# A Gibbs Sampler for Multivariate Linear Regression

@article{Mantz2015AGS, title={A Gibbs Sampler for Multivariate Linear Regression}, author={Adam B. Mantz}, journal={Monthly Notices of the Royal Astronomical Society}, year={2015}, volume={457}, pages={1279-1288} }

Kelly (2007, hereafter K07) described an efficient algorithm, using Gibbs sampling, for performing linear regression in the fairly general case where non-zero measurement errors exist for both the covariates and response variables, where these measurements may be correlated (for the same data point), where the response variable is affected by intrinsic scatter in addition to measurement error, and where the prior distribution of covariates is modeled by a flexible mixture of Gaussians rather…

## 15 Citations

### A Bayesian approach to linear regression in astronomy

- Physics
- 2015

Linear regression is common in astronomical analyses. I discuss a Bayesian hierarchical modeling of data with heteroscedastic and possibly correlated measurement errors and intrinsic scatter. The…

### Coping with selection effects: a Primer on regression with truncated data

- MathematicsMonthly Notices of the Royal Astronomical Society
- 2019

The finite sensitivity of instruments or detection methods means that data sets in many areas of astronomy, for example cosmological or exoplanet surveys, are necessarily systematically incomplete.…

### KLLR: A Scale-dependent, Multivariate Model Class for Regression Analysis

- Computer ScienceThe Astrophysical Journal
- 2022

This work introduces and implements a class of kernel localized linear regression (KLLR) models, a natural extension to the commonly used linear models that allows the parameters of the linear model—normalization, slope, and covariance matrix—to be scale dependent.

### LoCuSS: scaling relations between galaxy cluster mass, gas, and stellar content

- PhysicsMonthly Notices of the Royal Astronomical Society
- 2019

We present a simultaneous analysis of galaxy cluster scaling relations between weak-lensing mass and multiple cluster observables, across a wide range of wavelengths, that probe both gas and stellar…

### Cosmology and Astrophysics from Relaxed Galaxy Clusters III: Thermodynamic Profiles and Scaling Relations

- Physics
- 2016

This is the third in a series of papers studying the astrophysics and cosmology of massive, dynamically relaxed galaxy clusters. Our sample comprises 40 clusters identified as being dynamically…

### CCCP and MENeaCS: (updated) weak-lensing masses for 100 galaxy clusters

- PhysicsMonthly Notices of the Royal Astronomical Society
- 2020

Large area surveys continue to increase the samples of galaxy clusters that can be used to constrain cosmological parameters, provided that the masses of the clusters are measured robustly. To…

### GalWeight Application: A Publicly Available Catalog of Dynamical Parameters of 1800 Galaxy Clusters from SDSS-DR13, (GalWCat19)

- PhysicsThe Astrophysical Journal Supplement Series
- 2019

Utilizing the SDSS-DR13 spectroscopic data set, we create a new publicly available catalog of 1800 galaxy clusters (GalWeight cluster catalog, GalWCat19) and a corresponding catalog of 34,471…

### Weighing the giants– V. Galaxy cluster scaling relations

- Physics
- 2016

We present constraints on the scaling relations of galaxy cluster X-ray luminosity, temperature and gas mass (and derived quantities) with mass and redshift, employing masses from robust weak…

### Centre-excised X-ray luminosity as an efficient mass proxy for future galaxy cluster surveys

- Physics
- 2018

The cosmological constraining power of modern galaxy cluster catalogs can be improved by obtaining low-scatter mass proxy measurements for even a small fraction of sources. In the context of large…

### X-Ray Scaling Relations for a Representative Sample of Planck-selected Clusters Observed with XMM-Newton

- PhysicsThe Astrophysical Journal
- 2020

We report the scaling relations derived by fitting the X-ray parameters determined from analyzing the XMM-Newton observations of 120 galaxy clusters in the Planck Early Sunyaev–Zel’dovich (SZ) sample…

## References

SHOWING 1-10 OF 23 REFERENCES

### Some Aspects of Measurement Error in Linear Regression of Astronomical Data

- Physics
- 2007

I describe a Bayesian method to account for measurement errors in linear regression of astronomical data. The method allows for heteroscedastic and possibly correlated measurement errors and…

### Hyper-Fit: Fitting Linear Models to Multidimensional Data with Multivariate Gaussian Uncertainties

- Computer SciencePublications of the Astronomical Society of Australia
- 2015

The general likelihood function to be maximised to recover the best fitting model is derived and applications to toy examples and to real astronomical data from the literature are included: the mass-size, Tully–Fisher, Fundamental Plane, and mass-spin-morphology relations.

### Selecting the precision parameter prior in Dirichlet process mixture models

- Computer Science
- 2012

### HIERARCHICAL PROBABILISTIC INFERENCE OF COSMIC SHEAR

- Physics
- 2014

Point estimators for the shearing of galaxy images induced by gravitational lensing involve a complex inverse problem in the presence of noise, pixelization, and model uncertainties. We present a…

### Bayesian Density Estimation and Inference Using Mixtures

- Mathematics
- 1995

Abstract We describe and illustrate Bayesian inference in models for density estimation using mixtures of Dirichlet processes. These models provide natural settings for density estimation and are…

### PICACS: self-consistent modelling of galaxy cluster scaling relations

- Physics
- 2014

In this paper, we introduce PICACS, a physically-motivated, internally consistent model of scaling relations between galaxy cluster masses and their observable properties. This model can be used to…

### Bayesian Data Analysis

- Mathematics, Computer Science
- 1995

Detailed notes on Bayesian Computation Basics of Markov Chain Simulation, Regression Models, and Asymptotic Theorems are provided.

### CHANDRA CLUSTER COSMOLOGY PROJECT. II. SAMPLES AND X-RAY DATA REDUCTION

- Physics
- 2009

We discuss the measurements of the galaxy cluster mass functions at z ≈ 0.05 and z ≈ 0.5 using high-quality Chandra observations of samples derived from the ROSAT PSPC All-Sky and 400 deg2 surveys.…

### Galaxy cluster X-ray luminosity scaling relations from a representative local sample (REXCESS)

- Physics
- 2009

We examine the X-ray luminosity scaling relations of 31 nearby galaxy clusters from the Representative XMM-Newton Cluster Structure Survey (REXCESS). The objects are selected only in X-ray…