scholarly journals A Bayesian Analysis of Spectral ARMA Model

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Manoel I. Silvestre Bezerra ◽  
Fernando Antonio Moala ◽  
Yuzo Iano
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Confidence Interval ◽  
Bayesian Analysis ◽  
Least Squares ◽  
Bayesian Approach ◽  
Arma Model ◽  
New Method ◽  
Posterior Distributions ◽  
Numerical Illustration

Bezerra et al. (2008) proposed a new method, based on Yule-Walker equations, to estimate the ARMA spectral model. In this paper, a Bayesian approach is developed for this model by using the noninformative prior proposed by Jeffreys (1967). The Bayesian computations, simulation via Markov Monte Carlo (MCMC) is carried out and characteristics of marginal posterior distributions such as Bayes estimator and confidence interval for the parameters of the ARMA model are derived. Both methods are also compared with the traditional least squares and maximum likelihood approaches and a numerical illustration with two examples of the ARMA model is presented to evaluate the performance of the procedures.

Bayesian Analysis of the Brown–Proschan Model

2015 ◽  
Vol 30 (1) ◽  
Author(s):  
Dinh Tuan Nguyen ◽  
Yann Dijoux ◽  
Mitra Fouladirad
Keyword(s):  
Weibull Distribution ◽  
Bayesian Analysis ◽  
Failure Rate ◽  
Bayesian Approach ◽  
Real Data ◽  
Posterior Distributions ◽  
Imperfect Maintenance ◽  
Maintenance Model ◽  
Informative Prior Distributions

AbstractThe paper presents a Bayesian approach of the Brown–Proschan imperfect maintenance model. The initial failure rate is assumed to follow a Weibull distribution. A discussion of the choice of informative and non-informative prior distributions is provided. The implementation of the posterior distributions requires the Metropolis-within-Gibbs algorithm. A study on the quality of the estimators of the model obtained from Bayesian and frequentist inference is proposed. An application to real data is finally developed.

Population Structure of Female and Immature Sperm Whales (Physeter macrocephalus) off the Galápagos Islands

1992 ◽  
Vol 49 (1) ◽  
pp. 78-84 ◽  
Author(s):  
Hal Whitehead ◽  
Susan Waters ◽  
Thomas Lyrholm
Keyword(s):  
Monte Carlo ◽  
Population Structure ◽  
Maximum Likelihood ◽  
Confidence Interval ◽  
Galapagos Islands ◽  
Physeter Macrocephalus ◽  
Galápagos Islands ◽  
Population Parameters ◽  
Sperm Whales ◽  
Population Simulation

The structure of the population of female and immature sperm whales (Physeter macrocephalus) in the region of the Galápagos Islands was studied using individual photographic identifications of 1285 animals collected between 1985 and 1989. Population parameters were estimated using a maximum-likelihood mark–recapture estimate permitting emigration from the study area in which identifications are collected and then reimmigration back into it. Because permanent associations among whales violated assumptions of independence, confidence intervals for the estimates were constructed using Monte-Carlo population simulation. The analysis suggested that there is a population of very approximately 200 whales in the study area around the islands at any time. These were part of a larger population numbering between 2600 and 5300 individuals (95% confidence interval). An average of 39–94% (95% confidence interval) of the whales left the study area in any month, with a similar number immigrating.

scholarly journals EMPIRICAL CHARACTERISTIC FUNCTION IN TIME SERIES ESTIMATION

2002 ◽  
Vol 18 (3) ◽  
pp. 691-721 ◽  
Author(s):  
John L. Knight ◽  
Jun Yu
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Characteristic Function ◽  
Estimation Method ◽  
Arma Model ◽  
Weight Functions ◽  
Regularity Conditions ◽  
Empirical Characteristic Function ◽  
Finite Sample ◽  
Monte Carlo Studies

Because the empirical characteristic function (ECF) is the Fourier transform of the empirical distribution function, it retains all the information in the sample but can overcome difficulties arising from the likelihood. This paper discusses an estimation method via the ECF for strictly stationary processes. Under some regularity conditions, the resulting estimators are shown to be consistent and asymptotically normal. The method is applied to estimate the stable autoregressive moving average (ARMA) models. For the general stable ARMA model for which the maximum likelihood approach is not feasible, Monte Carlo evidence shows that the ECF method is a viable estimation method for all the parameters of interest. For the Gaussian ARMA model, a particular stable ARMA model, the optimal weight functions and estimating equations are given. Monte Carlo studies highlight the finite sample performances of the ECF method relative to the exact and conditional maximum likelihood methods.

Determining Power and Sample Size for Simple and Complex Mediation Models

2017 ◽  
Vol 8 (4) ◽  
pp. 379-386 ◽  
Author(s):  
Alexander M. Schoemann ◽  
Aaron J. Boulton ◽  
Stephen D. Short
Keyword(s):  
Monte Carlo ◽  
Confidence Interval ◽  
Sample Size ◽  
Indirect Effect ◽  
Power Analysis ◽  
New Method ◽  
Computational Time ◽  
Personality Psychology ◽  
Mediation Analyses ◽  
Mediation Models

Mediation analyses abound in social and personality psychology. Current recommendations for assessing power and sample size in mediation models include using a Monte Carlo power analysis simulation and testing the indirect effect with a bootstrapped confidence interval. Unfortunately, these methods have rarely been adopted by researchers due to limited software options and the computational time needed. We propose a new method and convenient tools for determining sample size and power in mediation models. We demonstrate our new method through an easy-to-use application that implements the method. These developments will allow researchers to quickly and easily determine power and sample size for simple and complex mediation models.

Estimation of Models with Variable Coefficients

1991 ◽  
Vol 3 ◽  
pp. 27-49 ◽  
Author(s):  
John E. Jackson
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Maximum Likelihood ◽  
Least Squares ◽  
Generalized Least Squares ◽  
Ordinary Least Squares ◽  
Variable Coefficients ◽  
Coefficient Estimates ◽  
Explanatory Variables ◽  
Varying Coefficients

The ordinary least squares (OLS) estimator gives biased coefficient estimates if coefficients are not constant for all cases but vary systematically with the explanatory variables. This article discusses several different ways to estimate models with systematically and randomly varying coefficients using estimated generalized least squares and maximum likelihood procedures. A Monte Carlo simulation of the different methods is presented to illustrate their use and to contrast their results to the biased results obtained with ordinary least squares. Several applications of the methods are discussed and one is presented in detail. The conclusion is that, in situations with variables coefficients, these methods offer relatively easy means for overcoming the problems.

scholarly journals Automated Graduation using Bayesian Trans-dimensional Models

2011 ◽  
Vol 5 (2) ◽  
pp. 231-251 ◽  
Author(s):  
R.J. Verrall ◽  
S. Haberman
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Bayesian Approach ◽  
Model Uncertainty ◽  
Weighted Average ◽  
New Method ◽  
Reversible Jump ◽  
Standard Methods ◽  
Wide Range

AbstractThis paper presents a new method of graduation which uses parametric formulae together with Bayesian reversible jump Markov chain Monte Carlo methods. The aim is to provide a method which can be applied to a wide range of data, and which does not require a lot of adjustment or modification. The method also does not require one particular parametric formula to be selected: instead, the graduated values are a weighted average of the values from a range of formulae. In this way, the new method can be seen as an automatic graduation method which we believe can be applied in many cases without any adjustments and provide satisfactory graduated values. An advantage of a Bayesian approach is that it allows for model uncertainty unlike standard methods of graduation.

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