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Bunouf P. Bayesian estimation of the binomial parameter in sequential experiments. Stat Methods Med Res 2023; 32:2158-2171. [PMID: 37674462 DOI: 10.1177/09622802231199160] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/08/2023]
Abstract
This article presents an objective Bayesian approach to estimating the binomial parameter in group sequential experiments with a binary endpoint. The idea of deriving design-dependent priors was first introduced using Jeffreys criterion. Another class of priors was developed based on the reference prior theory. A theoretical framework was established showing that explicit reference to the experimental design in the prior is fully Bayesian justified. Using a design-dependent prior which generalizes the reference prior, I propose a comprehensive and unified approach to the point and the interval estimations in group sequential experiments, and I evidence the good frequentist properties of the posterior estimators through comparative studies with the existing methods. The effect of the prior correction on the posterior estimates is studied in three classical designs of clinical trials. Finally, I discuss the idea of using this approach as a default choice for estimation upon sequential experiment termination.
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2
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Bayesian linear models for cardinal paired comparison data. Comput Stat Data Anal 2022. [DOI: 10.1016/j.csda.2022.107481] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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3
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Bunouf P. An objective bayesian approach to estimation in multistage experiments. Stat Methods Med Res 2022; 31:1579-1589. [PMID: 35543014 DOI: 10.1177/09622802221099640] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
This article presents a Bayesian approach to estimation in multistage experiments based on the reference prior theory. The idea of deriving design-dependent priors was first introduced using Jeffreys' criterion. A theoretical framework was then established by showing that explicit reference to the design is fully Bayesian justified and Bayesian objectivity cannot ignore such information. Extending the work to multi-parameter problems, a general form of priors was derived from the reference prior theory. In this article, I evidence the good frequentist properties of the reference posterior estimators with normally distributed data. As a notable advance, I address the issue of the point and the interval estimations upon experiment termination. The approach is applied to a data set collected in a clinical trial in schizophrenia with the possibility to stop the trial early if interim results provide sufficient evidence of efficacy or futility. Finally, I discuss the idea of using the reference posterior estimators as a default choice for objective estimation in multistage experiment.
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Ramos PL, Dey DK, Louzada F, Ramos E. On Posterior Properties of the Two Parameter Gamma Family of Distributions. AN ACAD BRAS CIENC 2021; 93:e20190826. [PMID: 34877968 DOI: 10.1590/0001-3765202120190826] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2019] [Accepted: 02/08/2020] [Indexed: 11/22/2022] Open
Abstract
The gamma distribution has been extensively used in many areas of applications. In this paper, considering a Bayesian analysis we provide necessary and sufficient conditions to check whether or not improper priors lead to proper posterior distributions. Further, we also discuss sufficient conditions to verify if the obtained posterior moments are finite. An interesting aspect of our findings are that one can check if the posterior is proper or improper and also if its posterior moments are finite by looking directly in the behavior of the proposed improper prior. To illustrate our proposed methodology these results are applied in different objective priors.
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Affiliation(s)
- Pedro L Ramos
- Pontificia Universidad Católica de Chile, Facultad de Matemáticas, Vicuña, Mackenna, 4860, Macul, 7820436 Región Metropolitana, Chile
| | - Dipak K Dey
- University of Connecticut, Department of Statistics, 215 Glenbrook Rd. U-4120 Storrs, CT 06269-4120, USA
| | - Francisco Louzada
- Universidade de São Paulo, Instituto de Ciências Matemáticas e de Computação, Avenida Trabalhador São-carlense, 400, Centro, 13566-590 São Carlos, SP, Brazil
| | - Eduardo Ramos
- Universidade de São Paulo, Instituto de Ciências Matemáticas e de Computação, Avenida Trabalhador São-carlense, 400, Centro, 13566-590 São Carlos, SP, Brazil
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D’Andrea AME, Tomazella VLD, Aljohani HM, Ramos PL, Almeida MP, Louzada F, Verssani BAW, Gazon AB, Afify AZ. Objective bayesian analysis for multiple repairable systems. PLoS One 2021; 16:e0258581. [PMID: 34813589 PMCID: PMC8610278 DOI: 10.1371/journal.pone.0258581] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2021] [Accepted: 09/30/2021] [Indexed: 11/21/2022] Open
Abstract
This article focus on the analysis of the reliability of multiple identical systems that can have multiple failures over time. A repairable system is defined as a system that can be restored to operating state in the event of a failure. This work under minimal repair, it is assumed that the failure has a power law intensity and the Bayesian approach is used to estimate the unknown parameters. The Bayesian estimators are obtained using two objective priors know as Jeffreys and reference priors. We proved that obtained reference prior is also a matching prior for both parameters, i.e., the credibility intervals have accurate frequentist coverage, while the Jeffreys prior returns unbiased estimates for the parameters. To illustrate the applicability of our Bayesian estimators, a new data set related to the failures of Brazilian sugar cane harvesters is considered.
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Affiliation(s)
| | | | - Hassan M. Aljohani
- Department of Mathematics & Statistics, College of Science, Taif University, Taif, Saudi Arabia
| | - Pedro L. Ramos
- Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Macul, Santiago, Chile
- * E-mail:
| | - Marco P. Almeida
- Department of Statistics, Federal University of São Carlos, São Carlos, Brazil
- Institute of Mathematics and Computer Sciences, University of São Paulo, São Carlos, Brazil
| | - Francisco Louzada
- Institute of Mathematics and Computer Sciences, University of São Paulo, São Carlos, Brazil
| | | | - Amanda B. Gazon
- Department of Statistics, Federal University of São Carlos, São Carlos, Brazil
| | - Ahmed Z. Afify
- Department of Statistics, Mathematics and Insurance, Benha University, Benha, Egypt
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Jonas KG. Global Information for Multidimensional Tests. APPLIED PSYCHOLOGICAL MEASUREMENT 2021; 45:494-517. [PMID: 34866709 PMCID: PMC8640353 DOI: 10.1177/01466216211042803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
New measures of test information, termed global information, quantify test information relative to the entire range of the trait being assessed. Estimating global information relative to a non-informative prior distribution results in a measure of how much information could be gained by administering the test to an unspecified examinee. Currently, such measures have been developed only for unidimensional tests. This study introduces measures of multidimensional global test information and validates them in simulated data. Then, the utility of global test information is tested in neuropsychological data collected as part of Rush University's Memory and Aging Project. These measures allow for direct comparison of complex tests calibrated in different samples, facilitating test development and selection.
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Affiliation(s)
- Katherine G. Jonas
- Psychiatry and Behavioral Health, Stony Brook University, Stony Brook, NY, USA
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Zhang L, Shaby BA. Uniqueness and global optimality of the maximum likelihood estimator for the generalized extreme value distribution. Biometrika 2021. [DOI: 10.1093/biomet/asab043] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Summary
The three-parameter generalized extreme value distribution arises from classical univariate extreme value theory, and is in common use for analysing the far tail of observed phenomena, yet important asymptotic properties of likelihood-based estimation under this standard model have not been established. In this paper we prove that the maximum likelihood estimator is global and unique. An interesting secondary result entails the uniform consistency of a class of limit relations in a tight neighbourhood of the true shape parameter.
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Affiliation(s)
- Likun Zhang
- Climate and Ecosystem Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, U.S.A
| | - Benjamin A Shaby
- Department of Statistics, Colorado State University, Fort Collins, Colorado 80523, U.S.A
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Louzada F, Cuminato JA, Rodriguez OMH, Tomazella VLD, Ferreira PH, Ramos PL, Milani EA, Bochio G, Perissini IC, Gonzatto Junior OA, Mota AL, Alegría LFA, Colombo D, Perondi EA, Wentz AV, Júnior ALS, Barone DAC, Santos HFL, Magalhães MVC. Improved objective Bayesian estimator for a PLP model hierarchically represented subject to competing risks under minimal repair regime. PLoS One 2021; 16:e0255944. [PMID: 34383829 PMCID: PMC8360570 DOI: 10.1371/journal.pone.0255944] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2020] [Accepted: 07/27/2021] [Indexed: 11/22/2022] Open
Abstract
In this paper, we propose a hierarchical statistical model for a single repairable system subject to several failure modes (competing risks). The paper describes how complex engineered systems may be modelled hierarchically by use of Bayesian methods. It is also assumed that repairs are minimal and each failure mode has a power-law intensity. Our proposed model generalizes another one already presented in the literature and continues the study initiated by us in another published paper. Some properties of the new model are discussed. We conduct statistical inference under an objective Bayesian framework. A simulation study is carried out to investigate the efficiency of the proposed methods. Finally, our methodology is illustrated by two practical situations currently addressed in a project under development arising from a partnership between Petrobras and six research institutes.
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Affiliation(s)
- Francisco Louzada
- Institute of Mathematical and Computer Sciences (ICMC), University of São Paulo, São Carlos, SP, Brazil
| | - José A. Cuminato
- Institute of Mathematical and Computer Sciences (ICMC), University of São Paulo, São Carlos, SP, Brazil
| | | | - Vera L. D. Tomazella
- Department of Statistics (DEs), Federal University of São Carlos, São Carlos, SP, Brazil
| | - Paulo H. Ferreira
- Institute of Mathematical and Computer Sciences (ICMC), University of São Paulo, São Carlos, SP, Brazil
- Department of Statistics (DEst), Federal University of Bahia, Salvador, BA, Brazil
| | - Pedro L. Ramos
- Institute of Mathematical and Computer Sciences (ICMC), University of São Paulo, São Carlos, SP, Brazil
- Pontificia Universidad Católica de Chile, Facultad de Matemáticas, Macul, Santiago, Chile
| | - Eder A. Milani
- Institute of Mathematical and Computer Sciences (ICMC), University of São Paulo, São Carlos, SP, Brazil
- Institute of Mathematics and Statistics (IME), Federal University of Goiás, Goiânia, GO, Brazil
| | - Gustavo Bochio
- School of Engineering (EESC), University of São Paulo, São Carlos, SP, Brazil
| | - Ivan C. Perissini
- School of Engineering (EESC), University of São Paulo, São Carlos, SP, Brazil
| | - Oilson A. Gonzatto Junior
- Institute of Mathematical and Computer Sciences (ICMC), University of São Paulo, São Carlos, SP, Brazil
- * E-mail:
| | - Alex L. Mota
- Institute of Mathematical and Computer Sciences (ICMC), University of São Paulo, São Carlos, SP, Brazil
| | - Luis F. A. Alegría
- School of Engineering (EESC), University of São Paulo, São Carlos, SP, Brazil
| | - Danilo Colombo
- Leopoldo Américo Miguez de Mello Research and Development Center (CENPES—Petrobras), Rio de Janeiro, RJ, Brazil
| | - Eduardo A. Perondi
- Department of Mechanical Engineering, Federal University of Rio Grande do Sul, Porto Alegre, RS, Brazil
| | - André V. Wentz
- National Service of Industrial Training (SENAI), São Leopoldo, RS, Brazil
| | | | - Dante A. C. Barone
- Institute of Informatics (Inf), Federal University of Rio Grande do Sul, Porto Alegre, RS, Brazil
| | - Hugo F. L. Santos
- Leopoldo Américo Miguez de Mello Research and Development Center (CENPES—Petrobras), Rio de Janeiro, RJ, Brazil
| | - Marcus V. C. Magalhães
- Leopoldo Américo Miguez de Mello Research and Development Center (CENPES—Petrobras), Rio de Janeiro, RJ, Brazil
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Affiliation(s)
- Joseph Muré
- EDF Recherche et Développement and Université Paris Diderot
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10
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Bayesian Reference Analysis for the Generalized Normal Linear Regression Model. Symmetry (Basel) 2021. [DOI: 10.3390/sym13050856] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
This article proposes the use of the Bayesian reference analysis to estimate the parameters of the generalized normal linear regression model. It is shown that the reference prior led to a proper posterior distribution, while the Jeffreys prior returned an improper one. The inferential purposes were obtained via Markov Chain Monte Carlo (MCMC). Furthermore, diagnostic techniques based on the Kullback–Leibler divergence were used. The proposed method was illustrated using artificial data and real data on the height and diameter of Eucalyptus clones from Brazil.
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Ramos PL, Mota AL, Ferreira PH, Ramos E, Tomazella VLD, Louzada F. Bayesian analysis of the inverse generalized gamma distribution using objective priors. J STAT COMPUT SIM 2020. [DOI: 10.1080/00949655.2020.1830991] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Pedro L. Ramos
- Institute of Mathematical and Computer Sciences, University of São Paulo, São Carlos, Brazil
| | - Alex L. Mota
- Department of Statistics, Federal University of São Carlos, São Carlos, Brazil
| | - Paulo H. Ferreira
- Institute of Mathematical and Computer Sciences, University of São Paulo, São Carlos, Brazil
- Department of Statistics, Federal University of Bahia, Salvador, Brazil
| | - Eduardo Ramos
- Institute of Mathematical and Computer Sciences, University of São Paulo, São Carlos, Brazil
| | | | - Francisco Louzada
- Institute of Mathematical and Computer Sciences, University of São Paulo, São Carlos, Brazil
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Klebanov I, Sikorski A, Schütte C, Röblitz S. Objective priors in the empirical Bayes framework. Scand Stat Theory Appl 2020. [DOI: 10.1111/sjos.12485] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
| | | | - Christof Schütte
- Zuse Institute Berlin
- Department of Mathematics and Computer Science, Free University Berlin
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Lovric MM. Conflicts in Bayesian Statistics Between Inference Based on Credible Intervals and Bayes Factors. JOURNAL OF MODERN APPLIED STATISTICAL METHODS 2020. [DOI: 10.22237/jmasm/1556670540] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022]
Abstract
In frequentist statistics, point-null hypothesis testing based on significance tests and confidence intervals are harmonious procedures and lead to the same conclusion. This is not the case in the domain of the Bayesian framework. An inference made about the point-null hypothesis using Bayes factor may lead to an opposite conclusion if it is based on the Bayesian credible interval. Bayesian suggestions to test point-nulls using credible intervals are misleading and should be dismissed. A null hypothesized value may be outside a credible interval but supported by Bayes factor (a Type I conflict), or contrariwise, the null value may be inside a credible interval but not supported by the Bayes factor (Type II conflict). Two computer programs in R have been developed that confirm the existence of a countable infinite number of cases, for which Bayes credible intervals are not compatible with Bayesian hypothesis testing.
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Ramos PL, Louzada F, Ramos E, Dey S. The Fréchet distribution: Estimation and application - An overview. JOURNAL OF STATISTICS & MANAGEMENT SYSTEMS 2019. [DOI: 10.1080/09720510.2019.1645400] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- Pedro L. Ramos
- Institute of Mathematical and Computer Sciences, University of São Paulo, Avenida Trabalhador São-Carlense 400, 13566-590 Sao Carlos SP, Brazil
| | - Francisco Louzada
- Institute of Mathematical and Computer Sciences, University of São Paulo, Avenida Trabalhador São-Carlense 400, 13566-590 Sao Carlos SP, Brazil
| | - Eduardo Ramos
- Institute of Mathematical and Computer Sciences, University of São Paulo, Avenida Trabalhador São-Carlense 400, 13566-590 Sao Carlos SP, Brazil
| | - Sanku Dey
- Department of Statistics, St. Anthony’s College, Shillong 793001, Meghalaya, India
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16
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Ramos PL, Almeida MP, Tomazella VLD, Louzada F. Improved Bayes estimators and prediction for the Wilson-Hilferty distribution. AN ACAD BRAS CIENC 2019; 91:e20190002. [PMID: 31432908 DOI: 10.1590/0001-3765201920190002] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/02/2019] [Accepted: 06/10/2019] [Indexed: 11/21/2022] Open
Abstract
In this paper, we revisit the Wilson-Hilferty distribution and presented its mathematical properties such as the r-th moments and reliability properties. The parameters estimators are discussed using objective reference Bayesian analysis for both complete and censored data where the resulting marginal posterior intervals have accurate frequentist coverage. A simulation study is presented to compare the performance of the proposed estimators with the frequentist approach where it is observed a clear advantage for the Bayesian method. Finally, the proposed methodology is illustrated on three real datasets.
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Affiliation(s)
- Pedro L Ramos
- Departamento de Matemática Aplicada e Estatística, Universidade de São Paulo, Avenida TrabalhadorSão-Carlense, 400, 13566-590 São Carlos, SP, Brazil
| | - Marco P Almeida
- Departamento de Matemática Aplicada e Estatística, Universidade de São Paulo, Avenida TrabalhadorSão-Carlense, 400, 13566-590 São Carlos, SP, Brazil.,Departamento de Estatística, Universidade Federal de São Carlos, Rodovia Washington Luis, Km 235, 13565-905 São Carlos, SP, Brazil
| | - Vera L D Tomazella
- Departamento de Estatística, Universidade Federal de São Carlos, Rodovia Washington Luis, Km 235, 13565-905 São Carlos, SP, Brazil
| | - Francisco Louzada
- Departamento de Matemática Aplicada e Estatística, Universidade de São Paulo, Avenida TrabalhadorSão-Carlense, 400, 13566-590 São Carlos, SP, Brazil
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Muré J. Optimal compromise between incompatible conditional probability distributions, with application to Objective Bayesian Kriging. ESAIM-PROBAB STAT 2019. [DOI: 10.1051/ps/2018023] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
Abstract
Models are often defined through conditional rather than joint distributions, but it can be difficult to check whether the conditional distributions are compatible, i.e. whether there exists a joint probability distribution which generates them. When they are compatible, a Gibbs sampler can be used to sample from this joint distribution. When they are not, the Gibbs sampling algorithm may still be applied, resulting in a “pseudo-Gibbs sampler”. We show its stationary probability distribution to be the optimal compromise between the conditional distributions, in the sense that it minimizes a mean squared misfit between them and its own conditional distributions. This allows us to perform Objective Bayesian analysis of correlation parameters in Kriging models by using univariate conditional Jeffreys-rule posterior distributions instead of the widely used multivariate Jeffreys-rule posterior. This strategy makes the full-Bayesian procedure tractable. Numerical examples show it has near-optimal frequentist performance in terms of prediction interval coverage.
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Barrera M, Lira I, Sánchez-Sánchez M, Suárez-Llorens A. Bayesian treatment of results from radioanalytical measurements. Effect of prior information modification in the final value of the activity. Radiat Phys Chem Oxf Engl 1993 2019. [DOI: 10.1016/j.radphyschem.2018.11.023] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Duchi J, Khosravi K, Ruan F. Multiclass classification, information, divergence and surrogate risk. Ann Stat 2018. [DOI: 10.1214/17-aos1657] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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20
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Muñoz LM, Gelzer ARM, Fenton FH, Qian W, Lin W, Gilmour RF, Otani NF. Discordant Alternans as a Mechanism for Initiation of Ventricular Fibrillation In Vitro. J Am Heart Assoc 2018; 7:e007898. [PMID: 30371176 PMCID: PMC6201417 DOI: 10.1161/jaha.117.007898] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 03/02/2018] [Accepted: 06/19/2018] [Indexed: 11/16/2022]
Abstract
Background Ventricular tachyarrhythmias are often preceded by short sequences of premature ventricular complexes. In a previous study, a restitution-based computational model predicted which sequences of stimulated premature complexes were most likely to induce ventricular fibrillation in canines in vivo. However, the underlying mechanism, based on discordant-alternans dynamics, could not be verified in that study. The current study seeks to elucidate the mechanism by determining whether the spatiotemporal evolution of action potentials and initiation of ventricular fibrillation in in vitro experiments are consistent with model predictions. Methods and Results Optical mapping voltage signals from canine right-ventricular tissue (n=9) were obtained simultaneously from the entire epicardium and endocardium during and after premature stimulus sequences. Model predictions of action potential propagation along a 1-dimensional cable were developed using action potential duration versus diastolic interval data. The model predicted sign-change patterns in action potential duration and diastolic interval spatial gradients with posterior probabilities of 91.1%, and 82.1%, respectively. The model predicted conduction block with 64% sensitivity and 100% specificity. A generalized estimating equation logistic-regression approach showed that model-prediction effects were significant for both conduction block ( P<1×10-15, coefficient 44.36) and sustained ventricular fibrillation ( P=0.0046, coefficient, 1.63) events. Conclusions The observed sign-change patterns favored discordant alternans, and the model successfully identified sequences of premature stimuli that induced conduction block. This suggests that the relatively simple discordant-alternans-based process that led to block in the model may often be responsible for ventricular fibrillation onset when preceded by premature beats. These observations may aid in developing improved methods for anticipating block and ventricular fibrillation.
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Affiliation(s)
- Laura M. Muñoz
- School of Mathematical SciencesRochester Institute of TechnologyRochesterNY
| | | | | | | | | | - Robert F. Gilmour
- University of Prince Edward IslandCharlottetownPrince Edward IslandCanada
| | - Niels F. Otani
- School of Mathematical SciencesRochester Institute of TechnologyRochesterNY
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Apolloni B, Bassis S. The randomness of the inferred parameters. A machine learning framework for computing confidence regions. Inf Sci (N Y) 2018. [DOI: 10.1016/j.ins.2018.04.047] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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22
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Casadei D, Grunwald C, Kröninger K, Mentzel F. Objective Bayesian analysis of counting experiments with correlated sources of background. J Appl Stat 2018. [DOI: 10.1080/02664763.2017.1289367] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Diego Casadei
- School of Engineering, FHNW, Windisch, Switzerland
- School of Physics and Astronomy, University of Birmingham, Birmingham, UK
| | | | - Kevin Kröninger
- Lehrstuhl Experimentelle Physik IV, TU Dortmund, Dortmund, Germany
| | - Florian Mentzel
- Lehrstuhl Experimentelle Physik IV, TU Dortmund, Dortmund, Germany
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23
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Conceição KS, Tomazella V, Andrade MG, Louzada F. Biparametric zero-modified power series distributions: Bayesian analysis under a reference prior approach. COMMUN STAT-THEOR M 2017. [DOI: 10.1080/03610926.2016.1236960] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Katiane S. Conceição
- Department of Applied Mathematics and Statistics, Institute of Mathematics and Computer Science, University of São Paulo, São Paulo, Brazil
| | - Vera Tomazella
- Department of Statistics, Federal University of São Carlos, São Paulo, Brazil
| | - Marinho G. Andrade
- Department of Applied Mathematics and Statistics, Institute of Mathematics and Computer Science, University of São Paulo, São Paulo, Brazil
| | - Francisco Louzada
- Department of Applied Mathematics and Statistics, Institute of Mathematics and Computer Science, University of São Paulo, São Paulo, Brazil
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Ramos PL, Achcar JA, Moala FA, Ramos E, Louzada F. Bayesian analysis of the generalized gamma distribution using non-informative priors. STATISTICS-ABINGDON 2017. [DOI: 10.1080/02331888.2017.1327532] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Pedro L. Ramos
- Institute of Mathematical and Computer Sciences, USP, Sao Carlos, Brazil
| | - Jorge A. Achcar
- Social Medicine Department, Medical School, USP, Ribeirao Preto, Brazil
| | - Fernando A. Moala
- Department of Statistics, Sao Paulo State University, Presidente Prudente, Brazil
| | - Eduardo Ramos
- Institute of Mathematical and Computer Sciences, USP, Sao Carlos, Brazil
| | - Francisco Louzada
- Institute of Mathematical and Computer Sciences, USP, Sao Carlos, Brazil
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Tuyl F, Gerlach R, Mengersen K. Consensus priors for multinomial and binomial ratios. JOURNAL OF STATISTICAL THEORY AND PRACTICE 2016. [DOI: 10.1080/15598608.2016.1219684] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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27
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Villa C, Walker SG. An Objective Approach to Prior Mass Functions for Discrete Parameter Spaces. J Am Stat Assoc 2015. [DOI: 10.1080/01621459.2014.946319] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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28
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Fernandes AD, Macklaim JM, Linn TG, Reid G, Gloor GB. ANOVA-like differential expression (ALDEx) analysis for mixed population RNA-Seq. PLoS One 2013; 8:e67019. [PMID: 23843979 PMCID: PMC3699591 DOI: 10.1371/journal.pone.0067019] [Citation(s) in RCA: 429] [Impact Index Per Article: 39.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2012] [Accepted: 05/17/2013] [Indexed: 11/18/2022] Open
Abstract
Experimental variance is a major challenge when dealing with high-throughput sequencing data. This variance has several sources: sampling replication, technical replication, variability within biological conditions, and variability between biological conditions. The high per-sample cost of RNA-Seq often precludes the large number of experiments needed to partition observed variance into these categories as per standard ANOVA models. We show that the partitioning of within-condition to between-condition variation cannot reasonably be ignored, whether in single-organism RNA-Seq or in Meta-RNA-Seq experiments, and further find that commonly-used RNA-Seq analysis tools, as described in the literature, do not enforce the constraint that the sum of relative expression levels must be one, and thus report expression levels that are systematically distorted. These two factors lead to misleading inferences if not properly accommodated. As it is usually only the biological between-condition and within-condition differences that are of interest, we developed ALDEx, an ANOVA-like differential expression procedure, to identify genes with greater between- to within-condition differences. We show that the presence of differential expression and the magnitude of these comparative differences can be reasonably estimated with even very small sample sizes.
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Affiliation(s)
| | - Jean M. Macklaim
- Department of Biochemistry, The University of Western Ontario, London, Ontario, Canada
- Canadian Research & Development Centre for Probiotics, Lawson Health Research Institute, London, Ontario, Canada
| | - Thomas G. Linn
- Department of Microbiology & Immunology, The University of Western Ontario, London, Ontario, Canada
| | - Gregor Reid
- Department of Microbiology & Immunology, The University of Western Ontario, London, Ontario, Canada
- Department of Surgery, The University of Western Ontario, London, Ontario, Canada
- Canadian Research & Development Centre for Probiotics, Lawson Health Research Institute, London, Ontario, Canada
| | - Gregory B. Gloor
- Department of Biochemistry, The University of Western Ontario, London, Ontario, Canada
- Canadian Research & Development Centre for Probiotics, Lawson Health Research Institute, London, Ontario, Canada
- * E-mail:
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Leung B, Steele RJ. The value of a datum - how little data do we need for a quantitative risk analysis? DIVERS DISTRIB 2013. [DOI: 10.1111/ddi.12062] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022] Open
Affiliation(s)
| | - Russell J. Steele
- Department of Mathematics and Statistics; McGill University; Montreal; Quebec; H3A 0B9; Canada
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Lopes MVDO, da Silva VM, de Araujo TL. [Nursing diagnoses analysis under the bayesian perspective]. Rev Esc Enferm USP 2012; 46:994-1000. [PMID: 23018413 DOI: 10.1590/s0080-62342012000400030] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2011] [Accepted: 12/22/2011] [Indexed: 11/21/2022] Open
Abstract
The use of Bayesian statistical techniques is an approach that is well accepted and established in fields outside of nursing as a paradigm to reduce the uncertainty present in a given clinical situation. The purpose of this article is to provide guidance regarding the specific use of the Bayesian paradigm in the analysis of nursing diagnoses. The steps and interpretations of Bayesian analysis are discussed. One theoretical and one practical example of Bayesian analysis of nursing diagnoses are presented. It describes how the Bayesian approach can be used to summarize the available knowledge and make point and interval estimates of the true probability of a nursing diagnosis. It was concluded that the application of Bayesian statistical methods is an important tool for more accurate definition of probabilities related to nursing diagnoses.
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Vehtari A, Ojanen J. A survey of Bayesian predictive methods for model assessment, selection and comparison. STATISTICS SURVEYS 2012. [DOI: 10.1214/12-ss102] [Citation(s) in RCA: 172] [Impact Index Per Article: 14.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Komaki F. Asymptotically minimax Bayesian predictive densities for multinomial models. Electron J Stat 2012. [DOI: 10.1214/12-ejs700] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Apolloni B, Bassis S. Confidence About Possible Explanations. IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS. PART B, CYBERNETICS : A PUBLICATION OF THE IEEE SYSTEMS, MAN, AND CYBERNETICS SOCIETY 2011; 41:1639-53. [PMID: 21724515 DOI: 10.1109/tsmcb.2011.2158306] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
We revise the notion of confidence with which we estimate the parameters of a given distribution law in terms of their compatibility with the sample we have observed. This is a recent perspective that allows us to get a more intuitive feeling of the crucial concept of the confidence interval in parametric inference together with quick tools for exactly computing them even in conditions far from the common Gaussian framework where standard methods fail. The key artifact consists of working with a representation of the compatible parameters in terms of random variables without priors. This leads to new estimators that meet the most demanding requirements of the modern statistical inference in terms of learning algorithms. We support our methods with: a consistent theoretical framework, general-purpose estimation procedures, and a set of paradigmatic benchmarks.
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Sweeting T. Discussion of “Objective Priors: An Introduction for Frequentists” by M. Ghosh. Stat Sci 2011. [DOI: 10.1214/11-sts338b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Bernardo JM. Discussion of “Objective Priors: An Introduction for Frequentists” by M. Ghosh. Stat Sci 2011. [DOI: 10.1214/11-sts338a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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On the choice of a noninformative prior for Bayesian inference of discretized normal observations. Comput Stat 2011. [DOI: 10.1007/s00180-011-0251-7] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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de Castro M, Tomazella VLD. Does reference prior alleviate the incidental parameter problem? BRAZ J PROBAB STAT 2010. [DOI: 10.1214/09-bjps108] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Ebrahimi N, Soofi ES, Soyer R. On the Sample Information About Parameter and Prediction. Stat Sci 2010. [DOI: 10.1214/10-sts329] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Moala FA, Rodrigues J, Tomazella VLD. A Note on the Prior Distributions of Weibull Parameters for the Reliability Function. COMMUN STAT-THEOR M 2009. [DOI: 10.1080/03610920802362801] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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Kottas A, Sansó B. Bayesian mixture modeling for spatial Poisson process intensities, with applications to extreme value analysis. J Stat Plan Inference 2007. [DOI: 10.1016/j.jspi.2006.05.022] [Citation(s) in RCA: 53] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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