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 [email protected] 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.

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[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.

On Wed, Feb 12, 2020 at 1:09 PM Matt Maciejewski [email protected] wrote:

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

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