bsamGP: An R Package for Bayesian Spectral Analysis Models Using Gaussian Process Priors

Abstract

The Bayesian spectral analysis model (BSAM) is a powerful tool to deal with semiparametric methods in regression and density estimation based on the spectral representation of Gaussian process priors. The bsamGP package for R provides a comprehensive set of programs for the implementation of fully Bayesian semiparametric methods based on BSAM. Currently, bsamGP includes semiparametric additive models for regression, generalized models and density estimation. In particular, bsamGP deals with constrained regression models with monotone, convex/concave, S-shaped and U-shaped functions by modeling derivatives of regression functions as squared Gaussian processes. bsamGP also contains Bayesian model selection procedures for testing the adequacy of a parametric model relative to a non-specific semiparametric alternative and the existence of the shape restriction. To maximize computational efficiency, we carry out posterior sampling algorithms of all models using compiled Fortran code. The package is illustrated through Bayesian semiparametric analyses of synthetic data and benchmark data.

Flexible Bayesian quantile curve fitting with shape restrictions under the Dirichlet process mixture of the generalized asymmetric Laplace distribution

“…Subsequently, the Gaussian process g (≡ Z ) is expressed as an infinite series expansion with the Karhunen–Loéve representation in terms of the cosine basis functions given by All piecewise continuous functions on [0, 1] are expressed by the representation in Equation and the infinite sum is truncated at a sufficiently large J , with in practice (see, e.g., Lenk, 1999; Choi, Lee & Roy, 2009; Lenk & Choi, 2017). The Bayesian approach to exploiting the cosine series to represent a Gaussian process is known as the Bayesian spectral analysis model (Lenk & Choi, 2017; Jo et al, 2019), and the corresponding quantile regression model is referred to as the Bayesian spectral analysis quantile regression (BSAQ) hereafter.…”

“…Note that is only used for the FBSAQ with shape restrictions and that, since the spectral coefficients have a sign indeterminacy, we assume for identification (Lenk & Choi, 2017). For the remainder of this article, we set hyperparameters for , and , fixed as , , and as in Jo et al (2019) and Lenk & Choi (2017). To ensure the monotonicity of g ( x ), we assume with a default choice, we set , similar to the case with .…”

Bayesian semiparametric mixed effects models for meta‐analysis of the literature data : An application to cadmium toxicity studies

“…In the preliminary analysis, we model the nonlinear dose‐response function f (·) using the BSAR, 13,21 where f ( x ij ) is expressed as a finite cosine series expansion, , φ 0 ( x ij ) = 1, and , k ≥ 1. We then implement the initial Bayesian semiparametric mixed effect model with the companion R library bsamGP 22 . The top row of Figure 1 shows the overall dose‐response curve estimated in the preliminary analysis in panel (B), with the scatterplot for vs MG) in panel (A).…”

IP Promotion and Integrated Media Communication of Regional Culture in Second- and Third-Tier Cities Based on Bayesian Viewpoint Evolution Modeling

“…Experiments on two TWITTER corpora demonstrate the effectiveness of this Bayesian model for layering viewpoints. Literature [13] discusses the Bayesian Spectral Analysis Model (BSAM) as a powerful tool for dealing with semiparametric regression and density estimation methods based on a priori spectral representations of Gaussian processes. To improve computational efficiency, compiled Fortran code was used to perform a posteriori sampling algorithms for all models, and the good performance of the package was verified by semiparametric analysis of synthetic and benchmark data.…”