
624 Current Trends in Bayesian Methodology with Applications
computing toolbox and the hardware is a computer with two 2,496-core GPUs
(though in our implementation, we use only up to 1,000 cores).
30.3.1 Linear regression model with Student-t error
Consider a linear regression model with the Student-t erro r distribution as
follows
y
i
= x
′
i
β + σǫ
i
for i = 1, ..., n, (30.1)
where y
i
is the scalar dependent observa tion i, x
′
i
= (1 x
1i
x
2i
) is a row vector
of c ovariates, β is a column vector of length 3, σ is the scale par ameter, ǫ
i
is an error term which follows an independent standard Student-t, St(0, 1, ν)
distribution with ν ∈ (2 , 30) degrees of freedom. ...