Bayesian analysis of a sensitive proportion for a small area

윤원영,Balgobin Nandram,김달호 한국데이터정보과학회 2019 한국데이터정보과학회지 Vol.30 No.6

When respondents are asked to answer sensitive questions, they are more likely to response untruthfully as they hesitate to expose their identity. Warner (1965) proposed a randomized design that uses a randomization device that is designed to conceal individual response and protect the respondent privacy, to reduce the response bias that can be generated through this. After that, numerous survey designs to reduce the response bias were proposed, and various estimation and simulation methods were studied from the Bayesian perspective. This study proposes an analysis method that has taken account of small-area to minimize the posterior standard deviation of sensitive proportions in a survey with sensitive questions. Then it compares the results between the individual model and the small-area model through the simulation. In addition, this study applies the two models which has and has not considered the small-area to the actual survey with sensitive questionnaires related to the organizational commitment to the experienced employees. This study confirms the results based on real data.

Bayesian test of homogenity in small areas: A discretization approach

김민섭,Balgobin Nandram,김달호 한국데이터정보과학회 2017 한국데이터정보과학회지 Vol.28 No.6

This paper studies Bayesian test of homogeneity in contingency tables made by discretizing a continuous variable. Sometimes when we are considering events of interest in small area setup, we can think of discretization approaches about the continuous variable. If we properly discretize the continuous variable, we can find invisible relationships between areas (groups) and a continuous variable of interest. The proper discretization of the continuous variable can support the alternative hypothesis of the homogeneity test in contingency tables even if the null hypothesis was not rejected through k-sample tests involving one-way ANOVA. In other words, the proportions of variables with a particular level can vary from group to group by the discretization. If we discretize the the continuous variable, it can be treated as an analysis of the contingency table. In this case, the chi-squared test is the most commonly employed method. However, further discretization gives rise to more cells in the table. As a result, the count in the cells becomes smaller and the accuracy of the test becomes lower. To prevent this, we can consider the Bayesian approach and apply it to the setup of the homogeneity test.

Hierarchical Bayesian pattern mixture models for binary data from small area

안수경,Balgobin Nandram,김달호 한국데이터정보과학회 2019 한국데이터정보과학회지 Vol.30 No.6

The purpose of many surveys is to estimate the probability of a group having certain characteristics. However, if the survey has a lot of missing data, we may get incorrect results. So a lot of research has been done on missing data since the past. There are many methods to handle missing data, so it is better to use various methods than one. We estimate the proportion of finite population using the Bayesian method using the pattern mixture model for binary data. We consider a hierarchical Bayesian model to increase the reliability of small data. We have applied various cases on the hyperparameter of the prior distribution of proportion for nonresponse to confirm that the proportion estimate is not sensitive. We also confirmed that small area estimation is better than the individual area estimation.

Hierarchical Bayesian Inference of Binomial Data with Nonresponse

Han, Geunshik,Nandram, Balgobin The Korean Statistical Society 2002 Journal of the Korean Statistical Society Vol.31 No.1

We consider the problem of estimating binomial proportions in the presence of nonignorable nonresponse using the Bayesian selection approach. Inference is sampling based and Markov chain Monte Carlo (MCMC) methods are used to perform the computations. We apply our method to study doctor visits data from the Korean National Family Income and Expenditure Survey (NFIES). The ignorable and nonignorable models are compared to Stasny's method (1991) by measuring the variability from the Metropolis-Hastings (MH) sampler. The results show that both models work very well.

Bayesian pattern mixture model under nonignorable nonresponse for binary data

Sukyoung An,Balgobin Nandram,Dal Ho Kim 한국데이터정보과학회 2019 한국데이터정보과학회지 Vol.30 No.4

We consider a Bayesian pattern mixture model to estimate the proportion of the finite population with missing data. The pattern mixture approach is a way to model missing data. We describe the Bayesian model considering two cases for the parameter of a prior distribution. To fit the model, we use Markov chain Monte Carlo methods. We use the Gibbs sampler with grid method to get the samples of the parameters. We use the National Crime Survey data summarized by Stasny (1991) to estimate the proportion of the finite population. When considering two cases of the parameter of a prior distribution, we saw that the inference for the parameter was not sensitive in our proposed model.

Nonparametric Bayesian test of homogeneity using a discretization approach

MinSup Kim,Balgobin Nandram,Dal Ho Kim 한국데이터정보과학회 2018 한국데이터정보과학회지 Vol.29 No.1

In this paper, we consider nonparametric Bayesian test of homogeneity using a hierarchical multinomial model with Dirichlet process priors in small area setup. If we discretize a continuous variable properly, the discretization approach could find some association between the groups and the variable even if the groups are homogeneous through k-sample tests involving one-way ANOVA. It could also be used to look at heterogeneity at specific levels of the variable of interest among groups. We use the clustering by the k-means and Dirichlet process to discretize the continuous variable. When we discretize the continuous variable, it can be treated as an analysis of the contingency table. Then the chi-squared test is the most common thought. If more slices are added, however, chi-squared test is less accurate. So we use the Bayes factor through the nonparmetric Bayesian model and apply it to the test of homogeneity.

Bayesian analysis of a sensitive proportion

WonYoung Yun,Balgobin Nandram,Dal Ho Kim 한국데이터정보과학회 2019 한국데이터정보과학회지 Vol.30 No.4

Respondents tend to answer untruthfully when they are asked to response sensitive questions, as they are reluctant to expose their identity. In order to reduce the response bias that can be generated through this, Warner (1965) proposed a randomized design which uses a randomization device that conceals individual response and protects the respondent. Thereafter, various survey designs to reduce the response bias were proposed, and Bayesian estimation and simulation methods have also been studied. This study proposes an analysis method to reduce posterior standard deviations of the sensitive proportions in a survey with sensitive questions and compare the results with the existing analyzes through the simulation. In addition, this study applies the proposed analysis method to the actual survey with the sensitive questionnaires related to the organizational commitment to the experienced employees.

Bayesian test of homogenity in small areas: A discretization approach

Kim, Min Sup,Nandram, Balgobin,Kim, Dal Ho The Korean Data and Information Science Society 2017 한국데이터정보과학회지 Vol.28 No.6

This paper studies Bayesian test of homogeneity in contingency tables made by discretizing a continuous variable. Sometimes when we are considering events of interest in small area setup, we can think of discretization approaches about the continuous variable. If we properly discretize the continuous variable, we can find invisible relationships between areas (groups) and a continuous variable of interest. The proper discretization of the continuous variable can support the alternative hypothesis of the homogeneity test in contingency tables even if the null hypothesis was not rejected through k-sample tests involving one-way ANOVA. In other words, the proportions of variables with a particular level can vary from group to group by the discretization. If we discretize the the continuous variable, it can be treated as an analysis of the contingency table. In this case, the chi-squared test is the most commonly employed method. However, further discretization gives rise to more cells in the table. As a result, the count in the cells becomes smaller and the accuracy of the test becomes lower. To prevent this, we can consider the Bayesian approach and apply it to the setup of the homogeneity test.

Asymptotic equivalence between frequentist and Bayesian prediction limits for the Poisson distribution

Bejleri Valbona,Sartore Luca,Nandram Balgobin 한국통계학회 2022 Journal of the Korean Statistical Society Vol.51 No.3

Bayesian prediction limits are constructed based on some maximum allowed probability of wrong prediction. However, the frequency of wrong prediction in a long run often exceeds this probability. The literature on frequentist and Bayesian prediction limits, and their interpretation is sparse; more attention is given to prediction intervals obtained based on parameter estimates or empirical studies. Under the Poisson distribution, we investigate frequentist properties of Bayesian prediction limits derived from conjugate priors. The frequency of wrong prediction is used as a criterion for their comparison. Bayesian prediction based on the uniform and Jeffreys’ non-informative priors yield one sided prediction limits that can be interpreted in a frequentist context. It is shown here, by proving a theorem, that Bayesian lower prediction limit derived from Jeffreys’ noninformative prior is the only optimal (largest) Bayesian lower prediction limit that possesses frequentist properties. In addition, it is concluded as corollary that there is no prior distribution such that Bayesian upper and lower prediction limits obtained from it will both coincide with their respective frequentist prediction limits. Our results are based on asymptotic considerations. An example with real data is included, and the sensitivity of the Bayesian prediction limits with respect to conjugate priors is numerically explored through simulations.

Marginal Likelihoods for Bayesian Poisson Regression Models

Kim, Hyun-Joong,Balgobin Nandram,Kim, Seong-Jun,Choi, Il-Su,Ahn, Yun-Kee,Kim, Chul-Eung The Korean Statistical Society 2004 Communications for statistical applications and me Vol.11 No.2

The marginal likelihood has become an important tool for model selection in Bayesian analysis because it can be used to rank the models. We discuss the marginal likelihood for Poisson regression models that are potentially useful in small area estimation. Computation in these models is intensive and it requires an implementation of Markov chain Monte Carlo (MCMC) methods. Using importance sampling and multivariate density estimation, we demonstrate a computation of the marginal likelihood through an output analysis from an MCMC sampler.