scholarly journals On Model Comparison: Application of Savage-Dickey Density Ratio to Bayes Factor

2020 ◽  
pp. 25-46
Author(s):  
Olawale B. Akanbi ◽  
Olusanya E. Olubusoye ◽  
Samuel A. Babatunde
Keyword(s):  
Linear Regression ◽  
Gibbs Sampling ◽  
Posterior Distribution ◽  
Model Comparison ◽  
Bayes Factor ◽  
Density Ratio ◽  
Sampling Technique ◽  
Competing Models ◽  
Normal Gamma Prior ◽  
Joint Posterior Distribution

Bayes factor is a major Bayesian tool for model comparison especially when the model priors are the same. In this paper, the Savage-Dickey Density Ratio (SDDR) is used to derive the Bayes factor to select a model from two competing models under consideration in a normal linear regression with an independent normal-gamma prior. The Gibbs sampling technique for the joint posterior distribution with equal prior precision for both the unrestricted and restricted models is used to obtain the model estimates. The result shows that the Bayes factor gave more support to the unrestricted model against the restricted and was consistent irrespective of changes in sample size.

Uncertainty of prior and posterior model probability: Implications for interpreting Bayes factors

2021 ◽  
Author(s):  
John K. Kruschke
Keyword(s):  
Posterior Distribution ◽  
Bayesian Model ◽  
Model Comparison ◽  
Bayes Factor ◽  
Bayes Factors ◽  
Prior Model ◽  
Bayesian Hypothesis Testing ◽  
Bayesian Model Comparison ◽  
Posterior Model Probability ◽  
Model Probability

In most applications of Bayesian model comparison or Bayesian hypothesis testing, the results are reported in terms of the Bayes factor only, not in terms of the posterior probabilities of the models. Posterior model probabilities are not reported because researchers are reluctant to declare prior model probabilities, which in turn stems from uncertainty in the prior. Fortunately, Bayesian formalisms are designed to embrace prior uncertainty, not ignore it. This article provides a novel derivation of the posterior distribution of model probability, and shows many examples. The posterior distribution is useful for making decisions taking into account the uncertainty of the posterior model probability. Benchmark Bayes factors are provided for a spectrum of priors on model probability. R code is posted at https://osf.io/36527/. This framework and tools will improve interpretation and usefulness of Bayes factors in all their applications.

The Maple Syrup Problem Revisited: MCMC with Gibbs Sampling

2019 ◽  
pp. 247-266
Author(s):  
Therese M. Donovan ◽  
Ruth M. Mickey
Keyword(s):  
Monte Carlo ◽  
Gibbs Sampling ◽  
Posterior Distribution ◽  
Unknown Parameter ◽  
The Other ◽  
Sampling Step ◽  
Maple Syrup ◽  
Two Parameters ◽  
Special Case ◽  
Joint Posterior Distribution

This chapter introduces Markov Chain Monte Carlo (MCMC) with Gibbs sampling, revisiting the “Maple Syrup Problem” of Chapter 12, where the goal was to estimate the two parameters of a normal distribution, μ‎ and σ‎. Chapter 12 used the normal-normal conjugate to derive the posterior distribution for the unknown parameter μ‎; the parameter σ‎ was assumed to be known. This chapter uses MCMC with Gibbs sampling to estimate the joint posterior distribution of both μ‎ and σ‎. Gibbs sampling is a special case of the Metropolis–Hastings algorithm. The chapter describes MCMC with Gibbs sampling step by step, which requires (1) computing the posterior distribution of a given parameter, conditional on the value of the other parameter, and (2) drawing a sample from the posterior distribution. In this chapter, Gibbs sampling makes use of the conjugate solutions to decompose the joint posterior distribution into full conditional distributions for each parameter.

scholarly journals From theories to models to predictions: A Bayesian model comparison approach

2017 ◽  
Author(s):  
Jeffrey Rouder ◽  
Julia M. Haaf ◽  
Frederik Aust
Keyword(s):  
Statistical Models ◽  
Bayesian Model ◽  
Model Comparison ◽  
Bayes Factor ◽  
Significance Testing ◽  
Bayesian Model Comparison ◽  
Comparison Approach ◽  
Competing Models ◽  
Competing Hypotheses

A key goal in research is to use data to assess competing hypotheses or theories. Analternative to the conventional significance testing is Bayesian model comparison. The mainidea is that competing theories are represented by statistical models. In the Bayesianframework, these models then yield predictions about data even before the data are seen.How well the data match the predictions under competing models may be calculated, andthe ratio of these matches—the Bayes factor—is used to assess the evidence for one modelcompared to another. We illustrate the process of going from theories to models and topredictions in the context of two hypothetical examples about how exposure to media affectsattitudes toward refugees.

The Survivor Problem: Simple Linear Regression with MCMC

2019 ◽  
pp. 269-307
Author(s):  
Therese M. Donovan ◽  
Ruth M. Mickey
Keyword(s):  
Linear Regression ◽  
Gibbs Sampling ◽  
Formal Education ◽  
Predictive Distribution ◽  
Simple Linear Regression ◽  
Posterior Predictive Distribution ◽  
Reality Show ◽  
The Relationship ◽  
Joint Posterior Distribution

While one of the most common uses of Bayes’ Theorem is in the statistical analysis of a dataset (i.e., statistical modeling), this chapter examines another application of Gibbs sampling: parameter estimation for simple linear regression. In the “Survivor Problem,” the chapter considers the relationship between how many days a contestant lasts in a reality-show competition as a function of how many years of formal education they have. This chapter is a bit more complicated than the previous chapter because it involves estimation of the joint posterior distribution of three parameters. As in earlier chapters, the estimation process is described in detail on a step-by-step basis. Finally, the posterior predictive distribution is estimated and discussed. By the end of the chapter, the reader will have a firm understanding of the following concepts: linear equation, sums of squares, posterior predictive distribution, and linear regression with Markov Chain Monte Carlo and Gibbs sampling.

scholarly journals BAYESIAN ESTIMATION AND AN APPLICATION OF GIBBS SAMPLING TECHNIQUE AND RANDOM WALK METROPOLIS - HASTING ALGORITHM IN TWO PHASE LINEAR REGRESSION MODEL

2021 ◽  
pp. 76-80
Author(s):  
Maitreya N. Acharya
Keyword(s):  
Random Walk ◽  
Linear Regression ◽  
Regression Model ◽  
Bayesian Estimation ◽  
Gibbs Sampling ◽  
Linear Regression Model ◽  
Sampling Technique ◽  
Two Phase ◽  
Random Walk Metropolis ◽  
Metropolis Hasting Algorithm

Here, in this research paper, we have applied the Gibbs Sampling Technique and RWM-H (Random Walk Metropolis - Hasting) Algorithm for the Bayesian Estimation of m, β1, β2 and 1/2. Also we have assumed that at some point of time say 'm', the co-efficient of regression changes from β1 to β2. Further, we have discussed about the effects of prior information on the Bayes estimates on the basis of the TPLR (Two Phase Linear Regression) Model with a Bayesian approach.

scholarly journals MCMC and GLMs for estimating regression parameters

2019 ◽  
Vol 2 (1) ◽  
pp. 46-55
Author(s):  
Mahmoud ELsayed ◽  
Amr Soliman
Keyword(s):  
Linear Regression ◽  
Decision Maker ◽  
Gibbs Sampling ◽  
Posterior Distribution ◽  
R Package ◽  
Investment Strategy ◽  
Mcmc Method ◽  
Content Type ◽  
Regression Parameters ◽  
Alternative Techniques

Purpose The purpose of this study is to estimate the linear regression parameters using two alternative techniques. First technique is to apply the generalized linear model (GLM) and the second technique is the Markov Chain Monte Carlo (MCMC) method. Design/methodology/approach In this paper, the authors adopted the incurred claims of Egyptian non-life insurance market as a dependent variable during a 10-year period. MCMC uses Gibbs sampling to generate a sample from a posterior distribution of a linear regression to estimate the parameters of interest. However, the authors used the R package to estimate the parameters of the linear regression using the above techniques. Findings These procedures will guide the decision-maker for estimating the reserve and set proper investment strategy. Originality/value In this paper, the authors will estimate the parameters of a linear regression model using MCMC method via R package. Furthermore, MCMC uses Gibbs sampling to generate a sample from a posterior distribution of a linear regression to estimate parameters to predict future claims. In the same line, these procedures will guide the decision-maker for estimating the reserve and set proper investment strategy.

The Contribution of Sexual Identity Towards the Students’ Perception of Lesbian, Gay, Bisexual, and Transgender

10.32698/0642 ◽  
2019 ◽  
Vol 2 (2) ◽  
pp. 120
Author(s):  
Wiwi Delfita ◽  
Neviyarni S. ◽  
Riska Ahmad
Keyword(s):  
Regression Analysis ◽  
Linear Regression ◽  
Sexual Identity ◽  
Student Perceptions ◽  
Undergraduate Students ◽  
Linear Regression Analysis ◽  
Sampling Technique ◽  
Simple Linear Regression ◽  
Simple Linear Regression Analysis ◽  
Bisexual And Transgender

Some students perceive lesbian, gay, bisexual, and transgender (LGBT) positively, even though LGBT is a sexual deviation that is not appropriate with values and norms. There are several factors that influence an individual's perception of LGBT, including sexual identity. This study aims at looking at the contribution of sexual identity to student perceptions about LGBT. This research used a quantitative approach with a descriptive method and a simple linear regression analysis. The sample of this research was 385 taken from 15.752 undergraduate students of Universitas Negeri Padang which the sample was drawn by using the Slovin formula and continued with a Proportional Random Sampling technique. The instrument used was the Guttman model's sexual identity scale and the scale of students' perceptions of the LGBT Likert model. After analyzing the data with the descriptive technique and the simple linear regression analysis, the results showed that sexual identity significantly contributed to the students' perceptions of LGBT. This research has implications as a basis for counselors to help students avoid sexual identity mismatches and prevent the emergence of positive perceptions of LGBT.

Analisis Pengaruh Kepemimpinan dan Komunikasi Terhadap Motivasi dan Kinerja Pegawai (Satuan Polisi Pamong Praja Kota Surabaya)

2017 ◽  
Vol 2 (1) ◽  
Author(s):  
Muhammad Rodhiyallah ◽  
Amiartuti Kusmaningtyas ◽  
Hendro Tjahjono
Keyword(s):  
Linear Regression ◽  
Multiple Linear Regression ◽  
Sampling Technique ◽  
Employee Motivation ◽  
Leadership Communication ◽  
Dominant Effect ◽  
And Performance

The aim of the study was to analyze and determine the influence of leadership and communication, on employee motivation and performance at Satuan Polisi Pamong Praja Kota Surabaya. Branch, as many as 100 persons. Sampling technique samples (Slovin) data was analyzed with multiple linear regression with SPSS for windows program. The result of the research indicated that leadership, communication, and motivation simultaneously have significant effect on employees’ performances with determination value of 0,424 or 4,24%. Leadership, communication and motivation partially has significant effect on performance. Communication itself has dominant effect on employee’s performance.

PENGARUH INTELLECTUAL CAPITAL TERHADAP KINERJA KEUANGAN PADA PERUSAHAAN BARANG KONSUMSI YANG TERDAFTAR DI BEI TAHUN 2015-2017

2019 ◽  
Vol 3 (2) ◽  
pp. 26
Author(s):  
Niken Ayu Wulandari ◽  
Tegoeh Hari Abrianto ◽  
Edi Santoso
Keyword(s):  
Regression Analysis ◽  
Linear Regression ◽  
Financial Performance ◽  
Intellectual Capital ◽  
Stock Exchange ◽  
Linear Regression Analysis ◽  
Sampling Technique ◽  
Simple Linear Regression ◽  
Return On Equity ◽  
Asset Turnover

This research to analyze and evaluate intellectual capital on financial performance obtained by return on equity, asset turnover and growth in revenue. The population in this study are consumer goods companies listed on the Stock Exchange in 2015-2017. The research sample was received by 21 companies obtained by using purposive sampling technique. The analytical method used is simple linear regression analysis with the SPSS version 20 application and uses the VAICTM method to measure intellectual capital. The results of this study indicate that intellectual capital has a significant effect on financial performance generated by return on equity, but intellectual capital does not have a significant effect on financial performance required by asset turnover and growth in revenue.

Pengaruh Kualitas Produk, Kepuasan Pelanggan, Hambatan Beralih Dan Kepercayaan Merek Terhadap Retensi Pelanggan Wardah Kosmetik Di Kabupaten Klaten

2020 ◽  
Vol 17 (2) ◽  
Author(s):  
Amelia Galuh Werdaningrum ◽  
Faizal Ardiyanto
Keyword(s):  
Linear Regression ◽  
Customer Satisfaction ◽  
Multiple Linear Regression ◽  
Product Quality ◽  
Sampling Method ◽  
Customer Retention ◽  
Sampling Technique ◽  
Brand Trust ◽  
Probability Sampling ◽  
Switching Barriers

This research aims to determine the effect of product quality, customer satisfaction, switching barriers, and brand trust on customer retention. The sample in this research was 116 respondents of Wardah Cosmetics customers from Klaten Regency. This research used one of non probability sampling technique which is purposive sampling method. This study is also using multiple linear regression to analyze the collected data. The results in this research are product quality, customer satisfaction, switching barriers, and brand influence customer retention both partially and simultaneously.

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