# Bayesian measurement error models using finite mixtures of scale mixtures of skew-normal distributions

@article{BarbosaCabral2020BayesianME, title={Bayesian measurement error models using finite mixtures of scale mixtures of skew-normal distributions}, author={Celso R{\^o}mulo Barbosa Cabral and Nelson Lima de Souza and Jeremias Le{\~a}o}, journal={Journal of Statistical Computation and Simulation}, year={2020}, volume={92}, pages={623 - 644} }

We present a proposal to deal with the non-normality issue in the context of regression models with measurement errors when both the response and the explanatory variable are observed with error. We extend the normal model by jointly modelling the unobserved covariate and the random errors by a finite mixture of scale mixture of skew-normal distributions. This approach allows us to model data with great flexibility, accommodating skewness, heavy tails, and multi-modality. The main virtue of…

## 2 Citations

### Multivariate measurement error models with normal mean‐variance mixture distributions

- MathematicsStat
- 2022

The class of normal mean‐variance mixture (NMVM) distributions is a rich family of asymmetric and heavy‐tailed distributions and has been widely considered in parametric modeling of the data for…

### Bayesian Hierarchical Models For Multi-type Survey Data Using Spatially Correlated Covariates Measured With Error

- Computer Science
- 2022

A Bayesian implementation of a Hierarchical Generalized Transformation (HGT) model is adopted to deal with the non-conjugacy of non-Gaussian data models when estimated using a Latent Gaussian Process (LGP) model.

## References

SHOWING 1-10 OF 67 REFERENCES

### Multivariate measurement error models based on scale mixtures of the skew–normal distribution

- Mathematics
- 2010

Scale mixtures of the skew–normal (SMSN) distribution is a class of asymmetric thick–tailed distributions that includes the skew–normal (SN) distribution as a special case. The main advantage of…

### A robust multivariate measurement error model with skew-normal/independent distributions and Bayesian MCMC implementation

- Mathematics
- 2009

### Finite mixture of regression models for censored data based on scale mixtures of normal distributions

- Computer ScienceAdv. Data Anal. Classif.
- 2019

A simple EM-type algorithm is developed to perform maximum likelihood inference of the parameters in the proposed model of scale mixtures of normal distributions (SMN), which allows to model data with great flexibility, accommodating multimodality and heavy tails at the same time.

### Bayesian analysis of skew-normal independent linear mixed models with heterogeneity in the random-effects population

- Mathematics
- 2012

### A heteroscedastic measurement error model based on skew and heavy-tailed distributions with known error variances

- Mathematics
- 2018

ABSTRACT In this paper, we study inference in a heteroscedastic measurement error model with known error variances. Instead of the normal distribution for the random components, we develop a model…

### Multivariate mixture modeling using skew-normal independent distributions

- MathematicsComput. Stat. Data Anal.
- 2012

### Bayesian analysis of censored linear regression models with scale mixtures of normal distributions

- Mathematics
- 2015

As is the case of many studies, the data collected are limited and an exact value is recorded only if it falls within an interval range. Hence, the responses can be either left, interval or right…

### Bayesian analysis of censored linear regression models with scale mixtures of skew-normal distributions

- Mathematics
- 2017

In many studies, limited or censored data are collected. This occurs, in several practical situations, for reasons such as limitations of measuring equipment or from experimental design. Hence, the…

### Multivariate measurement error models based on Student-t distribution under censored responses

- MathematicsStatistics
- 2018

ABSTRACT Measurement error models constitute a wide class of models that include linear and nonlinear regression models. They are very useful to model many real-life phenomena, particularly in the…

### Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper)

- Mathematics
- 2004

Various noninformative prior distributions have been suggested for scale parameters in hierarchical models. We construct a new folded-noncentral-t family of conditionally conjugate priors for…