# How to choose a prior : family for a response with negative values?

I’m modeling percentage change in oxygen levels in the blood from a particular experiment. So my prior before seeing the data was an inverse gaussian distribution. But my data (response variable ) has some negative values. The family( ): Inverse.gaussian doesn’t take negative values. How should I go about this? [ https://rdrr.io/cran/brms/] My min and max range of values is (-23,40).With a mean of 4 and a median of 3.5. (Also this is a repeated measures data).The following is the histogram distribution of the data. The family function I mentioned here is from the 'brms' package.

• What do you mean by prior in here? family(), if I understand you correctly, is the distribution for the data, it has nothing to do with priors for the parameters. I'm also curious how oxygen level can be negative? – Tim Jun 10 '20 at 10:04
• @Tim I'm using this awesome package called: brms.They have this family function [ 'rdrr.io/cran/brms/']. – amarykya_ishtmella Jun 10 '20 at 10:14
• @Tim because the repose variable is a percentage change over time.So, it's the change of oxygen level in your blood after you did a workout(example) . This is fluctuating values. – amarykya_ishtmella Jun 10 '20 at 10:16
• In such case choice of inverse Gaussian is incorrect, but this is not a prior. – Tim Jun 10 '20 at 10:21

If your outcomes are relative changes, that can be either positive, or negative, choosing inverse Gaussian is a bad idea, because it is a distribution for non-negative outcomes. You didn't give us much details, but given that mean and median are very close and they seem to be lying approximately in the middle between minimum and maximum, it seems that your data is fairly symmetric, isn't it? If that is the case, why not using Gaussian as a likelihood function? If the data has long tails, then you could consider $$t$$-distribution. To be more precise, we are interested in conditional distribution $$E[Y|X]$$ of the outcomes, not the marginal distribution, but the above is an educated guess, given the limited information you've given us.
• @anamika_sen_ranjput the distribution you are talking about has nothing to do with prior, it is a likelihood function. Moreover, as stated above, it is not about marginal distribution, but conditional $E[Y|X]$, so the plot alone is not enough. Nontheles, I don't see reason why wouldn't you use Gaussian as likelihood in here? – Tim Jun 10 '20 at 14:37