• Title/Summary/Keyword: Bayesian Statistics Theory

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Bayesian Model Selection in Analysis of Reciprocals

  • Kang, Sang-Gil;Kim, Dal-Ho;Cha, Young-Joon
    • Journal of the Korean Data and Information Science Society
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    • v.16 no.4
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    • pp.1167-1176
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    • 2005
  • Tweedie (1957a) proposed a method for the analysis of residuals from an inverse Gaussian population paralleling the analysis of variance in normal theory. He called it the analysis of reciprocals. In this paper, we propose a Bayesian model selection procedure based on the fractional Bayes factor for the analysis of reciprocals. Using the proposed model selection procedures, we compare with the classical tests.

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Design and Implementation of Travel Mode Choice Model Using the Bayesian Networks of Data Mining (데이터마이닝의 베이지안 망 기법을 이용한 교통수단선택 모형의 설계 및 구축)

  • Kim, Hyun-Gi;Kim, Kang-Soo;Lee, Sang-Min
    • Journal of Korean Society of Transportation
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    • v.22 no.2 s.73
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    • pp.77-86
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    • 2004
  • In this study, we applied the Bayesian Network for the case of the mode choice models using the Seoul metropolitan area's house trip survey Data. Sex and age were used lot the independent variables for the explanation or the mode choice, and the relationships between the mode choice and the travellers' social characteristics were identified by the Bayesian Network. Furthermore, trip and mode's characteristics such as time and fare were also used for independent variables and the mode choice models were developed. It was found that the Bayesian Network were useful tool to overcome the problems which were in the traditional mode choice models. In particular, the various transport policies could be evaluated in the very short time by the established relation-ships. It is expected that the Bayesian Network will be utilized as the important tools for the transport analysis.

Bayesian Model Selection in Analysis of Reciprocals

  • Kang, Sang-Gil;Kim, Dal-Ho
    • 한국데이터정보과학회:학술대회논문집
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    • 2005.10a
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    • pp.85-93
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    • 2005
  • Tweedie (1957a) proposed a method for the analysis of residuals from an inverse Gaussian population paralleling the analysis of variance in normal theory. He called it the analysis of reciprocals. In this paper, we propose a Bayesian model selection procedure based on the fractional Bayes factor for the analysis of reciprocals. Using the proposed model procedures, we compare with the classical tests.

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Understanding Bayesian Experimental Design with Its Applications (베이지안 실험계획법의 이해와 응용)

  • Lee, Gunhee
    • The Korean Journal of Applied Statistics
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    • v.27 no.6
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    • pp.1029-1038
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    • 2014
  • Bayesian experimental design is a useful concept in applied statistics for the design of efficient experiments especially if prior knowledge in the experiment is available. However, a theoretical or numerical approach is not simple to implement. We review the concept of a Bayesian experiment approach for linear and nonlinear statistical models. We investigate relationships between prior knowledge and optimal design to identify Bayesian experimental design process characteristics. A balanced design is important if we do not have prior knowledge; however, prior knowledge is important in design and expert opinions should reflect an efficient analysis. Care should be taken if we set a small sample size with a vague improper prior since both Bayesian design and non-Bayesian design provide incorrect solutions.

Hypotheses testing of Bayes' theorem for fuzzy prior parameters (퍼지 사전 모수에 관한 베이지안 가설검정)

  • Kang Man-Ki;Chio Gue-Tak
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • 2005.11a
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    • pp.205-208
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    • 2005
  • We have fuzzy hypotheses testing from Bayesian statistics with ideas from fuzzy sets theory to generalize Bayesian methods both for samples of fuzzy data and for prior distributions with non-precise parameters. Appling the principle of agreement index, the posterior odds ratio in the favor of hypotheses $H_0$ is equal to product of the fuzzy odds ratio and the fuzzy likelihood ratio. If the Posterior odds ratio exceeds the grade judgement, we accept the hypothesis $H_0$ for the degree.

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Bayesian analysis of financial volatilities addressing long-memory, conditional heteroscedasticity and skewed error distribution

  • Oh, Rosy;Shin, Dong Wan;Oh, Man-Suk
    • Communications for Statistical Applications and Methods
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    • v.24 no.5
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    • pp.507-518
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    • 2017
  • Volatility plays a crucial role in theory and applications of asset pricing, optimal portfolio allocation, and risk management. This paper proposes a combined model of autoregressive moving average (ARFIMA), generalized autoregressive conditional heteroscedasticity (GRACH), and skewed-t error distribution to accommodate important features of volatility data; long memory, heteroscedasticity, and asymmetric error distribution. A fully Bayesian approach is proposed to estimate the parameters of the model simultaneously, which yields parameter estimates satisfying necessary constraints in the model. The approach can be easily implemented using a free and user-friendly software JAGS to generate Markov chain Monte Carlo samples from the joint posterior distribution of the parameters. The method is illustrated by using a daily volatility index from Chicago Board Options Exchange (CBOE). JAGS codes for model specification is provided in the Appendix.

Collaborative CRM using Statistical Learning Theory and Bayesian Fuzzy Clustering

  • Jun, Sung-Hae
    • Communications for Statistical Applications and Methods
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    • v.11 no.1
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    • pp.197-211
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    • 2004
  • According to the increase of internet application, the marketing process as well as the research and survey, the education process, and administration of government are very depended on web bases. All kinds of goods and sales which are traded on the internet shopping malls are extremely increased. So, the necessity of automatically intelligent information system is shown, this system manages web site connected users for effective marketing. For the recommendation system which can offer a fit information from numerous web contents to user, we propose an automatic recommendation system which furnish necessary information to connected web user using statistical learning theory and bayesian fuzzy clustering. This system is called collaborative CRM in this paper. The performance of proposed system is compared with the other methods using real data of the existent shopping mall site. This paper shows that the predictive accuracy of the proposed system is improved by comparison with others.

Recent advances in Bayesian inference of isolation-with-migration models

  • Chung, Yujin
    • Genomics & Informatics
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    • v.17 no.4
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    • pp.37.1-37.8
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    • 2019
  • Isolation-with-migration (IM) models have become popular for explaining population divergence in the presence of migrations. Bayesian methods are commonly used to estimate IM models, but they are limited to small data analysis or simple model inference. Recently three methods, IMa3, MIST, and AIM, resolved these limitations. Here, we describe the major problems addressed by these three software and compare differences among their inference methods, despite their use of the same standard likelihood function.

Constrained Bayes and Empirical Bayes Estimator Applications in Insurance Pricing

  • Kim, Myung Joon;Kim, Yeong-Hwa
    • Communications for Statistical Applications and Methods
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    • v.20 no.4
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    • pp.321-327
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    • 2013
  • Bayesian and empirical Bayesian methods have become quite popular in the theory and practice of statistics. However, the objective is to often produce an ensemble of parameter estimates as well as to produce the histogram of the estimates. For example, in insurance pricing, the accurate point estimates of risk for each group is necessary and also proper dispersion estimation should be considered. Well-known Bayes estimates (which is the posterior means under quadratic loss) are underdispersed as an estimate of the histogram of parameters. The adjustment of Bayes estimates to correct this problem is known as constrained Bayes estimators, which are matching the first two empirical moments. In this paper, we propose a way to apply the constrained Bayes estimators in insurance pricing, which is required to estimate accurately both location and dispersion. Also, the benefit of the constrained Bayes estimates will be discussed by analyzing real insurance accident data.

A Bayesian Approach to Paired Comparison of Several Products of Poisson Rates

  • Kim Dae-Hwang;Kim Hea-Jung
    • Proceedings of the Korean Statistical Society Conference
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    • 2004.11a
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    • pp.229-236
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    • 2004
  • This article presents a multiple comparison ranking procedure for several products of the Poisson rates. A preference probability matrix that warrants the optimal comparison ranking is introduced. Using a Bayesian Monte Carlo method, we develop simulation-based procedure to estimate the matrix and obtain the optimal ranking via a row-sum scores method. Necessary theory and two illustrative examples are provided.

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