Estimation of Probability Distribution and Its Application in Bayesian Classification and Maximum Likelihood Regression

Nonparametric estimation of cumulative distribution function and probability density function of continuous random variables is a basic and central problem in probability theory and statistics. Although many methods such as kernel density estimation have been presented, it is still quite a challengi...

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Bibliographic Details
Published in:Interdisciplinary sciences : computational life sciences Vol. 11; no. 3; pp. 559 - 574
Main Authors: Dai, Hao, Wang, Wei, Xu, Qin, Xiong, Yi, Wei, Dong-Qing
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2019
Springer Nature B.V
Subjects:
Algorithms
Bayes Theorem
Bayesian analysis
Biomedical and Life Sciences
Classification
Computational Biology - methods
Computational Biology/Bioinformatics
Computational Science and Engineering
Computer Appl. in Life Sciences
Computer simulation
Continuity (mathematics)
Distribution functions
Economic models
Health Sciences
Life Sciences
Likelihood Functions
Mathematical and Computational Physics
Mathematical models
Maximum likelihood estimation
Medicine
Models, Statistical
Monte Carlo simulation
Numerical methods
Original Research Article
Probability
Probability density functions
Probability distribution
Probability theory
Random variables
Regression Analysis
Regression models
Research Design
Spline functions
Statistical analysis
Statistical methods
Statistics for Life Sciences
Statistics, Nonparametric
Theoretical
Theoretical and Computational Chemistry
Distribution function estimation
Density function estimation
Bayesian classification
Spline regression
Smoothing spline
Maximum likelihood regression
ISSN:1913-2751, 1867-1462, 1867-1462
Online Access:Get full text
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Summary:Nonparametric estimation of cumulative distribution function and probability density function of continuous random variables is a basic and central problem in probability theory and statistics. Although many methods such as kernel density estimation have been presented, it is still quite a challenging problem to be addressed to researchers. In this paper, we proposed a new method of spline regression, in which the spline function could consist of totally different types of functions for each segment with the result of Monte Carlo simulation. Based on the new spline regression, a new method to estimate the distribution and density function was provided, which showed significant advantages over the existing methods in the numerical experiments. Finally, the density function estimation of high dimensional random variables was discussed. It has shown the potential to apply the method in classification and regression models.
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ISSN:1913-2751
1867-1462
1867-1462
DOI:10.1007/s12539-019-00343-w