• Journal of the Korean Statistical Society
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• 제24권1호
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• pp.31-44
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• 1995

In fitting a model, there always exists a discrepancy between the fitted model and the true functional relationship. In measuring this discrepancy, Box and Drapper (1959) used the criterion dividing the discrepancy into two parts which are the bias error part and the variance error one in single response case. In this paper, an optimum design which makes these two types of errors as small as possible is found by extending the Box and Drapper criterion to multiple response situation. Especially, a design is found to meat rotatability conditions when we fit a quadratic model to each response fearing cubic bias. Using the central composite design, an application of general results to a specific case is shown to help understanding the material.

• Journal of International Society for Simulation Surgery
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• 제2권1호
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• pp.26-32
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• 2015

Purpose When a surgeon examines the morphology of skull of patient, locations of craniometric landmarks of 3D computed tomography(CT) volume are one of the most important information for surgical purpose. The locations of craniometric landmarks can be found manually by surgeon from the 3D rendered volume or 2D sagittal, axial, and coronal slices which are taken by CT. Since there are many landmarks on the skull, finding these manually is time-consuming, exhaustive, and occasionally inexact. These inefficiencies raise a demand for a automatic localization technique for craniometric landmark points. So in this paper, we propose a novel method through which we can automatically find these landmark points, which are useful for surgical purpose. Materials and Methods At first, we align the experimental data (CT volumes) using Frankfurt Horizontal Plane (FHP) and Mid Sagittal Plane(MSP) which are defined by 3 and 2 cranial landmark points each. The target landmark of our experiment is the anterior nasal spine. Prior to constructing a statistical cubic model which would be used for detecting the location of the landmark from a given CT volume, reference points for the anterior nasal spine were manually chosen by a surgeon from several CT volume sets. The statistical cubic model is constructed by calculating weighted intensity means of these CT sets around the reference points. By finding the location where similarity function (squared difference function) has the minimal value with this model, the location of the landmark can be found from any given CT volume. Results In this paper, we used 5 CT volumes to construct the statistical cubic model. The 20 CT volumes including the volumes, which were used to construct the model, were used for testing. The range of age of subjects is up to 2 years (24 months) old. The found points of each data are almost close to the reference point which were manually chosen by surgeon. Also it has been seen that the similarity function always has the global minimum at the detection point. Conclusion Through the experiment, we have seen the proposed method shows the outstanding performance in searching the landmark point. This algorithm would make surgeons efficiently work with morphological informations of skull. We also expect the potential of our algorithm for searching the anatomic landmarks not only cranial landmarks.

• Journal of the Korean Statistical Society
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• 제30권4호
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• pp.645-660
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• 2001

In this paper we propose a goodness-of-fit test statistic for testing the (null) parametric model versus the (alternative) nonparametric model. Most of existing nonparametric test statistics are based on the residuals which are obtained by regressing the data to a parametric model. Our test is based on the bootstrap estimator of the probability that the smoothing parameter estimator is infinite when fitting residuals to cubic smoothing spline. Power performance of this test is investigated and is compared with many other tests. Illustrative examples based on real data sets are given.

• Asian Pacific Journal of Cancer Prevention
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• 제14권3호
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• pp.2097-2100
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• 2013

Background: To estimate the numbers and trends in cervix cancer cases visiting the Radiotherapy Department at Manipal Teaching Hospital, Pokhara, Nepal, statistical modelling from retrospective data was applied. Materials and Methods: A retrospective study was carried out on data for a total of 159 patients treated for cervix cancer at Manipal Teaching Hospital, Pokhara, Nepal, between $28^{th}$ September 2000 and $31^{st}$ December 2008. Theoretical statistics were used for statistical modelling and forecasting. Results: Using curve fitting method, Linear, Logarithmic, Inverse, Quadratic, Cubic, Compound, Power and Exponential growth models were validated. Including the constant term, none of the models fit the data well. Excluding the constant term, the cubic model demonstrated the best fit, with $R^2$=0.871 (p=0.004). In 2008, the observed and estimated numbers of cases were same (12). According to our model, 273 patients with cervical cancer are expected to visit the hospital in 2015. Conclusions: Our data predict a significant increase in cervical cancer cases in this region in the near future. This observation suggests the need for more focus and resource allocation on cervical cancer screening and treatment.

• Communications for Statistical Applications and Methods
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• 제9권3호
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• pp.799-808
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• 2002

This paper aims at selecting the multi-response design with γ responses minimizing the bias error caused by fitting inadequate models to responses, where the first order models are fitted to Ρ responses fearing the quadratic bias, while to other γ- Ρ responses, the quadratic models are fitted fearing the cubic biases in the cuboidal region of interest. Under the assumption of symmetric design, by minimizing the criterion which represents the amount of error caused by fitting inadequate models, the optimum design was found to be the one having the design moments of second order and the fourth order as 1/3 and l/5, respectively. Examples of the design meeting the required conditions are given for illustration.

• Steel and Composite Structures
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• 제42권4호
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• pp.477-487
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• 2022

The shear stiffness of headed-stud shear connectors has no unified definition due to the nonlinear characteristics of its load-slip relationship. A unified framework was firstly adopted to develop a general expression of shear load-slip equation for headed-stud shear connectors varying in a large parameter range based on both force and energy balance. The pre- and post-yield shear stiffness were then determined through bilinear idealization of proposed shear load-slip equation. An updated and carefully selected push-out test database of 157 stud shear connectors, conducting on studs 13~30mm in diameter and on concretes 30~180 MPa in cubic compressive strength, was used for model regression and sensitivity analysis of shear stiffness. An empirical calculation model was also established for the stud shear stiffness. Compared with the previous models through statistical analysis, the proposed model demonstrates a better performance to predict the shear load-slip response and stiffness of the stud shear connectors.

• Communications for Statistical Applications and Methods
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• 제30권1호
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• pp.95-107
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• 2023

Purpose: The statistical analysis of point processes on linear networks is a recent area of research that studies processes of events happening randomly in space (or space-time) but with locations limited to reside on a linear network. For example, traffic accidents happen at random places that are limited to lying on a network of streets. This paper applies techniques developed for point processes on linear networks and the tools available in the R-package spatstat to estimate the intensity of traffic accidents in Leon County, Florida. Methods: The intensity of accidents on the linear network of streets is estimated using log-linear Poisson models which incorporate cubic basis spline (B-spline) terms which are functions of the x and y coordinates. The splines used equally-spaced knots. Ten different models are fit to the data using a variety of covariates. The models are compared with each other using an analysis of deviance for nested models. Results: We found all covariates contributed significantly to the model. AIC and BIC were used to select 9 as the number of knots. Additionally, covariates have different effects such as increasing the speed limit would decrease traffic accident intensity by 0.9794 but increasing the number of lanes would result in an increase in the intensity of traffic accidents by 1.086. Conclusion: Our analysis shows that if other conditions are held fixed, the number of accidents actually decreases on roads with higher speed limits. The software we currently use allows our models to contain only spatial covariates and does not permit the use of temporal or space-time covariates. We would like to extend our models to include such covariates which would allow us to include weather conditions or the presence of special events (football games or concerts) as covariates.

• Bulletin of the Korean Chemical Society
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• 제12권3호
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• pp.334-342
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• 1991

To investigate the phase equilibria and structural properties of microemulsions, we study a simple phenomenological model on the basis of the cubic lattice cell with which the oil- and water-filled cells are connected one another, respectively. The surfactant is assumed to be insoluble in both oil and water, and to be adsorbed at the oil-water interface. The Schulman condition, according to which the lateral pressure of the surfactant layer is compensated by the oil-water interfacial tension, is found to hold to good approximation in the middle-phase microemulsion. Our results show that the oil- and water-filled domains in that microemulsion are about 50-150 $\AA$ across, and depend sensitively on the curvature parameters. The phase diagram is not symmetric in this model. It may be asymmetrized intrinsically by non-equivalency of oil and water. The two- and tree-phase equilibria including critical points and critical endpoints are found.

• Journal of Biosystems Engineering
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• 제20권4호
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• pp.333-342
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• 1995

The resistance to air flow through fruits and vegetables in bulk was an important consideration in the design of the pressure cooling system. The amount of resistance to air flow through produce in bulk normally depended upon air flow rate, stacking depth, porosity, stacking patterns and shape and site of product. But, there was not enough information relating the effects of those factors on air flow resistance. The objectives of this study were to investigate the effect of stacking depth, stacking patterns, porosity and airflow rate on airflow resistance and to develop a statistical model to predict static pressure drop across the produce bed as a function of air flow rate, stacking depth, bed porosity, and product size. Mandarins and tomatoes were used in the experiment. The airflow rate were in the range of 0.1~1.0 ㎥/s.$m^2$, the porosity were in the range of 0.25~0.45, the depth were in the range of 0.3~0.9m and the equivalent diameters were 5.3cm and 6.3cm for mandarins, and 6.5cm and 8.5cm for tomatoes. Three methods of stacking arrangement were used i.e. cubic, square staggered, and staggered stacking arrangement. The results were summarized as follows. 1. The pressure drops across produce bed increased in proportion to stacking depth and superficial air velocity and decreased in proportion to porosity. 2. The increasing rates of pressure drop according to stacking patterns with the increase of superficial air velocity were different one another. The staggered stacking arrangement produced the highest increasing rate and the cubic stacking arrangement produced the lowest increasing rate. But it could be assumed that the stacking patterns had not influenced greatly on pressure drops if it was of equal porosity. 3. The statistical models to predict the pressure drop across produce bed as a function of superficial air velocity, stacking depth, porosity, and product diameter were developed from these experiments.

• Journal of Microbiology and Biotechnology
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• 제15권1호
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• pp.197-201
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• 2005

A novel chitinase-producing bacterial strain of Pantoea dispersa was isolated from the sea near Bhavnagar, India for efficient disposal of chitinous waste from the seafood processing industry. The medium components were optimized by using a cubic model in the central composite design for increasing chitinase production. The optimal concentrations for higher production of chitinase were (g l-1) chitin, 10.0; urea, 0.35; MgSO4 7H2O, 0.08, and CaCl2, 0.15. Here, peptone (0.05 g l-1) was used as a constant variant in all trials. Using a statistical optimization method, the chitinase production was found to increase from 108 to 486.4 units ml-1. Chitin was prepared from the crustacean waste, and Fourier Transform Infrared (FTIR) Spectroscopy was used to characterize the isolated chitin. Chitinous waste degradation was studied in terms of chitinase production.