized Polynomial

Abstract Many industrial and environmental processes are characterized as complex spatio-temporal systems. Such systems known as distributed parameter systems (DPSs) are usually highly complex and it is difficult to establish the relation between model inputs, model outputs and model parameters. Moreover, the solutions of physics-based models commonly differ somehow from the measurements. In this work, appropriate Uncertainty Quantification (UQ) approaches are selected and combined systematically to analyze and identify systems. However, there are two main challenges when applying the UQ approaches to nonlinear distributed parameter systems. These are: (1) how uncertainties are modeled and (2) the computational effort, as the conventional methods require numerous evaluations of the model to compute the probability density function of the response. This paper presents a framework to solve these two issues. Within the Bayesian framework, incomplete knowledge about the system is considered as uncertainty of the system. The uncertainties are represented by random variables, whose probability density function can be achieved by converting the knowledge of the parameters using the Principle of Maximum Entropy. The generalized Polynomial Chaos (gPC) expansion is employed to reduce the computational effort. The framework using gPC based on Bayesian UQ proposed in this work is capable of analyzing systems systematically and reducing the disagreement between model predictions and measurements of the real processes to fulfill user defined performance criteria. The efficiency of the framework is assessed by applying it to a benchmark model (neutron diffusion equation) and to a model of a complex rheological forming process. These applications illustrate that the framework is capable of systematically analyzing the system and optimally calibrating the model parameters.

scholarly journals Qualitative Properties of Randomized Maximum Entropy Estimates of Probability Density Functions

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 548
Author(s):  
Yuri S. Popkov
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Maximum Entropy ◽  
Density Function ◽  
Lagrange Multipliers ◽  
Real Data ◽  
Model Parameters ◽  
Lake Area ◽  
Data Set ◽  
Maximum Entropy Estimation

The problem of randomized maximum entropy estimation for the probability density function of random model parameters with real data and measurement noises was formulated. This estimation procedure maximizes an information entropy functional on a set of integral equalities depending on the real data set. The technique of the Gâteaux derivatives is developed to solve this problem in analytical form. The probability density function estimates depend on Lagrange multipliers, which are obtained by balancing the model’s output with real data. A global theorem for the implicit dependence of these Lagrange multipliers on the data sample’s length is established using the rotation of homotopic vector fields. A theorem for the asymptotic efficiency of randomized maximum entropy estimate in terms of stationary Lagrange multipliers is formulated and proved. The proposed method is illustrated on the problem of forecasting of the evolution of the thermokarst lake area in Western Siberia.

Structural health monitoring by probability density function of autoregressive-based damage features and fast distance correlation method

2021 ◽  
pp. 107754632110201
Author(s):  
Mohammad Ali Heravi ◽  
Seyed Mehdi Tavakkoli ◽  
Alireza Entezami
Keyword(s):  
Time Series ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Large Scale ◽  
Hypothesis Test ◽  
Correlation Method ◽  
Model Parameters ◽  
Density Estimator ◽  
Distance Correlation

In this article, the autoregressive time series analysis is used to extract reliable features from vibration measurements of civil structures for damage diagnosis. To guarantee the adequacy and applicability of the time series model, Leybourne–McCabe hypothesis test is used. Subsequently, the probability density functions of the autoregressive model parameters and residuals are obtained with the aid of a kernel density estimator. The probability density function sets are considered as damage-sensitive features of the structure and fast distance correlation method is used to make decision for detecting damages in the structure. Experimental data of a well-known three-story laboratory frame and a large-scale bridge benchmark structure are used to verify the efficiency and accuracy of the proposed method. Results indicate the capability of the method to identify the location and severity of damages, even under the simulated operational and environmental variability.

MULTIVARIATE PARTIAL DIFFERENTIAL EQUATION DESCRIBING THE EVOLUTION OF A GAUSSIAN PROCESS

2009 ◽  
Vol 09 (04) ◽  
pp. 493-518
Author(s):  
MURAD S. TAQQU ◽  
MARK VEILLETTE
Keyword(s):  
Differential Equation ◽  
Probability Density Function ◽  
Differential Equations ◽  
Gaussian Process ◽  
Probability Density ◽  
Density Function ◽  
Single Equation ◽  
Marginal Probability ◽  
Partial Differential ◽  
Finite Dimensional

If {X(t), t ≥ 0} is a Gaussian process, the diffusion equation characterizes its marginal probability density function. How about finite-dimensional distributions? For each n ≥ 1, we derive a system of partial differential equations which are satisfied by the probability density function of the vector (X(t1), …, X(tn)). We then show that these differential equations determine uniquely the finite-dimensional distributions of Gaussian processes. We also discuss situations where the system can be replaced by a single equation, which is either one member of the system, or an aggregate equation obtained by summing all the equations in the system.

Local Selection of Model Parameters in Probability Density Function Estimation

2006 ◽  
pp. 292-301
Author(s):  
Ezequiel López-Rubio ◽  
Juan Miguel Ortiz-de-Lazcano-Lobato ◽  
Domingo López-Rodríguez ◽  
Enrique Mérida-Casermeiro ◽  
María del Carmen Vargas-González
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Model Parameters ◽  
Function Estimation ◽  
Local Selection ◽  
Density Function Estimation ◽  
Selection Of
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