Analytic posteriors for Pearson's correlation coefficient

Accurately grasping the spatial distribution characteristics of fractures is an important basis for computation and analysis of rock engineering. On the basis of field investigation, probability statistics, and numerical simulation, the fast modeling method of fracture with special probability and statistical distribution is proposed. The server connection between COMSOL and MATLAB is established. In the COMSOL with MATLAB programming environment, the fast modeling program of fissure space structure is developed. Aiming at the difficulty of mesh generation due to high fracture aspect ratio, programming language was used to interpolate the material parameters of fissure space structure and construct the equivalent assignment method of fissure space structure. Based on the field fracture investigation in an underground mine, probabilistic data analysis of fracture data is carried out, and the fast modeling and equivalent assignment method is applied to realize the efficient modeling and assignment for the field investigation of fissure spatial structure.

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“…The criteria for Pearson test are as follows: The value of the critical value

χ^{2}

is less than the level of the Pearson

χ_{σ}^{2}

(through the look‐up table), and we accept the probability density function of the assumed distribution fitting.…”

Section: Rapid Modeling Methods For Spatial Structure Of Rock Massmentioning

confidence: 99%

Rapid modeling of space structure of rock mass and the method of equivalent assignment

Luo

Qin

Wang

et al. 2019

Energy Science & Engineering

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“…The same two desiderata that Jeffreys formulated for his one-sample t test were extended and used to construct Bayes factors for correlations (e.g., Ly et al (2018b)), linear regression (e.g., Bayarri et al (2012), Liang et al (2008), and Zellner and Siow (1980)), ANOVA (e.g., Rouder et al (2012)), and generalised linear models (e.g., Li and Clyde (2018))-scenarios that are highly relevant to contemporary empirical researchers.…”

Section: Second Desideratum: Availability For Common Statistical Scenmentioning

confidence: 99%

The Bayesian Methodology of Sir Harold Jeffreys as a Practical Alternative to the P Value Hypothesis Test

Stefan

Doorn

et al. 2020

Comput Brain Behav

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Despite an ongoing stream of lamentations, many empirical disciplines still treat the p value as the sole arbiter to separate the scientific wheat from the chaff. The continued reign of the p value is arguably due in part to a perceived lack of workable alternatives. In order to be workable, any alternative methodology must be (1) relevant: it has to address the practitioners' research question, which-for better or for worse-most often concerns the test of a hypothesis, and less often concerns the estimation of a parameter; (2) available: it must have a concrete implementation for practitioners' statistical workhorses such as the t test, regression, and ANOVA; and (3) easy to use: methods that demand practitioners switch to the theoreticians' programming tools will face an uphill struggle for adoption. The above desiderata are fulfilled by Harold Jeffreys's Bayes factor methodology as implemented in the open-source software JASP. We explain Jeffreys's methodology and showcase its practical relevance with two examples.

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“…33 It can be calculated by the following equation. Therefore, the mutual effects of each pair of factors need to be analyzed, and the factors with remarkable mutual effects should be considered to remove from the AHP model.…”

Section: Factor Correlation Analysismentioning

confidence: 99%

“…Pearson's correlation coefficient was used to represent the correlation of each pair of factors. 33 It can be calculated by the following equation. where r is Pearson's correlation coefficient, X and Y are the values of arbitrary two group of data, and N is the number of specimens.…”

Section: Factor Correlation Analysismentioning

confidence: 99%

A comprehensive approach for fracability evaluation in naturally fractured sandstone reservoirs based on analytical hierarchy process method

Yang

et al. 2019

Energy Science & Engineering

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The tight sandstone gas reservoir in southern Songliao Basin is naturally fractured and is characterized by its low porosity and permeability. Large‐scale hydraulic fracturing is the most effective way to develop this tight gas reservoir. Quantitative evaluation of fracability is essential for optimizing a fracturing reservoir. In this study, nine fracability‐related factors, particularly mechanical brittleness, unconfined compressive strength (UCS), mineral brittleness, cohesion, internal friction angle (IFA), natural fracture, fracture toughness, horizontal stress difference, and fracture barrier were obtained based on a series of petrophysical and geomechanical experiments. Taking above factors into consideration, a modified comprehensive evaluation model is proposed based on analytic hierarchy process (AHP) method. The UCS and IFA were removed from the AHP model based on the results of factor correlation analysis. The transfer matrix in the weighting procedure was applied to improve the consistency of judgment matrix, and the fuzzy matrix was employed to promote the objectiveness of final decision. The fracability evaluation of four reservoir intervals in Jinshan gas field was analyzed. Field fracturing tests were conducted to verify the feasibility of the proposed evaluation model. Results showed that the tubing pressure curve is more fluctuated in the reservoir interval with more developed natural fractures, and gas production is higher in the reservoir interval with greater fracability coefficient. The field test data coincide with the results of the proposed evaluation model.

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Analytic posteriors for Pearson's correlation coefficient

Cited by 202 publications

References 19 publications

Rapid modeling of space structure of rock mass and the method of equivalent assignment

Rapid modeling of space structure of rock mass and the method of equivalent assignment

The Bayesian Methodology of Sir Harold Jeffreys as a Practical Alternative to the P Value Hypothesis Test

A comprehensive approach for fracability evaluation in naturally fractured sandstone reservoirs based on analytical hierarchy process method

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