Gibbs samplers for Bayesian regression, mixtures and genomic prediction

BayesLinearHalfcauchy: normal regression with a half-Cauchy prior on sigma. FiniteMixtureGibbs: finite normal mixture. ContaminatedNormalOutliers: Box-Tiao outlier probabilities. BayesA and BayesB: marker-effect models of genomic prediction. GenomicReliability: 1 - PEV / sigma_a^2. The Philox stream and Marsaglia-Tsang gamma draws reproduce the Python arm morie.fn.bayesreg.

Usage

BayesLinearHalfcauchy(
  y,
  X,
  prior_var = 1e+06,
  scale = 25,
  ndraw = 2000,
  burn_in = 500,
  seed = 0
)

FiniteMixtureGibbs(y, K, ndraw = 2000, burn_in = 500, seed = 0, alpha = 1)

ContaminatedNormalOutliers(
  y,
  eps = 0.05,
  k = 5,
  ndraw = 2000,
  burn_in = 500,
  seed = 0
)

BayesA(y, M, nu = 4.012, s2 = NULL, ndraw = 2000, burn_in = 500, seed = 0)

BayesB(
  y,
  M,
  pi = 0.95,
  nu = 4.012,
  s2 = NULL,
  ndraw = 2000,
  burn_in = 500,
  seed = 0
)

GenomicReliability(pev, sigma2_a)

Arguments

y: Response.
X: Design matrix including the intercept.
prior_var: Prior variance of the coefficients.
scale: Half-Cauchy scale.
ndraw, burn_in: Retained and burn-in draws.
seed: Philox seed.
K: Number of mixture components.
alpha: Dirichlet concentration.
eps, k: Contamination probability and scale inflation.
M: Marker matrix (individuals by markers).
nu, s2: Scaled inverse chi-square degrees of freedom and scale.
pi: Proportion of markers without effect.
pev: Prediction error variances.
sigma2_a: Additive genetic variance.

Value

A list.

References

Gelman, A. (2006). Prior distributions for variance parameters in hierarchical models. Bayesian Analysis 1, 515-534.

Diebolt, J. and Robert, C. P. (1994). Estimation of finite mixture distributions through Bayesian sampling. Journal of the Royal Statistical Society B 56, 363-375.

Box, G. E. P. and Tiao, G. C. (1968). A Bayesian approach to some outlier problems. Biometrika 55, 119-129.

Meuwissen, T. H. E., Hayes, B. J. and Goddard, M. E. (2001). Prediction of total genetic value using genome-wide dense marker maps. Genetics 157, 1819-1829.

Examples

GenomicReliability(c(0.2, 0.5), 0.8)$reliability
#> [1] 0.750 0.375