Bayesian Estimation under Different Loss Functions Using Gamma Prior for the Case of Exponential Distribution

Hasan, Md. Rashidul; Baizid, Atikur Rahman

doi:10.3329/jsr.v1i1.29308

Cited by 10 publications

(10 citation statements)

References 3 publications

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“…This has been done particularly for LoR using the PR curve. The future work lies in modifying the algorithm for optimizing the loss function of the LoR classifier [21,22] to enhance the performance further compared to complex ML models.…”

Section: Discussionmentioning

confidence: 99%

Consensus of Feature Selection Methods and Reduced Generalization Gap Model to Improve Diagnosis of Heart Disease

Gupta¹,

Sedamkar²

2021

J. Sci. Res.

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Enhancing the diagnostic ability of Machine Learning models for acceptable prediction in the healthcare community is still a concern. There are critical care disease datasets available online on which researchers have experimented with a different number of instances and features for similar disease prediction. Further, different Machine Learning (ML) models have different preprocessing requirements. Framingham heart disease data is multicollinear and has missing values. Thus, the proposed model aims to explore the differential preprocessing needs of ML models followed by feature selection in consensus with domain experts and feature extraction to resolve multicollinearity issues. Missing values have been imputed differently for each feature. The work also identifies optimal train set size by plotting a learning curve that provides a minimum generalization gap. When testing is done on this hyperparameter tuned model, performance is enhanced with respect to the F score weighted by support and stratification since the data is imbalanced. Experimental results demonstrate improvement in performance metrics, i.e., weighted F score, precision, recall, accuracy up to 3 %, and F1 score by 8 % for Logistic Regression Classifier with the proposed model. Further, the time required for hyperparameter tuning is reduced by 50% for tree-based models, particularly Classification and Regression Tree (CART).

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Section: Discussionmentioning

confidence: 99%

Consensus of Feature Selection Methods and Reduced Generalization Gap Model to Improve Diagnosis of Heart Disease

Gupta¹,

Sedamkar²

2021

J. Sci. Res.

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“…Determining the hyperparameters is important for the posterior distribution and increases the accuracy of the parameter estimation. Two different loss functions, squared-error and quadratic [12], for parameter estimation based on the classical Bayesian approach were used in this study.…”

Section: -Discussionmentioning

confidence: 99%

“…The quadratic loss function which is a non-negative symmetric and continuous loss function of parameter 𝜃 and estimate of 𝜃 ̂ for the Bayesian estimator is defined as [12];…”

Section: -2-2-the Bayesian Estimator Of Parameter 𝜽 For Quadratic Loss (Ql) Functionmentioning

confidence: 99%

Bayesian Approaches for Poisson Distribution Parameter Estimation

Supharakonsakun

2021

Emerg Sci J

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The Bayesian approach, a non-classical estimation technique, is very widely used in statistical inference for real world situations. The parameter is considered to be a random variable, and knowledge of the prior distribution is used to update the parameter estimation. Herein, two Bayesian approaches for Poisson parameter estimation by deriving the posterior distribution under the squared error loss or quadratic loss functions are proposed. Their performances were compared with frequentist (maximum likelihood estimator) and Empirical Bayes approaches through Monte Carlo simulations. The mean square error was used as the test criterion for comparing the methods for point estimation; the smallest value indicates the best performing method with the estimated parameter value closest to the true parameter value. Coverage Probabilities (CPs) and average lengths (ALs) were obtained to evaluate the performances of the methods for constructing confidence intervals. The results reveal that the Bayesian approaches were excellent for point estimation when the true parameter value was small (0.5, 1 and 2). In the credible interval comparison, these methods obtained CP values close to the nominal 0.95 confidence level and the smallest ALs for large sample sizes (50 and 100), when the true parameter value was small (0.5, 1 and 2). Doi: 10.28991/esj-2021-01310 Full Text: PDF

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“…The Bayesian analysis of the unknown parameters is studied by many researchers, for example, Hasan and Baizid [8] discussed the Bayesian analysis of the parameter of Exponential distribution, Canavos and Taokas [9] presented the Bayesian analysis of the Weibull distribution. Guure et.al [10] explored the Bayesian estimation of two-parameter Weibull distribution using an extension of Jeffrey's' prior information.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Estimation of the Shape Parameter of Lomax Distribution under Uniform and Jeffery Prior with Engineering Applications

Ijaz

2021

Gazi University Journal of Science

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In engineering, it is usual to model the data so as to make a decision under the problem of uncertainty. Commonly, the data in engineering is skewed to the right, and the skewed distributions in statistics are the appropriate models for making a decision under the Bayesian paradigm. To model the lifetime of an electronic device, an engineer can use the Bayesian estimators to compute the effect of the evidence in increasing the probability for the lifetime of an electronic device by using the prior information. This study presents an estimation of the shape parameter of Lomax distribution under Uniform and Jeffery prior by adopting SELF, QELF, WSELF, and the PELF. The significance of various estimators is compared and presented in graphs using simulated data under the Bayesian paradigm. It was determined that under a uniform prior, Bayes estimator under weighted error loss function (BWEL) provides a better result than others. Under Jeffery prior, the precautionary error loss function (BPEL) leads to a better result than others. Moreover, an application to engineering is also presented for illustration purposes.

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Bayesian Estimation under Different Loss Functions Using Gamma Prior for the Case of Exponential Distribution

Cited by 10 publications

References 3 publications

Consensus of Feature Selection Methods and Reduced Generalization Gap Model to Improve Diagnosis of Heart Disease

Consensus of Feature Selection Methods and Reduced Generalization Gap Model to Improve Diagnosis of Heart Disease

Bayesian Approaches for Poisson Distribution Parameter Estimation

Bayesian Estimation of the Shape Parameter of Lomax Distribution under Uniform and Jeffery Prior with Engineering Applications

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