Journal ArticleDOI
Bayesian Free-Knot Monotone Cubic Spline Regression
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In this article, a new Bayesian approach for monotone curve fitting based on the isotonic regression model is proposed, where the unknown linear regression function is approximated by a cubic spline and the constraints are represented by the intersection of quadratic cones.Abstract:
This article proposes a new Bayesian approach for monotone curve fitting based on the isotonic regression model. The unknown monotone regression function is approximated by a cubic spline and the constraints are represented by the intersection of quadratic cones. We treat the number and locations of knots as free parameters and use reversible jump Markov chain Monte Carlo to obtain posterior samples of knot configurations. Given the number and locations of the knots, second-order cone programming is used to estimate the remaining parameters. Simulation results suggest the method performs well and we illustrate the approach using the ASA car data.read more
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Bayesian estimation and inference for generalised partial linear models using shape-restricted splines
TL;DR: A Bayesian approach to generalised partial linear regression models is proposed, where regression functions are modelled nonparametrically using regression splines, with assumptions about shape and smoothness, which shows that the inference methods have desirable Bayesian and frequentist properties.
Journal ArticleDOI
A semiparametric probit model for case 2 interval-censored failure time data.
Xiaoyan Lin,Lianming Wang +1 more
TL;DR: This paper proposes to approximate the unknown nonparametric nondecreasing function in the probit model with a linear combination of monotone splines, leading to only a finite number of parameters to estimate.
Journal ArticleDOI
Semiparametric Bayes’ Proportional Odds Models for Current Status Data with Underreporting
Lianming Wang,David B. Dunson +1 more
TL;DR: A semiparametric Bayesian proportional odds model is proposed in which the baseline event time distribution is estimated nonparametrically by using adaptive monotone splines in a logistic regression model and the potential risk factors are included in the parametric part of the mean structure.
Journal ArticleDOI
Bayesian analysis of shape-restricted functions using Gaussian process priors
TL;DR: This paper proposes a Bayesian method to estimate shape-restricted functions using Gaussian process priors and modify the basic model with a spike-and-slab prior that improves model fit when the true function is on the boundary of the constraint space.
Journal ArticleDOI
Semiparametric regression with shape-constrained penalized splines
TL;DR: This work employs Markov chain Monte Carlo (MCMC) methods for model fitting, using a truncated prior distribution to impose the requisite shape restrictions on penalized splines within a linear mixed model framework.
References
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Journal ArticleDOI
Reversible jump Markov chain Monte Carlo computation and Bayesian model determination
TL;DR: In this article, the authors propose a new framework for the construction of reversible Markov chain samplers that jump between parameter subspaces of differing dimensionality, which is flexible and entirely constructive.
Journal ArticleDOI
Applications of second-order cone programming
TL;DR: In this paper, an efficient primal-dual interior-point method for solving second-order cone programs (SOCP) is presented. But it is not a generalization of interior point methods for convex problems.
Book
Order restricted statistical inference
TL;DR: In this paper, a set of multinomial parameters are derived about distributions subject to shape restrictions, and a conditional expectation given a sigma-lattice is given in a more general setting.
Journal ArticleDOI
Second-order cone programming
Farid Alizadeh,Donald Goldfarb +1 more
TL;DR: SOCP formulations are given for four examples: the convex quadratically constrained quadratic programming (QCQP) problem, problems involving fractional quadRatic functions, and many of the problems presented in the survey paper of Vandenberghe and Boyd as examples of SDPs can in fact be formulated as SOCPs and should be solved as such.