The Practice of Prior Elicitation

2019 ◽  
pp. 61-92
Author(s):  
Timothy H. Montague ◽  
Karen L. Price ◽  
John W. Seaman
Keyword(s):  
Prior Elicitation

scholarly journals Penalized complexity priors for degrees of freedom in Bayesian P-splines

2016 ◽  
Vol 16 (6) ◽  
pp. 429-453 ◽  
Author(s):  
Massimo Ventrucci ◽  
Håvard Rue
Keyword(s):  
Random Field ◽  
Markov Random Field ◽  
Smooth Function ◽  
Degrees Of Freedom ◽  
Penalized Splines ◽  
Prior Elicitation ◽  
Gaussian Markov Random Field ◽  
Markov Random ◽  
Gaussian Data

Bayesian penalized splines (P-splines) assume an intrinsic Gaussian Markov random field prior on the spline coefficients, conditional on a precision hyper-parameter [Formula: see text]. Prior elicitation of [Formula: see text] is difficult. To overcome this issue, we aim to building priors on an interpretable property of the model, indicating the complexity of the smooth function to be estimated. Following this idea, we propose penalized complexity (PC) priors for the number of effective degrees of freedom. We present the general ideas behind the construction of these new PC priors, describe their properties and show how to implement them in P-splines for Gaussian data.

scholarly journals Prior Elicitation, Assessment and Inference with a Dirichlet Prior

Entropy ◽  
2017 ◽  
Vol 19 (10) ◽  
pp. 564 ◽  
Author(s):  
Michael Evans ◽  
Irwin Guttman ◽  
Peiying Li
Keyword(s):  
Prior Elicitation ◽  
Dirichlet Prior

Graphical prior elicitation in univariate models

2017 ◽  
Vol 47 (10) ◽  
pp. 2906-2924 ◽  
Author(s):  
Christopher J. Casement ◽  
David J. Kahle
Keyword(s):  
Prior Elicitation

scholarly journals Power Prior Elicitation in Bayesian Quantile Regression

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Rahim Alhamzawi ◽  
Keming Yu
Keyword(s):  
Quantile Regression ◽  
Prior Distribution ◽  
Likelihood Function ◽  
Real Data ◽  
Laplace Distribution ◽  
Scale Mixture ◽  
Prior Elicitation ◽  
Bayesian Quantile Regression ◽  
Critical Issues ◽  
Power Prior

We address a quantile dependent prior for Bayesian quantile regression. We extend the idea of the power prior distribution in Bayesian quantile regression by employing the likelihood function that is based on a location-scale mixture representation of the asymmetric Laplace distribution. The propriety of the power prior is one of the critical issues in Bayesian analysis. Thus, we discuss the propriety of the power prior in Bayesian quantile regression. The methods are illustrated with both simulation and real data.

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