Marginal probability density function of granular quantization error in uniform quantizers

2001 ◽  
Vol 47 (3) ◽  
pp. 1237-1242
Author(s):  
P. Carbone ◽  
D. Petri
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Quantization Error ◽  
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.

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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