A technique for obtaining probabilities of correct selection in a two-stage selection problem

Biometrika ◽  
1971 ◽  
Vol 58 (3) ◽  
pp. 615-623 ◽  
Author(s):  
PAUL N. SOMERVILLE
Keyword(s):  
Selection Problem ◽  
Correct Selection ◽  
Two Stage

scholarly journals Two-Stage Fuzzy Portfolio Selection Problem with Transaction Costs

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Yanju Chen ◽  
Ye Wang
Keyword(s):  
Transaction Costs ◽  
Portfolio Selection ◽  
Optimal Solution ◽  
Single Stage ◽  
Selection Problem ◽  
Stage Model ◽  
Two Stage ◽  
Portfolio Selection Problem ◽  
Fuzzy Portfolio Selection ◽  
Proposed Model

This paper studies a two-period portfolio selection problem. The problem is formulated as a two-stage fuzzy portfolio selection model with transaction costs, in which the future returns of risky security are characterized by possibility distributions. The objective of the proposed model is to achieve the maximum utility in terms of the expected value and variance of the final wealth. Given the first-stage decision vector and a realization of fuzzy return, the optimal value expression of the second-stage programming problem is derived. As a result, the proposed two-stage model is equivalent to a single-stage model, and the analytical optimal solution of the two-stage model is obtained, which helps us to discuss the properties of the optimal solution. Finally, some numerical experiments are performed to demonstrate the new modeling idea and the effectiveness. The computational results provided by the proposed model show that the more risk-averse investor will invest more wealth in the risk-free security. They also show that the optimal invested amount in risky security increases as the risk-free return decreases and the optimal utility increases as the risk-free return increases, whereas the optimal utility increases as the transaction costs decrease. In most instances the utilities provided by the proposed two-stage model are larger than those provided by the single-stage model.

scholarly journals A Two-Stage Method Based on Multiobjective Differential Evolution for Gene Selection

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Shuangbao Song ◽  
Xingqian Chen ◽  
Zheng Tang ◽  
Yuki Todo
Keyword(s):  
Gene Expression ◽  
Feature Selection ◽  
Multiobjective Optimization ◽  
Differential Evolution ◽  
Gene Selection ◽  
Feature Selection Method ◽  
Selection Method ◽  
Selection Problem ◽  
Objective Functions ◽  
Two Stage

Microarray gene expression data provide a prospective way to diagnose disease and classify cancer. However, in bioinformatics, the gene selection problem, i.e., how to select the most informative genes from thousands of genes, remains challenging. This problem is a specific feature selection problem with high-dimensional features and small sample sizes. In this paper, a two-stage method combining a filter feature selection method and a wrapper feature selection method is proposed to solve the gene selection problem. In contrast to common methods, the proposed method models the gene selection problem as a multiobjective optimization problem. Both stages employ the same multiobjective differential evolution (MODE) as the search strategy but incorporate different objective functions. The three objective functions of the filter method are mainly based on mutual information. The two objective functions of the wrapper method are the number of selected features and the classification error of a naive Bayes (NB) classifier. Finally, the performance of the proposed method is tested and analyzed on six benchmark gene expression datasets. The experimental results verified that this paper provides a novel and effective way to solve the gene selection problem by applying a multiobjective optimization algorithm.

scholarly journals Nonparametric Methods and Evolutionary Algorithms in Genetic Epidemiology

2018 ◽  
Author(s):  
Colleen Molloy Farrelly
Keyword(s):  
Random Forest ◽  
Evolutionary Algorithms ◽  
Variable Selection ◽  
Genetic Epidemiology ◽  
Regression Models ◽  
Selection Problem ◽  
High Dimensionality ◽  
Two Stage ◽  
Selection Methodology ◽  
Variable Selection Problem

Paper overviews variable selection problem in high dimensionality, particularly focused on genetic psychiatry and genetic epidemiology in general. Genetic and quantum evolutionary algorithms, tree-based classification/regression models, random forest, and other approaches are detailed. Paper concludes with a roadmap for new algorithm and two-stage selection methodology.

A TWO-STAGE DECISION APPROACH TO THE SELECTION PROBLEM

1972 ◽  
Vol 25 (2) ◽  
pp. 274-282
Author(s):  
Donald A. Rock ◽  
John L. Barone ◽  
Robert F. Boldt
Keyword(s):  
Selection Problem ◽  
Two Stage

A TWO STAGE DECISION APPROACH TO THE SELECTION PROBLEM

1968 ◽  
Vol 1968 (1) ◽  
pp. i-19
Author(s):  
Donald A. Rock ◽  
John L. Barone ◽  
Robert F. Boldt
Keyword(s):  
Selection Problem ◽  
Two Stage

scholarly journals Two-stage procedures for selecting the best diagnostic biomarkers

2008 ◽  
Vol 366 (1874) ◽  
pp. 2293-2299
Author(s):  
Aiyi Liu ◽  
Chengqing Wu ◽  
Kai F Yu
Keyword(s):  
Joint Distribution ◽  
Nuisance Parameters ◽  
Correct Selection ◽  
Diagnostic Biomarker ◽  
Two Stage ◽  
Classification Rate ◽  
Diagnostic Biomarkers ◽  
Probability Of Correct Selection ◽  
Simulation Results ◽  
Dichotomous Outcomes

Considered in the paper is the problem of selecting a diagnostic biomarker that has the highest classification rate among several candidate markers with dichotomous outcomes. The probability of correct selection depends on a number of nuisance parameters from the joint distribution of the biomarkers and thus can be substantially affected if these nuisance parameters are misspecified. A two-stage procedure is proposed to compute the needed sample size that achieves the desired level of correct selection, as so confirmed by simulation results.

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