• Communications for Statistical Applications and Methods
• /
• v.9 no.3
• /
• pp.825-834
• /
• 2002

Poisson processes are widely used in reliability and survival analysis. In particular, multiple event time data in survival analysis are routinely analyzed by use of Poisson processes. In this paper, we consider large sample properties of nonparametric Bayesian models for Poisson processes. We prove that the posterior distribution of the cumulative intensity function of Poisson processes is consistent under regularity conditions on priors which are Levy processes.

• Korean Journal of Cognitive Science
• /
• v.20 no.3
• /
• pp.335-355
• /
• 2009

We examined risk judgment and the accuracy of inference based on two kinds of probabilities in a Bayesian inference task: the death probability from a disease (base rates) and the probability of having a disease with positive results in the screening test (posterior probabilities). Risk information were presented in either a probability or a frequency format. In Study 1, we found a numerical format effect for both base rate and posterior probability. Participants rated information as riskier and inferred more accurately in the frequency condition than in the probability condition for both base rate and posterior probability. However, there was no frequency range effect, which suggested that the ranges of frequency format did not influence risk ratings. In order to find out how the analytic thought system influences risk ratings, we compared the ratings of a computation condition and those of a no-computation condition and still found the numerical format effect in computation condition. In Study 2, we examined the numerical format effect and frequency range effect in a high and a low probability condition and found the numerical format effect at each probability level. This result suggests that people feel riskier in the frequency format than in the probability format regardless of the base rates and the posterior probability. We also found a frequency range effect only for the low base rate condition. Our results were discussed in terms of the dual process theories.

• The Journal of the Korea Contents Association
• /
• v.21 no.11
• /
• pp.77-86
• /
• 2021

A method of constructing a war simulation based on Bayesian Inference was proposed as a method of constructing heterogeneous historical war data obtained with a time difference into a single model. A method of applying a linear regression model can be considered as a method of predicting future battles by analyzing historical war results. However it is not appropriate for two heterogeneous types of historical data that reflect changes in the battlefield environment due to different times to be suitable as a single linear regression model and violation of the model's assumptions. To resolve these problems a Bayesian inference method was proposed to obtain a post-distribution by assuming the data from the previous era as a non-informative prior distribution and to infer the final posterior distribution by using it as a prior distribution to analyze the data obtained from the next era. Another advantage of the Bayesian inference method is that the results sampled by the Markov Chain Monte Carlo method can be used to infer posterior distribution or posterior predictive distribution reflecting uncertainty. In this way, it has the advantage of not only being able to utilize a variety of information rather than analyzing it with a classical linear regression model, but also continuing to update the model by reflecting additional data obtained in the future.

• Journal of the Korean Statistical Society
• /
• v.34 no.2
• /
• pp.85-98
• /
• 2005

A Bayesian analysis for the product of different powers of k independent Poisson rates, written ${\theta}$, is developed. This is done by considering a prior for ${\theta}$ that satisfies the differential equation due to Tibshirani and induces a proper posterior distribution. The Gibbs sampling procedure utilizing the rejection method is suggested for the posterior inference of ${\theta}$. The procedure is straightforward to specify distributionally and to implement computationally, with output readily adapted for required inference summaries. A salient feature of the procedure is that it provides a unified method for inferencing ${\theta}$ with any type of powers, and hence it solves all the existing problems (in inferencing ${\theta}$) simultaneously in a completely satisfactory way, at least within the Bayesian framework. In two examples, practical applications of the procedure is described.

• Journal of the Korean Data and Information Science Society
• /
• v.10 no.1
• /
• pp.119-133
• /
• 1999

A Markov Chain Monte Carlo method is developed to compute the software reliability model. We consider computation problem for determining of posterior distibution in Bayseian inference. Metropolis algorithms along with Gibbs sampling are proposed to preform the Bayesian inference of the Mixed model with record value statistics. For model determiniation, we explored the prequential conditional predictive ordinate criterion that selects the best model with the largest posterior likelihood among models using all possible subsets of the component intensity functions. To relax the monotonic intensity function assumptions. A numerical example with simulated data set is given.

• Nuclear Engineering and Technology
• /
• v.56 no.7
• /
• pp.2704-2710
• /
• 2024

Nuclear archaeology research provides scientific methods to reconstruct the operating histories of fissile material production facilities to account for past fissile material production. While it has typically focused on analyzing material in permanent reactor structures, spent fuel or high-level waste also hold information about the reactor operation. In this computational study, we explore a Bayesian inference framework for reconstructing the operational history from measurements of isotope ratios from a sample of nuclear waste. We investigate two different inference models. The first model discriminates between three potential reactors of origin (Magnox, PWR, and PHWR) while simultaneously reconstructing the fuel burnup, time since irradiation, initial enrichment, and average power density. The second model reconstructs the fuel burnup and time since irradiation of two batches of waste in a mixed sample. Each of the models is applied to a set of simulated test data, and the performance is evaluated by comparing the highest posterior density regions to the corresponding parameter values of the test dataset. Both models perform well on the simulated test cases, which highlights the potential of the Bayesian inference framework and opens up avenues for further investigation.

• Communications for Statistical Applications and Methods
• /
• v.22 no.6
• /
• pp.557-573
• /
• 2015

In this paper we develop a Bayesian inference for a multiplicative double seasonal autoregressive (DSAR) model by implementing a fast, easy and accurate Gibbs sampling algorithm. We apply the Gibbs sampling to approximate empirically the marginal posterior distributions after showing that the conditional posterior distribution of the model parameters and the variance are multivariate normal and inverse gamma, respectively. The proposed Bayesian methodology is illustrated using simulated examples and real-world time series data.

• Communications for Statistical Applications and Methods
• /
• v.14 no.1
• /
• pp.121-131
• /
• 2007

In this paper, we examine the problem of estimating the sensitive characteristics and behaviors in a multinomial randomized response model using Bayesian approach. We derived a posterior distribution for parameter of interest for multinomial randomized response model. Based on the posterior distribution, we also calculated a credible intervals and mean squared error (MSE). We finally compare the maximum likelihood estimator and the Bayes estimator in terms of MSE.

• 한국데이터정보과학회:학술대회논문집
• /
• 2005.10a
• /
• pp.27-34
• /
• 2005

We consider the problem of estimating the system reliability noninformative priors when both stress and strength follow generalized gamma distributions. We first derive Jeffreys' prior, group ordering reference priors, and matching priors. We investigate the propriety of posterior distributions and provide marginal posterior distributions under those noninformative priors. We also examine whether the reference priors satisfy the probability matching criterion.

• Communications for Statistical Applications and Methods
• /
• v.21 no.3
• /
• pp.261-274
• /
• 2014

In this paper we develop Bayes and empirical Bayes estimators of the finite population mean with the assumption of posterior linearity rather than normality of the superpopulation under the balanced loss function. We compare the performance of the optimal Bayes estimator with ones of the classical sample mean and the usual Bayes estimator under the squared error loss with respect to the posterior expected losses, risks and Bayes risks when the underlying distribution is normal as well as when they are binomial and Poisson.