A MCMC-method for models with continuous latent responses

Psychometrika ◽  
2002 ◽  
Vol 67 (3) ◽  
pp. 335-350 ◽  
Author(s):  
Gunter Maris ◽  
Eric Maris
Keyword(s):  
Mcmc Method ◽  
Latent Responses

Probabilistic models of the strut efficiency factor for RC deep beams with MCMC method

2020 ◽  
Vol 21 (3) ◽  
pp. 917-933
Author(s):  
Xi Liu ◽  
Tao Wu ◽  
Yuanyuan An ◽  
Yang Liu
Keyword(s):  
Probabilistic Models ◽  
Efficiency Factor ◽  
Mcmc Method ◽  
Deep Beams ◽  
Rc Deep Beams

Standard Error Estimation of 3PL IRT True Score Equating With an MCMC Method

2008 ◽  
Vol 33 (3) ◽  
pp. 257-278 ◽  
Author(s):  
Yuming Liu ◽  
E. Matthew Schulz ◽  
Lei Yu
Keyword(s):  
Bootstrap Method ◽  
Standard Errors ◽  
True Score ◽  
Mcmc Method ◽  
Test Form ◽  
True Score Equating ◽  
Standard Error Estimation ◽  
Equivalent Test ◽  
Mean Square Errors ◽  
The Bootstrap Method

A Markov chain Monte Carlo (MCMC) method and a bootstrap method were compared in the estimation of standard errors of item response theory (IRT) true score equating. Three test form relationships were examined: parallel, tau-equivalent, and congeneric. Data were simulated based on Reading Comprehension and Vocabulary tests of the Iowa Tests of Basic Skills®. For parallel and congeneric test forms within valid IRT true score ranges, the pattern and magnitude of standard errors of IRT true score equating estimated by the MCMC method were very close to those estimated by the bootstrap method. For tau-equivalent test forms, the pattern of standard errors estimated by the two methods was also similar. Bias and mean square errors of equating produced by the MCMC method were smaller than those produced by the bootstrap method; however, standard errors were larger. In educational testing, the MCMC method may be used as an additional or alternative procedure to the bootstrap method when evaluating the precision of equating results.

scholarly journals Are Entrepreneurs More Likely to Be Obese?

2021 ◽  
Author(s):  
Yibing Wang ◽  
Xueling Qu ◽  
Haitao Wang
Keyword(s):  
Regression Models ◽  
Longitudinal Survey ◽  
Health Interventions ◽  
Health Departments ◽  
Entrepreneurial Success ◽  
Obesity Risk ◽  
Mcmc Method ◽  
Bayesian Mcmc ◽  
Ols Regression ◽  
National Health Care

Background: Entrepreneurs not only promote a nation’s economic growth but also increase employment. The risk of obesity among entrepreneurs may bring heavy economic burdens not only to the entrepreneurs but also to the national health care system. We aimed to examine the association between entrepreneurship and the risk of obesity. Methods: We utilized data from the 2015 Harmonized China Health and Retirement Longitudinal Survey, including 2,802 individuals aged between 45 and 65 with complete data. This study used BMI (Body Mass Index) (kg/m2 ) as an indicator of obesity risk. Entrepreneurs were defined as those respondents who run their own businesses as main jobs. We used multivariate OLS regression models and Bayesian Markov Chain Monte Carlo (MCMC) method to examine the link of entrepreneurship and obesity risk. Results: The multivariate OLS regression results showed that entrepreneurship was positively associated with BMI (P<0.01). The Bayesian MCMC results indicated that the posterior mean was (0.597, 90% HPD CI: 0.319, 0.897), demonstrating that entrepreneurship was indeed significantly positively associated with the risk of obesity. Conclusion: Being an entrepreneur is positively associated with the risk of obesity. As obesity can cause diseases such as hypertension, diabetes, coronary heart disease and stroke, the health departments should take necessary health interventions to prevent entrepreneurs from being obese in order to increase their entrepreneurial success.

Modeling the crashes count using finite mixture models

2019 ◽  
Vol 7 (1) ◽  
pp. 13-27
Author(s):  
Safaa K. Kadhem ◽  
Sadeq A. Kadhim
Keyword(s):  
Bayesian Inference ◽  
Mixture Models ◽  
Gibbs Sampler ◽  
Simulation Study ◽  
Finite Mixture Models ◽  
Synthetic Data ◽  
Finite Mixture Model ◽  
Finite Mixture ◽  
Model Parameters ◽  
Mcmc Method

"This paper aims at the modeling the crashes count in Al Muthanna governance using finite mixture model. We use one of the most common MCMC method which is called the Gibbs sampler to implement the Bayesian inference for estimating the model parameters. We perform a simulation study, based on synthetic data, to check the ability of the sampler to find the best estimates of the model. We use the two well-known criteria, which are the AIC and BIC, to determine the best model fitted to the data. Finally, we apply our sampler to model the crashes count in Al Muthanna governance.

Parallel MCMC methods for global optimization

2019 ◽  
Vol 25 (3) ◽  
pp. 227-237
Author(s):  
Lihao Zhang ◽  
Zeyang Ye ◽  
Yuefan Deng
Keyword(s):  
Monte Carlo ◽  
Global Optimization ◽  
Statistical Theory ◽  
Simulated Annealing ◽  
Parallel Computers ◽  
Mcmc Methods ◽  
Benchmark Function ◽  
Mcmc Method ◽  
Validation And Verification ◽  
Parallel Scheme

Abstract We introduce a parallel scheme for simulated annealing, a widely used Markov chain Monte Carlo (MCMC) method for optimization. Our method is constructed and analyzed under the classical framework of MCMC. The benchmark function for optimization is used for validation and verification of the parallel scheme. The experimental results, along with the proof based on statistical theory, provide us with insights into the mechanics of the parallelization of simulated annealing for high parallel efficiency or scalability for large parallel computers.

scholarly journals Joint state-parameter estimation of a nonlinear stochastic energy balance model from sparse noisy data

2019 ◽  
Vol 26 (3) ◽  
pp. 227-250 ◽  
Author(s):  
Fei Lu ◽  
Nils Weitzel ◽  
Adam H. Monahan
Keyword(s):  
Parameter Estimation ◽  
Energy Balance ◽  
Noisy Data ◽  
State Parameter ◽  
Energy Balance Model ◽  
Balance Model ◽  
Spatiotemporal Modeling ◽  
Mcmc Method ◽  
Physical Constraints ◽  
Observation Noise

Abstract. While nonlinear stochastic partial differential equations arise naturally in spatiotemporal modeling, inference for such systems often faces two major challenges: sparse noisy data and ill-posedness of the inverse problem of parameter estimation. To overcome the challenges, we introduce a strongly regularized posterior by normalizing the likelihood and by imposing physical constraints through priors of the parameters and states. We investigate joint parameter-state estimation by the regularized posterior in a physically motivated nonlinear stochastic energy balance model (SEBM) for paleoclimate reconstruction. The high-dimensional posterior is sampled by a particle Gibbs sampler that combines a Markov chain Monte Carlo (MCMC) method with an optimal particle filter exploiting the structure of the SEBM. In tests using either Gaussian or uniform priors based on the physical range of parameters, the regularized posteriors overcome the ill-posedness and lead to samples within physical ranges, quantifying the uncertainty in estimation. Due to the ill-posedness and the regularization, the posterior of parameters presents a relatively large uncertainty, and consequently, the maximum of the posterior, which is the minimizer in a variational approach, can have a large variation. In contrast, the posterior of states generally concentrates near the truth, substantially filtering out observation noise and reducing uncertainty in the unconstrained SEBM.

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