Learning kμ decision trees on the uniform distribution

Abstract:The problem of deciding the optimal sequence of diagnostic tests can be structured in decision trees, but unmanageable bushy decision trees result when the sequence of two or more tests is investigated. Most modelling techniques include tests on the basis of gain in certainty. The aim of this study was to explore a model for optimizing the sequence of diagnostic tests based on efficiency criteria. The probability modifying plot shows, when in a specific test sequence further testing is redundant and which costs are involved. In this way different sequences can be compared. The model is illustrated with data on urinary tract infection. The sequence of diagnostic tests was optimized on the basis of efficiency, which was either defined as the test sequence with the least number of tests or the least total cost for testing. Further research on the model is needed to handle current limitations.

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Automated Development of Clinical Strategies Using Multistage Decision Analysis

Methods of Information in Medicine ◽

10.1055/s-0038-1635469 ◽

1986 ◽

Vol 25 (04) ◽

pp. 207-214 ◽

Cited By ~ 3

Author(s):

P. Glasziou

Keyword(s):

Decision Tree ◽

Decision Analysis ◽

Decision Trees ◽

Optimal Strategy ◽

Cholestatic Jaundice ◽

Clinical Strategies ◽

Simultaneous Study

SummaryThe development of investigative strategies by decision analysis has been achieved by explicitly drawing the decision tree, either by hand or on computer. This paper discusses the feasibility of automatically generating and analysing decision trees from a description of the investigations and the treatment problem. The investigation of cholestatic jaundice is used to illustrate the technique.Methods to decrease the number of calculations required are presented. It is shown that this method makes practical the simultaneous study of at least half a dozen investigations. However, some new problems arise due to the possible complexity of the resulting optimal strategy. If protocol errors and delays due to testing are considered, simpler strategies become desirable. Generation and assessment of these simpler strategies are discussed with examples.

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Generation of Correlated Logistic-Normal Random Variates for Medical Decision Trees

Methods of Information in Medicine ◽

10.1055/s-0038-1634534 ◽

1998 ◽

Vol 37 (03) ◽

pp. 235-238 ◽

Cited By ~ 1

Author(s):

M. El-Taha ◽

D. E. Clark

Keyword(s):

Monte Carlo ◽

Decision Trees ◽

Computer Algebra ◽

Taylor Series ◽

Computer Algebra System ◽

Random Variable ◽

Monte Carlo Analysis ◽

Normal Random Variable ◽

Medical Decision ◽

Theoretical Results

AbstractA Logistic-Normal random variable (Y) is obtained from a Normal random variable (X) by the relation Y = (ex)/(1 + ex). In Monte-Carlo analysis of decision trees, Logistic-Normal random variates may be used to model the branching probabilities. In some cases, the probabilities to be modeled may not be independent, and a method for generating correlated Logistic-Normal random variates would be useful. A technique for generating correlated Normal random variates has been previously described. Using Taylor Series approximations and the algebraic definitions of variance and covariance, we describe methods for estimating the means, variances, and covariances of Normal random variates which, after translation using the above formula, will result in Logistic-Normal random variates having approximately the desired means, variances, and covariances. Multiple simulations of the method using the Mathematica computer algebra system show satisfactory agreement with the theoretical results.

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Levels taxation countries the EU and Ukraine’s

Problems of Innovation and Investment Development ◽

10.33813/2224-1213.19.2019.12 ◽

2019 ◽

pp. 131-160

Author(s):

Helena Borzenko ◽

Tamara Panfilova ◽

Mikhail Litvin

Keyword(s):

European Union ◽

Uniform Distribution ◽

Tax Burden ◽

Tax System ◽

Tax Legislation ◽

Improvement Process ◽

Tax Systems ◽

Historical Comparative ◽

Different Levels ◽

The Eu

Purpose articles rassm and experience and benefits systems taxation countries European Union, manifestation iti the main limitations domestic taxlegislation and wired STI their comparisons. In general iti ways the provisiontax reporting countries Eurozone in the appropriate organs, dove STI need theintroduction Ukraine electronic methods receiving and processing such reports.define iti key directions reforming domestic tax legislation. Methodology research is to use aggregate methods: dialectical, statistical, historical, comparative. Scientific novelty is to are provided recommendations for improvement ofefficiency systems taxation of our states in international ratings characterizingtax institutions country. Therefore, despite some problems in legislation heldcomparative study systems taxation EU and Ukraine. Conclucions Coming fromof this, the main directions reforming tax systems Ukraine, in our opinion,today should become: improvement process administration, reduce scales evasiontaxes, provision more uniform distribution tax burden between taxpayers, themaximum cooperation tax bodies different levels as well adjustment systemselectronic interactions tax authorities and payers, tax system must contain ascan less unfounded benefits, consistent with the general by politics pricing.

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Statistical Justification of Pearson's Criterion for Testing a Complex Hypothesis on the Uniform Distribution

Mechanical Engineering and Computer Science ◽

10.24108/0418.0001392 ◽

2018 ◽

pp. 45-53

Author(s):

T. V. Oblakova

Keyword(s):

Uniform Distribution ◽

Degrees Of Freedom ◽

Likelihood Function ◽

Random Number Generator ◽

Maximum Likelihood Estimates ◽

Chi Square ◽

Main Hypothesis ◽

Pearson Criterion ◽

Complex Hypothesis ◽

Uniform Law

The paper is studying the justification of the Pearson criterion for checking the hypothesis on the uniform distribution of the general totality. If the distribution parameters are unknown, then estimates of the theoretical frequencies are used [1, 2, 3]. In this case the quantile of the chi-square distribution with the number of degrees of freedom, reduced by the number of parameters evaluated, is used to determine the upper threshold of the main hypothesis acceptance [7]. However, in the case of a uniform law, the application of Pearson's criterion does not extend to complex hypotheses, since the likelihood function does not allow differentiation with respect to parameters, which is used in the proof of the theorem mentioned [7, 10, 11].A statistical experiment is proposed in order to study the distribution of Pearson statistics for samples from a uniform law. The essence of the experiment is that at first a statistically significant number of one-type samples from a given uniform distribution is modeled, then for each sample Pearson statistics are calculated, and then the law of distribution of the totality of these statistics is studied. Modeling and processing of samples were performed in the Mathcad 15 package using the built-in random number generator and array processing facilities.In all the experiments carried out, the hypothesis that the Pearson statistics conform to the chi-square law was unambiguously accepted (confidence level 0.95). It is also statistically proved that the number of degrees of freedom in the case of a complex hypothesis need not be corrected. That is, the maximum likelihood estimates of the uniform law parameters implicitly used in calculating Pearson statistics do not affect the number of degrees of freedom, which is thus determined by the number of grouping intervals only.

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