Sampling Truncated Normal, Beta, and Gamma Densities

Damien, Paul; Walker, Stephen G.

doi:10.1198/10618600152627906

Cited by 92 publications

(88 citation statements)

References 10 publications

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“…In addition to the sampling methods based on rejection sampling and Gibbs sampler, there are other methods including techniques based on the slice sampler (Neal (2003)), see Damien and Walker (2001) and Liechty and Lu (2010). In a recent paper, Yu and Tian (2011) propose methods using EM algorithm and a non-iterative inverse Bayes formulae sampling procedure.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Efficient Sampling Methods for Truncated Multivariate Normal and Student-tDistributions Subject to Linear Inequality Constraints

Ghosh

2015

Journal of Statistical Theory and Practice

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Sampling from a truncated multivariate distribution subject to multiple linear inequality constraints is a recurring problem in many areas in statistics and econometrics, such as the order restricted regressions, censored data models, and shape-restricted nonparametric regressions. However, the sampling problem remains non-trivial due to the analytically intractable normalizing constant of the truncated multivariate distribution. We first develop an efficient rejection sampling method for the truncated univariate normal distribution, and analytically establish its superiority in terms of acceptance rates compared to some of the popular existing methods. We then extend our methodology to obtain samples from a truncated multivariate normal distribution subject to convex polytope restriction regions. Finally, we generalize the sampling method to truncated multivariate Student-t distributions. Empirical results are presented to illustrate the superior performance of our proposed Gibbs sampler in terms of various criteria (e.g., accuracy, mixing and convergence rate).

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Section: Conclusion and Discussionmentioning

confidence: 99%

Efficient Sampling Methods for Truncated Multivariate Normal and Student-tDistributions Subject to Linear Inequality Constraints

Ghosh

2015

Journal of Statistical Theory and Practice

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“…Thus, it is necessary to consider an index that identifies an individual's situation in each category c. In this section, we propose a new measure of subjective well-being. We calculate the following probability r (z i |γ c , y i ), which denotes the difference between 12 We can utilize the method proposed by Damien and Walker (2001) for sampling truncated normal variables.…”

Section: New Measure Of Subjective Well-beingmentioning

confidence: 99%

Measuring inequality of subjective well-being: A Bayesian approach

Hasegawa

Ueda

2011

The Journal of Socio-Economics

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This article proposes a new measure for inequality of subjective wellbeing and shows the empirical results using a Bayesian ordered probit model. We introduce a new concept called "regret" as a measure for inequality of subjective well-being. Regret is the probability with which a respondent who chooses an option in a multiple-choice question pertaining to subjective well-being does not choose any other option indicative of better well-being. Regret is estimated in connection with demographic factors using the Markov chain Monte Carlo (MCMC) method and data of the World Values Survey. Furthermore, the relationships between regret and GDP per capita and the changes therein are shown to investigate those between inequality of subjective well-being and economic conditions.

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“…We can utilize Damien and Walker's (2001) algorithm for sampling from a truncated normal distribution.…”

Section: A Derivation Of Algorithm 1 A1 Fcd Of ϕmentioning

confidence: 99%

Bayesian Dynamic Panel-Ordered Probit Model and Its Application to Subjective Well-Being

Hasegawa

2009

Communications in Statistics - Simulation and Computation

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Sampling Truncated Normal, Beta, and Gamma Densities

Cited by 92 publications

References 10 publications

Efficient Sampling Methods for Truncated Multivariate Normal and Student-tDistributions Subject to Linear Inequality Constraints

Efficient Sampling Methods for Truncated Multivariate Normal and Student-tDistributions Subject to Linear Inequality Constraints

Measuring inequality of subjective well-being: A Bayesian approach

Bayesian Dynamic Panel-Ordered Probit Model and Its Application to Subjective Well-Being

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