• Journal of the Korean Statistical Society
• /
• v.25 no.3
• /
• pp.359-368
• /
• 1996

The maximum likelihood estimation is discussed for the NLAR model with Laplacian marginals. Since the explicit form of the estimates cannot be obtained due to the complicated nature of the likelihood function we utilize the automatic computer optimization subroutine using a direct search complex algorithm. The conditional least square estimates are used as initial estimates in maximum likelihood procedures. The results of a simulation study for the maximum likelihood estimates of the NLAR(1) and the NLAR(2) models are presented.

• Proceedings of the Korean Statistical Society Conference
• /
• 2000.11a
• /
• pp.193-200
• /
• 2000

Modelling the dependence via random effects in censored multivariate survival data has recently received considerable attention in the biomedical literature. The random effects models model not only the conditional survival times but also the conditional hazard rate. Systematic likelihood inference for the models with random effects is possible using Lee and Nelder's (1996) hierarchical-likelihood (h-likelihood). The purpose of this presentation is to introduce Ha et al.'s (2000a,b) inferential methods for the random effects models via the h-likelihood, which provide a conceptually simple, numerically efficient and reliable inferential procedures.

• Communications for Statistical Applications and Methods
• /
• v.16 no.6
• /
• pp.971-978
• /
• 2009

Poisson generalized linear mixed models(GLMMs) have been widely used for the analysis of clustered or correlated count data. For the inference marginal likelihood, which is obtained by integrating out random effects is often used. It gives maximum likelihood(ML) estimator, but the integration is usually intractable. In this paper, we propose how to obtain the ML estimator via Laplace approximation based on hierarchical-likelihood (h-likelihood) approach under the Poisson GLMMs. In particular, the h-likelihood avoids the integration itself and gives a statistically efficient procedure for various random-effect models including GLMMs. The proposed method is illustrated using two practical examples and simulation studies.

• Proceedings of the Korea Water Resources Association Conference
• /
• 2021.06a
• /
• pp.127-127
• /
• 2021

In order to estimate parameter uncertainty of hydrological models, the consideration of the likelihood functions which provide reliable parameters of model is necessary. In this study, the Bayesian Markov Chain Monte Carlo (MCMC) method with informal likelihood functions is used to analyze the uncertainty of parameters of the SURR model for estimating the hourly streamflow of Gunnam station of Imjin basin, Korea. Three events were used to calibrate and one event was used to validate the posterior distributions of parameters. Moreover, the performance of four informal likelihood functions (Nash-Sutcliffe efficiency, Normalized absolute error, Index of agreement, and Chiew-McMahon efficiency) on uncertainty of parameter is assessed. The indicators used to assess the uncertainty of the streamflow simulation were P-factor (percentage of observed streamflow included in the uncertainty interval) and R-factor (the average width of the uncertainty interval). The results showed that the sensitivities of parameters strongly depend on the likelihood functions and vary for different likelihood functions. The uncertainty bounds illustrated the slight differences from various likelihood functions. This study confirms the importance of the likelihood function selection in the application of Bayesian MCMC to the uncertainty assessment of the SURR model.

• Journal of The Geomorphological Association of Korea
• /
• v.25 no.2
• /
• pp.1-14
• /
• 2018

The main objective of this paper is to classify properties of the locational environment for each debris type by calculating likelihood ratio based on the correlation between the distributions for each type of debris landform. A total of 8 thematic maps, like as elevation, slope, aspect, curvature, topographic wetness index (TWI), soil drainage, geology, and landcover including with GIS spatial information generally used in this type of debris landform analysis. The results of this study showed that the block stream had a high likelihood ratio compared to talus in areas with relatively high elevation; and concerning slope, the block stream had a high likelihood ratio in a relatively low region than talus. Concerning aspect, a clear correlation could not be analyzed for each debristype, and concerning curvature, the block stream displayed a developed slope on the more concave valley than the talus. Analysis concerning TWI, the block stream displayed a higher likelihood ratio in wider sections than talus, and concerning soil drainage, the talus and block stream both displayed a high likelihood ratio in regions with well-drained soil. The talus displayed a high likelihood ratio in the order of metamorphic rocks, sedimentary rocks, and granite, while the block stream displayed a high likelihood ratio in the order of volcanic rocks, granite, and sedimentary rocks. In addition, concerning landcover, the likelihood ratio had the most concentrated distributed compared to natural bare land only concerning talus. Based on the likelihood ratio result, it can be used as basic data for extracting the possible areas of distribution for each debris type through the GIS spatial integration method.

• MALSORI
• /
• no.51
• /
• pp.71-84
• /
• 2004

In this paper, we propose the automatic speech database verification method(or called automatic verification) based on confidence measure for a large speech database. This method verifies the consistency between given transcription and speech using the confidence measure. The automatic verification process consists of two stages : the word-level likelihood computation stage and multi-level likelihood ratio computation stage. In the word-level likelihood computation stage, we calculate the word-level likelihood using the viterbi decoding algorithm and make the segment information. In the multi-level likelihood ratio computation stage, we calculate the word-level and the phone-level likelihood ratio based on confidence measure with anti-phone model. By automatic verification, we have achieved about 61% error reduction. And also we can reduce the verification time from 1 month in manual to 1-2 days in automatic.

• Journal of the Korean Statistical Society
• /
• v.26 no.3
• /
• pp.397-405
• /
• 1997

Recently maximum likelihood estimators using unconditional likelihood function are used for testing unit roots. When one wants to use this method the determinant term of initial values in the multivariate unconditional likelihood function produces a complicated function of the elements in the coefficient matrix and variance matrix. In this paper an approximation of the determinant term is calculated and based on this aproximation an approximated unconditional likelihood function is calculated. The approximated unconditional maximum likelihood estimators can be used to test for unit roots. When multivariate process has one unit root the limiting distribution obtained by this method and the limiting distribution using exact unconditional likelihood function are the same.

• Proceedings of the Korean Statistical Society Conference
• /
• 2003.05a
• /
• pp.79-84
• /
• 2003

Likelihood estimation in random-effect models is often complicated because the marginal likelihood involves an analytically intractable integral. Numerical integration such as Gauss-Hermite quadrature is an option, but is generally not recommended when the dimensionality of the integral is high. An alternative is the use of hierarchical likelihood, which avoids such burdensome numerical integration. These two approaches for fitting binary data are compared and the advantages of using the hierarchical likelihood are discussed. Random-effect models for binary outcomes and for bivariate binary-continuous outcomes are considered.

• Communications for Statistical Applications and Methods
• /
• v.23 no.6
• /
• pp.563-574
• /
• 2016

In this study, we propose several simultaneous tests to detect the difference between means and variances for the two-sample problem when the underlying distribution is normal. For this, we apply the likelihood ratio principle and propose a likelihood ratio test. We then consider a union-intersection test after identifying the likelihood statistic, a product of two individual likelihood statistics, to test the individual sub-null hypotheses. By noting that the union-intersection test can be considered a simultaneous test with combination function, also we propose simultaneous tests with combination functions to combine individual tests for each sub-null hypothesis. We apply the permutation principle to obtain the null distributions. We then provide an example to illustrate our proposed procedure and compare the efficiency among the proposed tests through a simulation study. We discuss some interesting features related to the simultaneous test as concluding remarks. Finally we show the expression of the likelihood ratio statistic with a product of two individual likelihood ratio statistics.

• Communications for Statistical Applications and Methods
• /
• v.15 no.6
• /
• pp.969-976
• /
• 2008

Mixed linear models have been widely used in various correlated data including multivariate survival data. In this paper we extend hierarchical-likelihood(h-likelihood) approach for mixed linear models with right censored data to that for left censored data. We also allow a general random-effect structure and propose the estimation procedure. The proposed method is illustrated using a numerical data set and is also compared with marginal likelihood method.