scholarly journals Markov Chain Monte Carlo Estimation of the Law of the Mean of a Dirichlet Process

Bernoulli ◽  
2001 ◽  
Vol 7 (4) ◽  
pp. 573 ◽  
Author(s):  
Alessandra Guglielmi ◽  
Richard L. Tweedie
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Dirichlet Process ◽  
The Mean ◽  
Monte Carlo Estimation ◽  
The Law

THE MEAN WAITING TIME FOR A PATTERN

1999 ◽  
Vol 13 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Sheldon M. Ross
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Waiting Time ◽  
Random Variables ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Mean Waiting Time ◽  
The Mean ◽  
Mean Time

Consider a sequence of independent and identically distributed random variables along with a specified set of k-vectors. We present an expression for E [T], the mean time until the last k observed random variables fall within this set. Not only can this expression often be used to obtain bounds on E[T], it also gives rise to an efficient way of approximating E[T] by a simulation. Specific lower and upper bounds for E[T] are also derived. These latter bounds are given in terms of a parameter, and a Markov chain Monte Carlo approach to approximate this parameter by a simulation is indicated. The results of this paper are illustrated by considering the problem of determining the mean time until a sequence of k-valued random variables has a run of size k that encompasses each value.

scholarly journals Markov chain Monte Carlo estimation of quantiles

2014 ◽  
Vol 8 (2) ◽  
pp. 2448-2478 ◽  
Author(s):  
Charles R. Doss ◽  
James M. Flegal ◽  
Galin L. Jones ◽  
Ronald C. Neath
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Monte Carlo Estimation

scholarly journals Inverse modeling of cloud-aerosol interactions – Part 2: Sensitivity tests on liquid phase clouds using a Markov Chain Monte Carlo based simulation approach

2011 ◽  
Vol 11 (7) ◽  
pp. 20051-20105 ◽  
Author(s):  
D. G. Partridge ◽  
J. A. Vrugt ◽  
P. Tunved ◽  
A. M. L. Ekman ◽  
H. Struthers ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Standard Deviation ◽  
Mass Fraction ◽  
Cloud Model ◽  
Number Concentration ◽  
Geometric Standard Deviation ◽  
Accumulation Mode ◽  
The Mean

Abstract. This paper presents a novel approach to investigate cloud-aerosol interactions by coupling a Markov Chain Monte Carlo (MCMC) algorithm to a pseudo-adiabatic cloud parcel model. Despite the number of numerical cloud-aerosol sensitivity studies previously conducted few have used statistical analysis tools to investigate the sensitivity of a cloud model to input aerosol physiochemical parameters. Using synthetic data as observed values of cloud droplet number concentration (CDNC) distribution, this inverse modelling framework is shown to successfully converge to the correct calibration parameters. The employed analysis method provides a new, integrative framework to evaluate the sensitivity of the derived CDNC distribution to the input parameters describing the lognormal properties of the accumulation mode and the particle chemistry. To a large extent, results from prior studies are confirmed, but the present study also provides some additional insightful findings. There is a clear transition from very clean marine Arctic conditions where the aerosol parameters representing the mean radius and geometric standard deviation of the accumulation mode are found to be most important for determining the CDNC distribution to very polluted continental environments (aerosol concentration in the accumulation mode >1000 cm−3) where particle chemistry is more important than both number concentration and size of the accumulation mode. The competition and compensation between the cloud model input parameters illustrate that if the soluble mass fraction is reduced, both the number of particles and geometric standard deviation must increase and the mean radius of the accumulation mode must increase in order to achieve the same CDNC distribution. For more polluted aerosol conditions, with a reduction in soluble mass fraction the parameter correlation becomes weaker and more non-linear over the range of possible solutions (indicative of the sensitivity). This indicates that for the cloud parcel model used herein, the relative importance of the soluble mass fraction appears to decrease if the number or geometric standard deviation of the accumulation mode is increased. This study demonstrates that inverse modelling provides a flexible, transparent and integrative method for efficiently exploring cloud-aerosol interactions efficiently with respect to parameter sensitivity and correlation.

scholarly journals Bayesian adaptive Markov chain Monte Carlo estimation of genetic parameters

Heredity ◽  
2012 ◽  
Vol 109 (4) ◽  
pp. 235-245 ◽  
Author(s):  
B Mathew ◽  
A M Bauer ◽  
P Koistinen ◽  
T C Reetz ◽  
J Léon ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Genetic Parameters ◽  
Monte Carlo Estimation ◽  
Estimation Of Genetic Parameters
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