• Journal of the Korean Statistical Society
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• v.31 no.1
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• pp.63-75
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• 2002

Most attempts at Bayesian analysis of neural networks involve hierarchical modeling. We believe that similar results can be obtained with simpler models that require less computational effort, as long as appropriate restrictions are placed on parameters in order to ensure propriety of posterior distributions. In particular, we adopt a model first introduced by Lee (1999) that utilizes an improper prior for all parameters. Straightforward Gibbs sampling is possible, with the exception of the bias parameters, which are embedded in nonlinear sigmoidal functions. In addition to the problems posed by nonlinearity, direct sampling from the posterior distributions of the bias parameters is compounded due to the duplication of hidden nodes, which is a source of multimodality. In this regard, we focus on sampling from the marginal posterior distribution of the bias parameters with Markov chain Monte Carlo methods that combine traditional Metropolis sampling with a slice sampler described by Neal (1997, 2001). The methods are illustrated with data examples that are largely confined to the analysis of nonparametric regression models.

• Communications for Statistical Applications and Methods
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• v.29 no.4
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• pp.471-486
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• 2022

Autoregressive moving average (ARMA) models involve nonlinearity in the model coefficients because of unobserved lagged errors, which complicates the likelihood function and makes the posterior density analytically intractable. In order to overcome this problem of posterior analysis, some approximation methods have been proposed in literature. In this paper we first review the main analytic approximations proposed to approximate the posterior density of ARMA models to be analytically tractable, which include Newbold, Zellner-Reynolds, and Broemeling-Shaarawy approximations. We then use the Kullback-Leibler divergence to study the relation between these three analytic approximations and to measure the distance between their derived approximate posteriors for ARMA models. In addition, we evaluate the impact of the approximate posteriors distance in Bayesian estimates of mean and precision of the model coefficients by generating a large number of Monte Carlo simulations from the approximate posteriors. Simulation study results show that the approximate posteriors of Newbold and Zellner-Reynolds are very close to each other, and their estimates have higher precision compared to those of Broemeling-Shaarawy approximation. Same results are obtained from the application to real-world time series datasets.

• Journal of Dental Rehabilitation and Applied Science
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• v.17 no.4
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• pp.283-305
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• 2001

The purpose of this study was to analyze the stress distribution of condylar regions and edentulous mandible with implant-supported cantilever prostheses on the certain conditions, such as amount of load, location of load, direction of load, fixation or non-fixation on the condylar regions. Three dimensional finite element analysis was used for this study. FEM model was created by using commercial software, ANSYS(Swanson, Inc., U.S.A.). Fixed model which was fixed on the condylar regions was modeled with 74323 elements and 15387 nodes and spring model which was sprung on the condylar regions was modeled with 75020 elements and 15887 nodes. Six Br${\aa}$nemark implants with 3.75 mm diameter and 13 mm length were incorporated in the models. The placement was 4.4 mm from the midline for the first implant; the other two in each quardrant were 6.5 mm apart. The stress distribution on each model through the designed mandible was evaluated under 500N vertical load, 250N horizontal load linguobuccally, buccal 20 degree 250N oblique load and buccal 45 degree 250N oblique load. The load points were at 0 mm, 10 mm, 20 mm along the cantilever prostheses from the center of the distal fixture. The results were as follows; 1. The stress distribution of condylar regions between two models showed conspicuous differences. Fixed model showed conspicuous stress concentration on the condylar regions than spring model under vertical load only. On the other hand, spring model showed conspicuous stress concentration on the condylar regions than fixed model under 250N horizontal load linguobuccally, buccal 20 degree 250N oblique load and buccal 45 degree 250N oblique load. 2. Fixed model showed stress concentration on the posterior and mesial side of working and balancing condylar necks but spring model showed stress concentration on the posterior and mesial side of working condylar neck and the posterior and lateral side of balancing condylar neck under vertical load. 3. Fixed model showed stress concentration on the posterior and lateral side of working condylar neck and the anterior and mesial side of balancing condylar neck but spring model showed stress concentration on the anterior sides of working and balancing condylar necks under horizontal load linguobuccally. 4. Fixed model showed stress concentration on the posterior side of working condylar neck and the posterior and lateral side of balancing condylar neck but spring model showed stress concentration on the anterior side of working condylar neck and the anterior and lateral side of balancing condylar neck under buccal 20 degree oblique load. 5. Fixed model showed stress concentration on the anterior and lateral side of working condylar neck and the posterior and mesial side of balancing condylar neck but spring model showed stress concentration on the anterior side of working condylar neck and the anterior and lateral side of balancing condylar neck under buccal 45 degree oblique load.. 6. The stress distribution of bone around implants between two models revealed difference slightly. In general, magnitude of Von Mises stress was the greatest at the bone around the most distal implant and the progressive decrease more and more mesially. Under vertical load, the stress values were similar between implant neck and superstructure vertically, besides the greatest on the distal side horizontally. 7. Under horizontal load linguobuccally, buccal 20 degree oblique load and buccal 45 degree oblique load, the stress values were the greatest on the implant neck vertically, and great on the labial and lingual sides horizontally. After all, it was considered that spring model was an indispensable condition for the comprehension of the stress distributions of condylar regions.

• Journal of the Korean Data and Information Science Society
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• v.22 no.2
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• pp.361-369
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• 2011

In this paper, we develop the reference and the matching priors for the reliability function of two-parameter exponential distribution. We derive the reference priors and the matching prior, and prove the propriety of joint posterior distribution under the general prior including the reference priors and the matching prior. Through the sim-ulation study, we show that the proposed reference priors match the target coverage probabilities in a frequentist sense.

• Journal of the Korean Statistical Society
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• v.32 no.3
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• pp.289-298
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• 2003

We consider the estimation problem for the scale parameter of the Rayleigh distribution using weighted balanced loss function (WBLF) which reflects both goodness of fit and precision. Under WBLF, we obtain the optimal estimator which creates a kind of balance between Bayesian and non-Bayesian estimation. We also deal with the estimation of R ＝ P(Y < X) when Y and X are two independent but not identically distributed Rayleigh distribution under squared error loss function.

• The Journal of Korean Academy of Prosthodontics
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• v.36 no.6
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• pp.878-887
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• 1998

Although attachments have been utilized for a retainer of removable prostheses during several decades, there is little information on the force distribution by the attachments. This study was undertaken to evaluate the stress patterns developed by partial dentures employing rigid attachments on the supporting structures. Four types of the mandibular removable partial dentures were designed depending upon the position of the rigid attachment and the existency of lingual bracing. Under 100N of vertical and 25N of lateral loads on the 1st and 2nd lower molar of partial denture, stress distribution patterns and displacement were analysed with three dimensional finite element method by ANSYS version 5.3. 1. The highest stresses were concentrated on the distal alveolar crest of posterior abutment and the second stresses on the apical region of posterior abutment in the models. 2. The greatest displacement were shown on the distal alveolar crest of posterior abutment and the second displacement on the distal alveolar crest of anterior abutment in the models. 3. There was little difference between the models with intraoral attachment and those with extracoronal attachment. 4. There was little difference between the models with and without the lingual bracing.

• Structural Engineering and Mechanics
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• v.37 no.4
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• pp.427-442
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• 2011

In fatigue life design of mechanical components, uncertainties arising from materials and manufacturing processes should be taken into account for ensuring reliability. A common practice is to apply a safety factor in conjunction with a physics model for evaluating the lifecycle, which most likely relies on the designer's experience. Due to conservative design, predictions are often in disagreement with field observations, which makes it difficult to schedule maintenance. In this paper, the Bayesian technique, which incorporates the field failure data into prior knowledge, is used to obtain a more dependable prediction of fatigue life. The effects of prior knowledge, noise in data, and bias in measurements on the distribution of fatigue life are discussed in detail. By assuming a distribution type of fatigue life, its parameters are identified first, followed by estimating the distribution of fatigue life, which represents the degree of belief of the fatigue life conditional to the observed data. As more data are provided, the values will be updated to reduce the credible interval. The results can be used in various needs such as a risk analysis, reliability based design optimization, maintenance scheduling, or validation of reliability analysis codes. In order to obtain the posterior distribution, the Markov Chain Monte Carlo technique is employed, which is a modern statistical computational method which effectively draws the samples of the given distribution. Field data of turbine components are exploited to illustrate our approach, which counts as a regular inspection of the number of failed blades in a turbine disk.

• Journal of The Korean Society of Integrative Medicine
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• v.5 no.4
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• pp.1-9
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• 2017

Purpose : This study was conducted among 195 adults in their 20s. To analyze the impact of the slope types of the scapulae on the plantar surface of the foot, the average pressure (AP), the maximum pressure (MP), the average of local distribution values, and the average movement of the center of pressure (COP) of the different slope types of the scapulae were compared. Method : The anterior-posterior slopes of the scapulae were measured by comparing the slopes of the left and right sides of the scapulae based on the differences in the height and the slope of the coracoid process and the angulus inferior scapulae. Those whose left side of the scapulae had an anterior slope were categorized as type 1, and those whose right side of the scapulae had an anterior slope, as type 2. The average plantar pressure, the center of plantar pressure, the maximum plantar pressure, and local distribution values were analyzed using a plantar pressure analyzer of the FSA. Result : In terms of the AP of the left and right feet, there was no statistically significant difference both in types 1 and 2 on the left and right feet. The comparison results of the MP and the average of local distribution values of the two slope types of the scapulae showed that there was no statistically significant difference on the X-axis both in types 1 and 2 on the left and right feet, but that there was a large statistically significant difference on the Y-axis both in types 1 and 2. That is, the MP of the right foot of the left anterior slope type was located more on the hindfoot than that of the right anterior slope type, and the MP of the left foot of the left anterior slope type was located more on the hindfoot than that of right anterior slope type. Conclusion : This study can be used as fundamental data to predict differences in the location and size of the COP and changes in plantar pressure distribution depending on the slope types of the scapulae, and control the distribution for therapeutic purposes.

• The Journal of Advanced Prosthodontics
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• v.8 no.4
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• pp.304-312
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• 2016

PURPOSE. The aim of this study was to investigate the stress distribution of 2-short implants (2SIs) installed in a severely atrophic maxillary molar site. MATERIALS AND METHODS. Three different diameters of internal connection implants were modeled: narrow platform (NP), regular platform (RP), and wide platform (WP). The maxillary first molars were restored with one implant or two short implants. Three 2SI models (NP-oblique, NP-vertical, and NP-horizontal) and four single implant models (RP and WP in a centered or cantilevered position) were used. Axial and oblique loadings were applied on the occlusal surface of the crown. The von Mises stress values were measured at the bone-implant, peri-implant bone, and implant/abutment complex. RESULTS. The highest stress distribution at the bone-implant interface and the peri-implant bone was noticed in the RP group, and the lowest stress distribution was observed in the 2SI groups. Cantilevered position showed unfavorable stress distribution with axial loading. 2SI types did not affect the stress distribution in oblique loading. The number and installation positions of the implant, rather than the bone level, influenced the stress distribution of 2SIs. The implant/abutment complex of WP presented the highest stress concentration while that of 2SIs showed the lowest stress concentration. CONCLUSION. 2SIs may be useful for achieving stable stress distribution on the surrounding bone and implant-abutment complex in the atrophic posterior maxilla.

• IEIE Transactions on Smart Processing and Computing
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• v.4 no.4
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• pp.202-208
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• 2015

In this study, we propose a new inference algorithm for a multiclass Gaussian process classification model using a variational EM framework and the Laplace approximation (LA) technique. This is performed in two steps, called expectation and maximization. First, in the expectation step (E-step), using Bayes' theorem and the LA technique, we derive the approximate posterior distribution of the latent function, indicating the possibility that each observation belongs to a certain class in the Gaussian process classification model. In the maximization step, we compute the maximum likelihood estimators for hyper-parameters of a covariance matrix necessary to define the prior distribution of the latent function by using the posterior distribution derived in the E-step. These steps iteratively repeat until a convergence condition is satisfied. Moreover, we conducted the experiments by using synthetic data and Iris data in order to verify the performance of the proposed algorithm. Experimental results reveal that the proposed algorithm shows good performance on these datasets.