allow using student_t instead of gaussian for likelihood

[jgabry]

For stan_glm with a suitable outcome (and maybe stan_lmer), we should provide an option to use the t distribution as the likelihood instead of a Gaussian.

Perhaps we just follow BDA3 17.2 and use the fact that

y_i ~ t_v(m, s^2)

is equivalent to

y_i | V_i ~ N(m, V_i)
V_i ~ scaled-inv-chi-sq(v, s^2)

[bgoodri]

We're going to also need a prior on the degrees of freedom. Aki suggested gamma with shape 2 and rate 0.1
https://github.com/stan-dev/stan/wiki/Prior-Choice-Recommendations

[jgabry]

@bgoodri Do you think the approach in my initial comment is preferable to implementing the student_t likelihood the same way we do the others? Might it be more efficient to not estimate all N of the V_i terms and instead just use y ~ student_t(...)? I'm not sure.

[bgoodri]

Yeah, although we would have to create a family object for the t
distribution.

On Mon, Jan 18, 2016 at 1:39 PM, Jonah Gabry notifications@github.com
wrote:

@bgoodri https://github.com/bgoodri Do you think the approach in my
initial comment is preferable to implementing the student_t likelihood the
same way we do the others? Might it be more efficient to not estimate all N
of the V_i terms and instead just use y ~ student_t(...)? I'm not sure.

—
Reply to this email directly or view it on GitHub
#35 (comment).

[maciematt]

Hi All - just wondering if adding a Student's t distribution for likelihood is still being considered? Or was this effort conclusively discontinued?

[bgoodri]

We certainly haven't ruled out including it; we just haven't included it yet.

…

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