• Journal of the Korean Data and Information Science Society
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• v.14 no.2
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• pp.385-391
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• 2003

A sequence of n Bernoulli trials which violates the constant success probability assumption is termed as "Poisson trials". In this paper, the recurrence formula for the r-th central moment of number of successes with n Poisson trials is derived. Romanovsky's method, based on the differentiation of characteristic function, is used in the derivation of recurrence formula for the central moments of conventional binomial distribution. Romanovsky's method is applied to that of Poisson trials in this paper. Some central moment calculation results are given to compare the central moments of Poisson trials with those of conventional binomial distribution.

• Communications for Statistical Applications and Methods
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• v.30 no.3
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• pp.291-309
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• 2023

Longitudinal count data has been widely collected in biomedical research, public health, and clinical trials. These repeated measurements over time on the same subjects need to account for an appropriate dependency. The Poisson regression model is the first choice to model the expected count of interest, however, this may not be an appropriate when data exhibit over-dispersion or under-dispersion. Recently, Conway-Maxwell-Poisson (CMP) distribution is popularly used as the distribution offers a flexibility to capture a wide range of dispersion in the data. In this article, we propose a Bayesian CMP regression model to accommodate over and under-dispersion in modeling longitudinal count data. Specifically, we develop a regression model with random intercept and slope to capture subject heterogeneity and estimate covariate effects to be different across subjects. We implement a Bayesian computation via Hamiltonian MCMC (HMCMC) algorithm for posterior sampling. We then compute Bayesian model assessment measures for model comparison. Simulation studies are conducted to assess the accuracy and effectiveness of our methodology. The usefulness of the proposed methodology is demonstrated by a well-known example of epilepsy data.

• Journal of Veterinary Clinics
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• v.28 no.1
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• pp.101-107
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• 2011

This study aimed to determine dose-response (DR) curve of avian influenza (AI) virus to predict the probability of illness or adverse health effects that may result from exposure to a pathogenic microorganism in a quantitative microbial risk assessment. To determine the parametric DR relationship of several strains of AI virus, 7 feeding trial data sets challenging humans (5 sets) and chickens (2 sets) for strains of H3N2 (4 sets), H5N1 (2 sets) and H1N1 (1 set) from the published literatures. Except for one data set (study with intra-tracheal inoculation for data set no. 6), all were obtained from the studies with intranasal inoculation. The data were analyzed using three types of DR model as the basis of heterogeneity in infectivity of AI strains in humans and chickens: exponential, beta-binomial and beta-Poisson. We fitted to the data using maximum likelihood estimation to get the parameter estimates of each model. The alpha and beta values of the beta-Poisson DR model ranged 0.06-0.19 and 1.7-48.8, respectively for H3N2 strain. Corresponding values for H5N1 ranged 0.464-0.563 and 97.3-99.4, respectively. For H1N1 the parameter values were 0.103 and 12.7, respectively. Using the exponential model, r (infectivity parameter) ranged from $1.6{\times}10^{-8}$ to $1.2{\times}10^{-5}$ for H3N2 and from $7.5{\times}10^{-3}$ to $4.0{\times}10^{-2}$ for H5N1, while the value was $1.6{\times}10^{-8}$ for H1N1. The beta-Poisson DR model provided the best fit to five of 7 data sets tested, and the estimated parameter values in betabinomial model were very close to those of beta-Poisson. Our study indicated that beta-binomial or beta-Poisson model could be the choice for DR modeling of AI, even though DR relationship varied depending on the virus strains studied, as indicated in prior studies. Further DR modeling should be conducted to quantify the differences among AI virus strains.

• Tunnel and Underground Space
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• v.16 no.4 s.63
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• pp.334-346
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• 2006

The discrete element code in 2-D, PFC2D, has been used as a tool to simulate various phenomena in rock mechanics and rock engineering. However, the code has an disadvantage that procedure to determine micro-parameters, namely properties of particles and contacts is repetitive and time-consuming. In this study, we analyzed the effect of micro-parameters(for generation of a contact-bonded model) on macro-properties(that were measured numerically by uniaxial compressive test). Based on the analysis, also, the time-saving and reliable method was suggested to determine a complete set of micro-parameters. In order to verify the suggested method, numerical specimens were generated in PFC2D for 10 different rock types at home and abroad. By the two trials for each specimen, in the result, the Young's modulus, Poisson's ratio and uniaxial compressive strength could be reproduced with being in relative error by about 5% to the values obtained by laboratory tests.

• Korean Journal of Ecology and Environment
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• v.39 no.1 s.115
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• pp.110-118
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• 2006

The Namyang Stream in Hwaong polder was planned for several water uses including recreation, where people can contact the water and consume some amount during the recreational activity. A human health risk was assessed from exposure to E. coli in the Namyang Stream, which receives partially treated wastewater from watershed. The QUAL2E model was applied to simulate stream water quality, and this model was calibrated and verified with field monitoring data. The calibration result showed a high correlation coefficient of greater than 0.9. The mean concentration of E. coli in the Namyang Stream from the QUAL2E output was in the range of 5,000 ${\sim}$ 8,000 MPN 100 mL^{-1}$, which exceeded national and international guidelines. The Beta-Poisson was used to estimate the microbial risk of pathogens ingestion and the Monte-Carlo analysis (10,000 trials) was used to estimate the risk characterization of uncertainty. The Microbial risk assessment showed that the risk ranged from 7.9 ${\times}\;10^{-6}\;to\;9.4\;{\times}10^{-6}$. Based on USEPA guidelines, the range of $10^{-6}\;to\;10^{-8}$ was considered reasonable levels of risk for communicable disease transmission from environmental exposure, and the risk above $10^{-4}$ was considered to be in the danger of infection. Therefore, water quality of the Namyang Stream might not be in the danger of infection although it exceeded national and international guidelines. However, it was in the range of communicable disease transmission, and thorough wastewater collection and treatment at the source is recommended to secure safe recreation water quality.

• Korean Journal of Ecology and Environment
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• v.38 no.2 s.112
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• pp.225-236
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• 2005

The protection of public health In wastewater reclamation and reuse is one of the most important issues. Monitoring data of Escherichia coli were collected from paddy rice plots in 2003 and 2004 experiments. Five treatments were used and each one was triplicated to evaluate the changes of E. coli: surface water, biofilter effluent (secondary level), UV-disinfected water and pond treatment. Microbial risk was quantified to assess human health risk by exposure to E. coli in paddy rice plots, which were irrigated with reclaimed wastewater. Beta-Poisson model was used to estimate the microbial risk of pathogen ingestion that may occur to farmer and neighbor children. Monte-Carlo analysis (10,000 trials) was used to estimate the risk characterization of uncertainty. In the following analysis, two scenarios were related to the reduction of risk against direct ingestion and exposure times. Scenarios A and B were assumed that the risk was 1,000 and 10,000 times lower than direct ingestion.'Golfers were assumed to be 0.001 L of reclaimed water by contact with balls and their cloths. Opportunity of contact in paddy rice field with pathogens was more frequent than handing golf balls, because of agricultural activity was practiced in ponded water in paddy rice culture. As a result of microbial risk assessment using total data of experimental period, risk value of E. coli in 2003 and 2004 experiment ranged from $10^{-5}$ to $10^{-8}$ and $10^{-4}$ to $10^{-8}$, respectively. The risk values in biofilter effluent irrigation was the highest, which is $10^{-4}$ in 2003 and $10^{-5}$ in 2004 experiments with scenario A. Ranges of $10^{-6}$ to $10^{-8}$ were considered at reasonable levels of risk for communicable disease transmission from environmental exposure and the risk value above $10^{-4}$ was considered to be attributable to the risk of infection. Irrigation with UV-disinfected water in the paddy field during the agricultural Period showed significantly lower microbial risk than others, and their levels of risk value were within the range of actual paddy rice field with surface water.

• Journal of Wetlands Research
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• v.16 no.3
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• pp.327-336
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• 2014

Submerged thin walls are extreme case of submerged rectangular blocks, and could be used for many purposes in rivers or coastal zones, e.g. to tsunami. To understand flow characteristics including flow and pressure fields around a specific submerged thin wall a numerical model was applied which includes computation of hydrodynamic pressure on ${\sigma}$-coordinate. ${\sigma}$-coordinate has strong merits for simulation of subcritical flow over mild-sloped beds. On the other hand ${\sigma}$-coordinate is quite poor to treat sharp structures on the bed. There have been a few trials to incorporate dynamic pressure in ${\sigma}$-coordinate by some researchers. One of the previous approaches includes process of sloving the Poisson equation. However, the above method includes many high-order terms, and requires long cpu for simulation. Another method SOLA was developed by Hirt et al. for computation of dynamic pressure, but it was valid for straight grid system only. Previous SOLA was modified for ${\sigma}$-coordinate for the present purpose and was adopted in a model system, CST3D. Computed flow field shows reasonable behaviour including vorticity is much stronger than the upstream and downstream of the structure. The model was verified to laboratory experiments at a 2DV flume. Time-average flow vectors were measured by using one-dimensional electro-magnetic velocimeter. Computed flow field agrees well with the measured flow field within 10 % error from the speed point of view at 5 profiles. It is thought that the modified SOLA scheme is useful for ${\sigma}$-coordinate system.