scholarly journals Penalized likelihood estimation of a trivariate additive probit model

Biostatistics ◽  
2017 ◽  
Vol 18 (3) ◽  
pp. 569-585 ◽  
Author(s):  
Panagiota Filippou ◽  
Giampiero Marra ◽  
Rosalba Radice
Keyword(s):  
Penalized Likelihood ◽  
Trust Region ◽  
Correlation Coefficients ◽  
Likelihood Estimation ◽  
Probit Model ◽  
R Package ◽  
Likelihood Method ◽  
Spatial Effects ◽  
Trust Region Algorithm ◽  
Smoothing Parameter Selection

SUMMARY This article proposes a penalized likelihood method to estimate a trivariate probit model, which accounts for several types of covariate effects (such as linear, nonlinear, random, and spatial effects), as well as error correlations. The proposed approach also addresses the difficulty in estimating accurately the correlation coefficients, which characterize the dependence of binary responses conditional on covariates. The parameters of the model are estimated within a penalized likelihood framework based on a carefully structured trust region algorithm with integrated automatic multiple smoothing parameter selection. The relevant numerical computation can be easily carried out using the SemiParTRIV() function in a freely available R package. The proposed method is illustrated through a case study whose aim is to model jointly adverse birth binary outcomes in North Carolina.

scholarly journals An optical model for deriving the spectral particulate backscattering coefficients in oceanic waters

Ocean Science ◽  
2013 ◽  
Vol 9 (6) ◽  
pp. 987-1001 ◽  
Author(s):  
S. P. Tiwari ◽  
P. Shanmugam
Keyword(s):  
Optical Model ◽  
Trust Region ◽  
Simulated Data ◽  
Correlation Coefficients ◽  
Least Square Method ◽  
Least Square ◽  
Data Set ◽  
New Model ◽  
Trust Region Algorithm ◽  
In Situ Data

Abstract. An optical model is developed based on the diffuse attenuation coefficient (Kd) to estimate particulate backscattering coefficients bbp(λ) in oceanic waters. A large in situ data set is used to establish robust relationships between bbp(530) and bbp(555) and Kd(490) using an efficient nonlinear least-square method which uses the trust region algorithm with Bisquare weights scheme to adjust the coefficients. These relationships are obtained with good correlation coefficients (R2 = 0.786 and 0.790), low root mean square error (RMSE = 0.00076 and 0.00072) and 95% confidence bounds. The new model is tested with three independent data sets: the NOMAD SeaWiFS Match ups, OOXIX IOP algorithm workshop evaluation data set (Version 2.0w APLHA), and IOCCG simulated data set. Results show that the new model makes good retrievals of bbp at all key wavelengths (from 412–683 nm), with statistically significant improvements over other inversion models. Thus, the new model has the potential to improve our present knowledge of particulate matter and their optical variability in oceanic waters.

scholarly journals An optical model for deriving the spectral particulate backscattering coefficients in clear and turbid coastal waters

2013 ◽  
Vol 10 (1) ◽  
pp. 261-290
Author(s):  
S. P. Tiwari ◽  
P. Shanmugam
Keyword(s):  
Coastal Waters ◽  
Optical Model ◽  
Trust Region ◽  
Correlation Coefficients ◽  
Least Square Method ◽  
Least Square ◽  
Data Set ◽  
New Model ◽  
Trust Region Algorithm ◽  
In Situ Data

Abstract. An optical model is developed based on the diffuse attenuation coefficient (Kd) to estimate particulate backscattering coefficients bbp(λ) in clear and turbid coastal waters. A large in-situ data set is used to establish robust relationships between bbp(530) and bbp(555) and Kd(490) using an efficient nonlinear least square method which uses the Trust-Region algorithm with Bisquare weights scheme to adjust the coefficients. These relationships are obtained with good correlation coefficients (R2 = 0.786 and 0.790), low Root Mean Square Error (RMSE = 0.00076 and 0.00072) and 95% confidence bounds. The new model is tested with two independent data sets such as the NOMAD SeaWiFS Match-ups and OOXIX IOP algorithm workshop evaluation data set (Version 2.0w APLHA). Results show that the new model makes good retrievals of bbp at all key wavelengths (from 412–683 nm), with statistically significant improvements over other inversion models. Thus, the new model has the potential to improve our knowledge of particulate matters and their optical variability in both clear and turbid coastal waters.

Estimating the Cost of Car Warranty in Indonesia using the Gertsbakh-Kordonsky Method

2020 ◽  
Vol 2 (1) ◽  
pp. 33-40
Author(s):  
Anggis Sagitarisman ◽  
Aceng Komarudin Mutaqin
Keyword(s):  
Maximum Likelihood ◽  
Likelihood Estimation ◽  
Type A ◽  
Claim Data ◽  
Likelihood Method ◽  
Selling Price ◽  
One Dimensional ◽  
Warranty Period ◽  
Kolmogorov Smirnov ◽  
Warranty Costs

AbstractCar manufacturers in Indonesia need to determine reasonable warranty costs that do not burden companies or consumers. Several statistical approaches have been developed to analyze warranty costs. One of them is the Gertsbakh-Kordonsky method which reduces the two-dimensional warranty problem to one dimensional. In this research, we apply the Gertsbakh-Kordonsky method to estimate the warranty cost for car type A in XYZ company. The one-dimensional data will be tested using the Kolmogorov-Smirnov to determine its distribution and the parameter of distribution will be estimated using the maximum likelihood method. There are three approaches to estimate the parameter of the distribution. The difference between these three approaches is in the calculation of mileage for units that do not claim within the warranty period. In the application, we use claim data for the car type A. The data exploration indicates the failure of car type A is mostly due to the age of the vehicle. The Kolmogorov-Smirnov shows that the most appropriate distribution for the claim data is the three-parameter Weibull. Meanwhile, the estimated using the Gertsbakh-Kordonsky method shows that the warranty costs for car type A are around 3.54% from the selling price of this car unit without warranty i.e. around Rp. 4,248,000 per unit.Keywords: warranty costs; the Gertsbakh-Kordonsky method; maximum likelihood estimation; Kolmogorov-Smirnov test.                                   AbstrakPerusahaan produsen mobil di Indonesia perlu menentukan biaya garansi yang bersifat wajar tidak memberatkan perusahaan maupun konsumen. Beberapa pendekatan statistik telah dikembangkan untuk menganalisis biaya garansi. Salah satunya adalah metode Gertsbakh-Kordonsky yang mereduksi masalah garansi dua dimensi menjadi satu dimensi. Pada penelitian ini, metode Gertsbakh-Kordonsky akan digunakan untuk mengestimasi biaya garansi untuk mobil tipe A pada perusahaan XYZ. Data satu dimensi hasil reduksi diuji kecocokan distribusinya menggunakan uji kecocokan Kolmogorov-Smirnov dan taksiran parameter distribusinya menggunakan metode penaksir kemungkinan maksimum. Ada tiga pendekatan yang digunakan untuk menaksir parameter distribusi. Perbedaan dari ketiga pendekatan tersebut terletak pada perhitungan jarak tempuh untuk unit yang tidak melakukan klaim dalam periode garansi. Sebagai bahan aplikasi, kami menggunakan data klaim unit mobil tipe A. Hasil eksplorasi data menunjukkan bahwa kegagalan mobil tipe A lebih banyak disebabkan karena faktor usia kendaraan. Hasil uji kecocokan distribusi untuk data hasil reduksi menunjukkan bahwa distribusi yang cocok adalah distribusi Weibull 3-parameter. Sementara itu, hasil perhitungan taksiran biaya garansi menunjukan bahwa taksiran biaya garansi untuk unit mobil tipe A sekitar 3,54% dari harga jual unit mobil tipe A tanpa garansi, atau sekitar Rp. 4.248.000,- per unit.Kata Kunci: biaya garansi; metode Gertsbakh-Kordonsky; penaksiran kemungkinan maksimum; uji Kolmogorov-Smirnov.

scholarly journals stochprofML: stochastic profiling using maximum likelihood estimation in R

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Lisa Amrhein ◽  
Christiane Fuchs
Keyword(s):  
Maximum Likelihood ◽  
Cell Fate ◽  
Likelihood Estimation ◽  
R Package ◽  
Cell Populations ◽  
Simulation Studies ◽  
Likelihood Principle ◽  
Maximum Likelihood Principle ◽  
Molecular Expression ◽  
Mixed Samples

Abstract Background Tissues are often heterogeneous in their single-cell molecular expression, and this can govern the regulation of cell fate. For the understanding of development and disease, it is important to quantify heterogeneity in a given tissue. Results We present the R package stochprofML which uses the maximum likelihood principle to parameterize heterogeneity from the cumulative expression of small random pools of cells. We evaluate the algorithm’s performance in simulation studies and present further application opportunities. Conclusion Stochastic profiling outweighs the necessary demixing of mixed samples with a saving in experimental cost and effort and less measurement error. It offers possibilities for parameterizing heterogeneity, estimating underlying pool compositions and detecting differences between cell populations between samples.

scholarly journals Modeling and Fault Diagnosis of Interturn Short Circuit for Five-Phase Permanent Magnet Synchronous Motor

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Jian-wei Yang ◽  
Man-feng Dou ◽  
Zhi-yong Dai
Keyword(s):  
Parameter Estimation ◽  
Fault Diagnosis ◽  
Permanent Magnet ◽  
Fault Tolerant ◽  
Short Circuit ◽  
Estimation Method ◽  
Trust Region ◽  
Fault Tolerant Control ◽  
Trust Region Algorithm ◽  
Parameter Estimation Method

Taking advantage of the high reliability, multiphase permanent magnet synchronous motors (PMSMs), such as five-phase PMSM and six-phase PMSM, are widely used in fault-tolerant control applications. And one of the important fault-tolerant control problems is fault diagnosis. In most existing literatures, the fault diagnosis problem focuses on the three-phase PMSM. In this paper, compared to the most existing fault diagnosis approaches, a fault diagnosis method for Interturn short circuit (ITSC) fault of five-phase PMSM based on the trust region algorithm is presented. This paper has two contributions. (1) Analyzing the physical parameters of the motor, such as resistances and inductances, a novel mathematic model for ITSC fault of five-phase PMSM is established. (2) Introducing an object function related to the Interturn short circuit ratio, the fault parameters identification problem is reformulated as the extreme seeking problem. A trust region algorithm based parameter estimation method is proposed for tracking the actual Interturn short circuit ratio. The simulation and experimental results have validated the effectiveness of the proposed parameter estimation method.

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