Choice of prior to restrict coefficient to negative values? I'm slightly embarassed to be asking this question, but I couldn't locate a satisfying reference. I'm a complete novice in Bayesian regression, working through the textbook Statistical Rethinking. In an example where weight is regressed on height, the author explains that it is sensible to restrict the coefficient on height to positive values. This is accomplished via the Log-normal distribution:
$$
 \beta \sim \text{Log-normal}(0, 1)\ ,
$$
for instance. My question is straightforward: is there a similarly natural choice if one wanted to restrict a coefficient to only take negative values? Does something naive like multiplying the log-normal distribution by $-1$ work?

The specifics of your prior will influence the posterior (e.g., $U(-2, -1)$ will be different from $-Log\_normal(0, 1)$), but any prior that has support on just the negative numbers will do the trick of keeping your posterior from having positive values. If the prior says that positive values are impossible, the posterior will say the same.
In other words, yes, just taking $-1$ times your log-normal distribution would work!
