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Objective Bayesian model selection in generalized regression

English title Objective Bayesian model selection in generalized regression
Applicant Held Leonhard
Number 159715
Funding scheme Project funding (Div. I-III)
Research institution Institut für Epidemiologie, Biostatistik und Prävention Universität Zürich
Institution of higher education University of Zurich - ZH
Main discipline Mathematics
Start/End 01.05.2015 - 30.04.2018
Approved amount 169'463.00
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All Disciplines (2)

Discipline
Mathematics
Medical Statistics

Keywords (4)

Generalized regression; g-prior; Bayes factor; Objective Bayesian model selection

Lay Summary (German)

Lead
In vielen quantitativen Forschungsgebieten werden statistische Regressionsmethoden verwendet. Die Auswahl eines geeigneten Regressionsmodells ist dabei ein zentraler Bestandteil. Die derzeit in der Praxis verwendeten Methoden zur Modellwahl sind aber in ihrem Einsatzfeld oft beschränkt oder haben unbefriedigende theoretische Eigenschaften. Objektive Bayesianische Methoden zur Modellwahl adressieren diese Probleme, sind derzeit aber nur für das lineare Regressionsmodell entwickelt.
Lay summary

Inhalt und Ziel des Forschungsprojektes

 

Unser Ziel ist es, objektive Bayesianische Modellwahl-Methoden für generalisierte Regressionsmodelle zu entwickeln. Dabei stehen Modelle, die in der biomedizinischen Forschung häufig verwendet werden, im Vordergrund, wie etwa das logistische Regressionsmodell, die Cox-Regression, und Modelle mit zufälligen Effekten. Wir werden wichtige theoretische Erkenntnisse gewinnen, die eine Anwendung von objektiven Bayesianischen Modellwahlverfahren in der Praxis ermöglichen.

 

 

Wissenschaftlicher und gesellschaftlicher Kontext des Forschungsprojekts

 

Unsere Arbeit wird zu verbesserten Modellwahlverfahren führen, die breite Einsatzmöglichkeiten in der biomedizinischen Forschung haben werden. So werden verbesserte klinische Prognosemodelle dabei helfen, das Risiko von Krankheiten in der personalisierten Medizin besser abzuschätzen.

 

 

Direct link to Lay Summary Last update: 14.04.2015

Responsible applicant and co-applicants

Employees

Publications

Publication
On p-values and Bayes factors
Held Leonhard, Ott Manuela (2018), On p-values and Bayes factors, in Annual Review of Statistics and Its Application, 5, 393-419.
How the maximal evidence of P-values against point null hypotheses depends on sample size
Held Leonhard, Ott Manuela (2016), How the maximal evidence of P-values against point null hypotheses depends on sample size, in The American Statistician, (4), 335-341.
Bayesian tail probabilities for decision making
Held Leonhard, Bayesian tail probabilities for decision making, in Lesaffre Emmanuel, Boulanger Bruno, Baio Gianluca (ed.).

Scientific events

Active participation

Title Type of contribution Title of article or contribution Date Place Persons involved
4th Meeting on Statistics (Statistics4@Florence) Poster How does the maximal evidence of P-values from Fisher's exact test depend on sample size? 04.07.2017 Florence, Italy Ott Manuela;
InSPiRe Conference on Methodology for Clinical Trials in Small Populations and Rare Diseases Talk given at a conference What's the evidence? On P-values and Bayes factors for small samples 27.04.2017 Warwick, Great Britain and Northern Ireland Held Leonhard;
Colloquium at the Department of Statistics, LMU Munich Individual talk What's the evidence? On P-values and Bayes factors 20.07.2016 Munich, Germany Held Leonhard;
i-Like Workshop 2016 Talk given at a conference Approximate Bayesian model selection for clinical prediction 23.06.2016 Lancaster, Great Britain and Northern Ireland Held Leonhard;
ISBA World Meeting 2016 Talk given at a conference Objective Bayesian model selection for Cox regression 15.06.2016 Sardinia, Italy Held Leonhard;
ISBA World Meeting 2016 Poster How the maximal evidence of P-values against point null hypotheses depends on sample size 15.06.2016 Sardinia, Italy Ott Manuela;
Bayes 2016 Conference Talk given at a conference What's the evidence? On P-values and Bayes factors 18.05.2016 Leuven, Belgium Held Leonhard;
Lecture Series at the Department of Mathematical Sciences, Norwegian University of Science and Technology Individual talk Objective Bayesian model selection 19.04.2016 Trondheim, Norway Held Leonhard;
Summer School, Doctoral Program in Statistics and Applied Probability Individual talk Objective Bayesian model selection in regression 02.09.2015 Ovronnaz, Switzerland Held Leonhard;
11th International Workshop on Objective Bayes Methodology (O-Bayes15) Poster Minimum Bayes factors that depend on the sample size 02.06.2015 Valencia, Spain Ott Manuela;


Awards

Title Year
Stata Corp @ISBA Junior Travel Support Grant 2016
O-Bayes15 Junior Travel Grant 2015

Use-inspired outputs

Associated projects

Number Title Start Funding scheme
189295 Reverse-Bayes Design and Analysis of Replication Studies 01.11.2019 Project funding (Div. I-III)

Abstract

This research proposal aims to develop novel statistical methodology for objectiveBayesian model selection in generalized regression models. There is now a large literatureon automatic and objective Bayesian model selection for the linear model, whichunburden the statistician from eliciting manually the parameter priors for all modelsin the absence of substantive prior information (Berger and Pericchi, 2001). Theg-prior, usually attributed to Zellner (1986) but already used by Copas (1983), is thestandard choice for the regression coefficients. However, for generalized linear modelsand further extensions, there are computational and conceptual problems with the g-priorapproach. Similarly, research on the appropriate prior distribution on the modelspace and the selection of the “best” model has been done mainly in the linear model,e. g. Scott and Berger (2006, 2010) and Barbieri and Berger (2004). We will fill thesegaps and will extend the scope of objective Bayesian model selection to generalizedregression models.
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