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Statistics with posterior probability and a PHC curve

Record Type:	Electronic resources : Monograph/item
Title/Author:	Statistics with posterior probability and a PHC curveby Hideki Toyoda.
Author:	Toyoda, Hideki.
Published:	Singapore :Springer Nature Singapore :2024.
Description:	xxiii, 404 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Probabilities.
Online resource:	https://doi.org/10.1007/978-981-97-3094-0
ISBN:	9789819730940$q(electronic bk.)

Statistics with posterior probability and a PHC curve
Toyoda, Hideki.

Statistics with posterior probability and a PHC curve[electronic resource] /by Hideki Toyoda. - Singapore :Springer Nature Singapore :2024. - xxiii, 404 p. :ill. (some col.), digital ;24 cm.

chapter01 Data summary and theoretical distribution -- chapter02 Posterior Distribution and Bayes' Theorem -- chapter03 Inference about a normal distribution -- chapter04 Generated quantities -- chapter05 phc curve and ROPE -- chapter06 Inference about two normal distributions -- chapter07 Group difference between two independent groups -- chapter08 Bivariate and multivariate data -- chapter09 difference score of paired two groups -- chapter10 Independent one-factor analysis -- chapter11 Independent two-factor analysis -- chapter12 Binomial distribution model -- chapter13 Multinomial distribution model -- chapter14 simple regression model -- chapter15 multiple regression model -- chapter16 Interpreting partial regression coefficients -- chapter17 Logistic regression / Meta-analysis -- chapter18 Poisson model / Log-linear model -- chapter19 Independent one-factor analysis with various distributions -- chapter20 Analysis of covariance / Propensity score -- chapter21 Advanced experimental design -- chapter22 Hierarchical linear model.

This textbook reconstructs the statistics curriculum from the perspective of posterior probability. In recent years, there have been several reports that the results of studies using significant tests cannot be reproduced. It is a problem called a "reproducibility crisis". For example, suppose we could reject the null hypothesis that "the average number of days to recovery in patients who took a new drug was the same as that in the control group". However, rejecting the null hypothesis is only a necessary condition for the new drug to be effective. Even if the necessary conditions are met, it does not necessarily mean that the new drug is effective. In fact, there are many cases where the effect is not reproduced. Sufficient conditions should be presented, such as "the average number of days until recovery in patients who take new drugs is sufficiently short compared to the control group, evaluated from a medical point of view", without paying attention to necessary conditions. This book reconstructs statistics from the perspective of PHC, i.e., probability that a research hypothesis is correct. For example, the PHC curve shows the posterior probability that the statement "The average number of days until recovery for patients taking a new drug is at least θ days shorter than that of the control group" is correct as a function of θ. Using the PHC curve makes it possible to discuss the sufficient conditions rather than the necessary conditions for being an efficient treatment. The value of statistical research should be evaluated with concrete indicators such as "90% probability of being at least 3 days shorter", not abstract metrics like the p-value.

ISBN: 9789819730940$q(electronic bk.)

Standard No.: 10.1007/978-981-97-3094-0doiSubjects--Topical Terms:

182046
Probabilities.

LC Class. No.: QA273

Dewey Class. No.: 519.2

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505 0 $a chapter01 Data summary and theoretical distribution -- chapter02 Posterior Distribution and Bayes' Theorem -- chapter03 Inference about a normal distribution -- chapter04 Generated quantities -- chapter05 phc curve and ROPE -- chapter06 Inference about two normal distributions -- chapter07 Group difference between two independent groups -- chapter08 Bivariate and multivariate data -- chapter09 difference score of paired two groups -- chapter10 Independent one-factor analysis -- chapter11 Independent two-factor analysis -- chapter12 Binomial distribution model -- chapter13 Multinomial distribution model -- chapter14 simple regression model -- chapter15 multiple regression model -- chapter16 Interpreting partial regression coefficients -- chapter17 Logistic regression / Meta-analysis -- chapter18 Poisson model / Log-linear model -- chapter19 Independent one-factor analysis with various distributions -- chapter20 Analysis of covariance / Propensity score -- chapter21 Advanced experimental design -- chapter22 Hierarchical linear model.
520 $a This textbook reconstructs the statistics curriculum from the perspective of posterior probability. In recent years, there have been several reports that the results of studies using significant tests cannot be reproduced. It is a problem called a "reproducibility crisis". For example, suppose we could reject the null hypothesis that "the average number of days to recovery in patients who took a new drug was the same as that in the control group". However, rejecting the null hypothesis is only a necessary condition for the new drug to be effective. Even if the necessary conditions are met, it does not necessarily mean that the new drug is effective. In fact, there are many cases where the effect is not reproduced. Sufficient conditions should be presented, such as "the average number of days until recovery in patients who take new drugs is sufficiently short compared to the control group, evaluated from a medical point of view", without paying attention to necessary conditions. This book reconstructs statistics from the perspective of PHC, i.e., probability that a research hypothesis is correct. For example, the PHC curve shows the posterior probability that the statement "The average number of days until recovery for patients taking a new drug is at least θ days shorter than that of the control group" is correct as a function of θ. Using the PHC curve makes it possible to discuss the sufficient conditions rather than the necessary conditions for being an efficient treatment. The value of statistical research should be evaluated with concrete indicators such as "90% probability of being at least 3 days shorter", not abstract metrics like the p-value.
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