scholarly journals Data simulation with Markov Chain Monte Carlo, Gibbs sampling, and Bayes (beta-binomial) methods as the parameter estimations of spatial bivariate probit regression model

2021 ◽  
Author(s):  
Dewi Retno Sari Saputro ◽  
Yuanita Kusuma Wardani ◽  
Nafisa Berliana Indah Pratiwi ◽  
Purnami Widyaningsih
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Regression Model ◽  
Gibbs Sampling ◽  
Probit Regression ◽  
Bivariate Probit ◽  
Data Simulation ◽  
Parameter Estimations

scholarly journals PENDUGAAN ANGKA KEMISKINAN DI KABUPATEN PADANG PARIAMAN MENGGUNAKAN SMALL AREA ESTIMATION DENGAN PENDEKATAN HIERARCHICAL BAYESIAN (HB) LOGLOGISTIK

2019 ◽  
Vol 8 (2) ◽  
pp. 76
Author(s):  
Jusri Repi Basri Yuliani ◽  
Maiyastri Maiyastri ◽  
Rita Diana
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Gibbs Sampling ◽  
Standard Error ◽  
Small Area ◽  
Small Area Estimation ◽  
Hierarchical Bayesian ◽  
Area Estimation ◽  
Level Model

Penelitian ini mengkaji tentang pendekatan Hierarchical Bayesian (HB) Loglogistik yang diaplikasikan pada Small Area Estimation (SAE) dengan tujuan mengestimasi tingkat kemiskinan di Kabupaten Padang Pariaman. Metode pendugaan area kecil yang digunakan pada penelitian ini adalah model level area dasar (basic area level model ) dengan bantuan variabel penyerta yang tersedia pada level kecamatan. Variabel penyerta yang digunakan pada penelitian ini yaitu rasio SLTA/Sederajat (X1), persentase keluarga pertanian (X2), rasio industri mikro kecil (X3), persentase buruh tani dalam setiap anggota keluarga (X4), kepadatan penduduk (X5), dan persentase penduduk pelanggan listrik PLN (X6). Bentuk integrasi yang kompleks dari sebaran peluang bersyarat pada model diselesaikan menggunakan Markov Chain Monte Carlo (MCMC) dengan menerapkan algortima Gibbs Sampling dan bantuan software WinBugs 1.4.3. Hasil estimasi menggunkan model HB yang diperoleh dibandingkan dengan hasil estimasi pendugaan langsung dengan memperhatikan nilai standard error sebagai tolok ukurnya. Hasil pendugaan tingkat kemiskinan untuk level kecamatan di Kabupaten Padang Pariaman dengan model HB menunjukkan nilai standard error yang kecil.Kata Kunci: Tingkat kemiskinan, Small Area Estimation, Hierarchical Bayesian

scholarly journals Conjugate Bayes for probit regression via unified skew-normal distributions

Biometrika ◽  
2019 ◽  
Vol 106 (4) ◽  
pp. 765-779 ◽  
Author(s):  
Daniele Durante
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Computational Methods ◽  
Graphical Models ◽  
Building Blocks ◽  
Probit Regression ◽  
Conjugate Priors ◽  
Dichotomous Data ◽  
Skew Normal

Summary Regression models for dichotomous data are ubiquitous in statistics. Besides being useful for inference on binary responses, these methods serve as building blocks in more complex formulations, such as density regression, nonparametric classification and graphical models. Within the Bayesian framework, inference proceeds by updating the priors for the coefficients, typically taken to be Gaussians, with the likelihood induced by probit or logit regressions for the responses. In this updating, the apparent absence of a tractable posterior has motivated a variety of computational methods, including Markov chain Monte Carlo routines and algorithms that approximate the posterior. Despite being implemented routinely, Markov chain Monte Carlo strategies have mixing or time-inefficiency issues in large-$p$ and small-$n$ studies, whereas approximate routines fail to capture the skewness typically observed in the posterior. In this article it is proved that the posterior distribution for the probit coefficients has a unified skew-normal kernel under Gaussian priors. This result allows efficient Bayesian inference for a wide class of applications, especially in large-$p$ and small-to-moderate-$n$ settings where state-of-the-art computational methods face notable challenges. These advances are illustrated in a genetic study, and further motivate the development of a wider class of conjugate priors for probit models, along with methods for obtaining independent and identically distributed samples from the unified skew-normal posterior.

The estimated parameter of logistic regression model by Markov Chain Monte Carlo method with multicollinearity

2020 ◽  
Vol 36 (4) ◽  
pp. 1253-1259
Author(s):  
Autcha Araveeporn ◽  
Yuwadee Klomwises
Keyword(s):  
Monte Carlo ◽  
Logistic Regression ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Maximum Likelihood ◽  
Regression Model ◽  
Ridge Regression ◽  
Logistic Regression Model ◽  
Classical Method ◽  
Likelihood Method

Markov Chain Monte Carlo (MCMC) method has been a popular method for getting information about probability distribution for estimating posterior distribution by Gibbs sampling. So far, the standard methods such as maximum likelihood and logistic ridge regression methods have represented to compare with MCMC. The maximum likelihood method is the classical method to estimate the parameter on the logistic regression model by differential the loglikelihood function on the estimator. The logistic ridge regression depends on the choice of ridge parameter by using crossvalidation for computing estimator on penalty function. This paper provides maximum likelihood, logistic ridge regression, and MCMC to estimate parameter on logit function and transforms into a probability. The logistic regression model predicts the probability to observe a phenomenon. The prediction accuracy evaluates in terms of the percentage with correct predictions of a binary event. A simulation study conducts a binary response variable by using 2, 4, and 6 explanatory variables, which are generated from multivariate normal distribution on the positive and negative correlation coefficient or called multicollinearity problem. The criterion of these methods is to compare by a maximum of predictive accuracy. The outcomes find that MCMC satisfies all situations.

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