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TBASS: A Robust Adaptation of Bayesian Adaptive Spline Surfaces

The R package TBASS is an extension of the BASS package created by Francom and Sansó (2019). The package is used to fit a Bayesian multivariate adaptive spline to a dataset that either follows a Student’s t-distribution or has outliers. Much of the framework for TBASS is adapted from the concepts of Bayesian Multivariate Adaptive Regression Splines (BMARS), specifically the work done by Denison, Mallick, and Smith (1998). The spline function is fit using a Reversible-Jump Markov Chain Monte Carlo algorithm,. By including this more robust generalization, a dataset with outliers can be accurately fit using the BMARS model, without the possibility of overfitting or variance inflation.

97 MATHEMATICS AND COMPUTING↗

Materials Data on TbAsS by Materials Project

TbAsS is Matlockite structured and crystallizes in the monoclinic P2_1/c space group. The structure is three-dimensional. Tb3+ is bonded in a 5-coordinate geometry to four equivalent As1- and five equivalent S2- atoms. There are a spread of Tb–As bond distances ranging from 3.11–3.18 Å. There are a spread of Tb–S bond distances ranging from 2.81–2.87 Å. As1- is bonded in a 8-coordinate geometry to four equivalent Tb3+ and four equivalent As1- atoms. There are a spread of As–As bond distances ranging from 2.55–2.91 Å. S2- is bonded to five equivalent Tb3+ atoms to form a mixture of distorted edge and corner-sharing STb5 trigonal bipyramids.

36 MATERIALS SCIENCE↗

Materials Data on TbAsSe by Materials Project

TbAsSe crystallizes in the orthorhombic Pnma space group. The structure is three-dimensional. Tb3+ is bonded in a 9-coordinate geometry to four equivalent As1- and five equivalent Se2- atoms. There are a spread of Tb–As bond distances ranging from 3.08–3.18 Å. There are four shorter (2.91 Å) and one longer (3.05 Å) Tb–Se bond lengths. As1- is bonded in a 8-coordinate geometry to four equivalent Tb3+ and four equivalent As1- atoms. There are two shorter (2.59 Å) and two longer (3.00 Å) As–As bond lengths. Se2- is bonded in a 5-coordinate geometry to five equivalent Tb3+ atoms.

36 MATERIALS SCIENCE↗