Article
Mathematics
Richard A. Chechile
Summary: Bertrand's paradox, a problem in geometric probability, has remained unsolved for over a century. This paper resolves the paradox by clarifying the primary variate and imposing constraints on the random process. The same steps also solve the Bing-Fisher problem, and rebut philosophical arguments against Bayesian inference.
Article
Statistics & Probability
Andrew Fowlie
Summary: In an attempt to address the Jeffreys-Lindley paradox, we explore finding priors that are completely indifferent to sample size. We show that while an improper scale-invariant prior is obtained, a truncated scale-invariant prior can delay the dependence on sample size. Additionally, we shed light on the paradox by relating it to the improper nature of the scale-invariant prior.
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
(2022)
Editorial Material
History & Philosophy Of Science
Jeremy Gray, Joshua L. Cherry, Eric-Jan Wagenmakers, Alexander Ly
Summary: This Editorial presents a discussion between the authors of the article "History and Nature of the Jeffreys-Lindley Paradox" (Arch Hist Exact Sci 77:25, 2023), Eric-Jan Wagenmakers and Alexander Ly, in the form of a comment and reply exchange.
ARCHIVE FOR HISTORY OF EXACT SCIENCES
(2023)
Article
Operations Research & Management Science
Muhammad Ali Nasir, Alaa M. Soliman, Muhammad Shahbaz
Summary: This study demonstrates the importance of macroeconomic policy coordination for financial stability, even in the face of challenges such as Jeffery-Lindley's paradox and the Global Financial Crisis. It also highlights the potential benefits of utilizing Frequentist and Bayesian estimation techniques as complementary frameworks rather than competing ones for achieving financial stability.
ANNALS OF OPERATIONS RESEARCH
(2021)
Article
History & Philosophy Of Science
Eric-Jan Wagenmakers, Alexander Ly
Summary: The Jeffreys-Lindley paradox uncovers a disagreement between Bayesian and frequentist hypothesis testing, bringing into question the essence of statistical inference. Contrary to popular belief, this paradox was central to the Bayesian testing methodology developed by Sir Harold Jeffreys in the late 1930s. Jeffreys demonstrated that the evidence for a point-null hypothesis H-0 is proportional to the square root of the sample size, challenging the practice of setting a constant multiple of the standard error as the threshold for rejecting H-0.
ARCHIVE FOR HISTORY OF EXACT SCIENCES
(2023)
Article
Mathematics
Mohamed Ali Ghorbel, Rahmouna Mecene
Summary: In this research, a new class of bivariate distributions called Bivariate Generalized Gamma-Lindley (BGGL) distribution with four parameters is proposed. The model combines independent Gamma random variables and bivariate generalized Lindley distribution. Various properties of the new bivariate distribution, such as graphical representation, joint moments, and correlation, are investigated. The distributions and moment properties of several random variables are derived when X-1 and X-2 follow the BGGL distribution. The expectation maximization (E.M) algorithm is elaborated for parameter estimation, and the applicability of the results is demonstrated through concrete examples.
MATHEMATICA SLOVACA
(2023)
Article
History & Philosophy Of Science
Stuart Brock, Joshua Glasgow
Summary: This paper argues that our understanding and intuition about paradoxes are paradoxical in nature. Specifically, it claims that our belief in the existence and nature of paradoxes contradicts a norm of rationality, which in itself is a paradox.
Article
Thermodynamics
Emad Awad, Trifce Sandev, Ralf Metzler, Aleksei Chechkin
Summary: Jeffreys equation extends diffusive laws for heat and particle transport, exhibiting various anomalous behaviors in mean squared displacement. Different approaches, such as fractional Taylor series and distributed-order derivatives, transform traditional laws into the time-fractional Jeffreys equation for practical applications.
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2021)
Article
Materials Science, Multidisciplinary
Shukri Klinaku
Summary: The triplet paradox is used to explain the twin paradox. After the journey, the travelling triplet cannot be younger or older than the other two triplets, who rest at either end of the travelling triplet's road!
RESULTS IN PHYSICS
(2023)
Article
Mathematics
Khaled S. Mekheimer, Bangalore M. Shankar, Shaimaa F. Ramadan, Hosahalli E. Mallik, Mohamed S. Mohamed
Summary: This study examines the impact of gold nanoparticles on the stability properties of convection in a vertical fluid layer saturated by a Jeffreys fluid, focusing on linear stability and critical parameters under different control parameters. The results indicate that in the presence of gold nanoparticles, Newtonian fluid has a stronger stabilizing effect compared to second-grade and Jeffreys fluids.
Article
Multidisciplinary Sciences
Ali Algarni
Summary: The study introduces a new distribution model for survival and lifetime data by extending the generalized Lindley distribution using the Marshall-Olkin method and its own sub-models. The research discusses statistical properties, reliability analysis, and statistical inference methods for the new family of distributions. Additionally, a simulation study compares the efficiency of different estimators based on the mean square error criterion, and a real data set analysis demonstrates the flexibility of the proposed model compared to other competitive distributions.
Article
Materials Science, Multidisciplinary
Aditya Kumar, Oscar Lopez-Pamies
Summary: While it was previously believed that cavitation in elastomers could be explained solely based on elasticity, recent research has shown that it is primarily a fracture phenomenon. This study aims to use a macroscopic phase-field theory to provide a detailed quantitative explanation of the seminal poker-chip experiments conducted by Gent and Lindley.
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
(2021)
Article
Multidisciplinary Sciences
Abdulhakim A. Al-Babtain, Ahmed M. Gemeay, Ahmed Z. Afify
Summary: This paper discusses the estimation of parameters for two discrete models, explores the finite sample properties, ranks the performance of proposed estimators, and derives important actuarial measures for the two models. A computational study and comparison with other distributions are conducted using data sets from the medicine field, including two COVID-19 data sets.
JOURNAL OF KING SAUD UNIVERSITY SCIENCE
(2021)
Article
Physics, Multidisciplinary
J. Guemez
Summary: The 'relativistic lever paradox' in the theory of relativity application to rotation processes is addressed by developing a covariant four-tensor equation to describe relativistic rigid rotation. The analysis of Lorentz transformation between frames S and (S) over bar shows that angular momentum and torque vary differently in different frames. This asynchronous formulation of relativity demonstrates the coherence of the description and resolves the paradox.
Article
Mathematics, Applied
Doaa Basalamah, Bader Alruwaili
Summary: In this study, we introduced the WLE notation for the weighted Lindley exponential distribution and investigated its mathematical properties and maximum likelihood estimation method. The results showed that this model exhibited superiority in fitting actual data sets.
Article
Biochemical Research Methods
Louis Raynal, Jean-Michel Marin, Pierre Pudlo, Mathieu Ribatet, Christian P. Robert, Arnaud Estoup
Article
Statistics & Probability
Espen Bernton, Pierre E. Jacob, Mathieu Gerber, Christian P. Robert
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
(2019)
Article
Computer Science, Software Engineering
Clement Robert, Thierry Sotiropoulos, Helene Waeselynck, Jeremie Guiochet, Simon Vernhes
EMPIRICAL SOFTWARE ENGINEERING
(2020)
Article
Statistics & Probability
David T. Frazier, Christian P. Robert, Judith Rousseau
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
(2020)
Article
Computer Science, Theory & Methods
Changye Wu, Christian P. Robert
STATISTICS AND COMPUTING
(2020)
Article
Agriculture, Dairy & Animal Science
M. Arnal, H. Larroque, H. Leclerc, V Ducrocq, C. Robert-Granie
JOURNAL OF DAIRY SCIENCE
(2020)
Article
Statistics & Probability
Christian P. Robert, Gareth Roberts
Summary: Rao-Blackwellization, a concept in the MCMC literature, has different meanings and connections with the original Rao-Blackwell theorem. It aims to reduce the variance of Monte Carlo approximations. This survey examines various interpretations of this term.
INTERNATIONAL STATISTICAL REVIEW
(2021)
Article
Physics, Fluids & Plasmas
C. Clanet, Hector Abel, E. Brunet, Francesco Grasso, C. Robert, C. Cohen
Summary: This study examined the aerodynamic force on a cyclist in time trial position in various wind conditions using a large-scale wind tunnel. A theoretical model was developed to explain experimental features, with a new analytical expression derived for total aerodynamic power and cycling speed in arbitrary crosswind conditions. The commonly used expression for power dissipation in crosswinds was found to require correction beyond pure head and tailwind limits.
PHYSICAL REVIEW FLUIDS
(2021)
Article
Statistics & Probability
Victor Elvira, Luca Martino, Christian P. Robert
Summary: This paper revisits the approximation of effective sample size (ESS) in the context of importance sampling and finds the existing approximations problematic. The authors propose new research directions for multiple importance sampling and alternative metrics.
INTERNATIONAL STATISTICAL REVIEW
(2022)
Editorial Material
Multidisciplinary Sciences
Christian P. Robert, Judith Rousseau
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2023)
Article
Mathematics, Applied
Espen Bernton, Pierre E. Jacob, Mathieu Gerber, Christian P. Robert
INFORMATION AND INFERENCE-A JOURNAL OF THE IMA
(2019)
Article
Agriculture, Dairy & Animal Science
Mathieu Arnal, Helene Larroque, Helene Leclerc, Vincent Ducrocq, Christele Robert-Granie
GENETICS SELECTION EVOLUTION
(2019)
Article
Mathematics, Applied
Marco Banterle, Clara Grazian, Anthony Lee, Christian P. Robert
FOUNDATIONS OF DATA SCIENCE
(2019)
Article
Automation & Control Systems
Aki Vehtari, Andrew Gelman, Tuomas Sivula, Pasi Jylanki, Dustin Tran, Swupnil Sahai, Paul Blomstedt, John P. Cunningham, David Schiminovich, Christian P. Robert
JOURNAL OF MACHINE LEARNING RESEARCH
(2020)
Article
Mathematics, Interdisciplinary Applications
Wu Changye, Christian P. Robert
CASE STUDIES IN APPLIED BAYESIAN DATA SCIENCE: CIRM JEAN-MORLET CHAIR, FALL 2018
(2020)
