Improved MCMC method for parameter estimation based on marginal probability density function

2013 ◽  
Vol 27 (6) ◽  
pp. 1771-1779 ◽  
Author(s):  
Dawn An ◽  
Joo-Ho Choi
Keyword(s):  
Parameter Estimation ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Marginal Probability ◽  
Mcmc Method

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.

scholarly journals A particle-filter framework for robust cryoEM 3D reconstruction

2018 ◽  
Author(s):  
Mingxu Hu ◽  
Hongkun Yu ◽  
Kai Gu ◽  
Kunpeng Wang ◽  
Siyuan Ren ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Probability Density Function ◽  
Particle Filter ◽  
Probability Density ◽  
Density Function ◽  
Sequential Monte Carlo ◽  
High Dimensional ◽  
Dimensional Parameter ◽  
Support Points ◽  
Estimated Parameters

AbstractElectron cryo-microscopy (cryoEM) is now a powerful tool in determining atomic structures of biological macromolecules under nearly natural conditions. The major task of single-particle cryoEM is to estimate a set of parameters for each input particle image to reconstruct the three-dimensional structure of the macromolecules. As future large-scale applications require increasingly higher resolution and automation, robust high-dimensional parameter estimation algorithms need to be developed in the presence of various image qualities. In this paper, we introduced a particle-filter algorithm for cryoEM, which was a sequential Monte Carlo method for robust and fast high-dimensional parameter estimation. The cryoEM parameter estimation problem was described by a probability density function of the estimated parameters. The particle filter uses a set of random and weighted support points to represent such a probability density function. The statistical properties of the support points not only enhance the parameter estimation with self-adaptive accuracy but also provide the belief of estimated parameters, which is essential for the reconstruction phase. The implementation of these features showed strong tolerance to bad particles and enabled robust defocus refinement, demonstrated by the remarkable resolution improvement at the atomic level.

scholarly journals Providing a New Approach for Modeling and Parameter Estimation of Probability Density Function of Noise in Digital Images

2015 ◽  
Vol 37 ◽  
pp. 182
Author(s):  
Hanif Yaghoobi ◽  
Keivan Maghooli ◽  
Alireza Ghahramani Barandagh
Keyword(s):  
Parameter Estimation ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Digital Images ◽  
Image Sensors ◽  
Arrival Process ◽  
Mean And Variance ◽  
Two Parameters ◽  
Generalized Probability

The main part of the noise in digital images arises when taking pictures or transmission. There is noise in the imagescaptured by the image sensors of the real world. Noise, based on its causes can have different probability density functions.For example, such a model is called the Poisson distribution function of the random nature of photon arrival process that isconsistent with the distribution of pixel values measured. The parameters of the noise probability density function (PDF)can be achieved to some extent the properties of the sensor. But, we need to estimate the parameters for imaging settings. Ifwe assume that the PDF of noise is approximately Gaussian, then we need only to estimate the mean and variance becausethe Gaussian PDF with only two parameters is determined. In fact, in many cases, PDF of noise is not Gaussian and it hasunknown distribution. In this study, we introduce a generalized probability density function for modeling noise in imagesand propose a method to estimate its parameters. Because the generalized probability density function has multipleparameters, so use common parameter estimation techniques such as derivative method to maximize the likelihood functionwould be extremely difficult. In this study, we propose the use of evolutionary algorithms for global optimization. Theresults show that this method accurately estimates the probability density function parameters.

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.

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