Thanks, this is great information! The concern you raised regarding distinguishing between philosophical theories and models makes a lot of sense. With that said, I donât currently feel super satisfied with the practical steps you suggested.
On the first note, the impact of the correlation depends on the structure of f. Suppose Iâm trying to estimate the total harms of eating chicken/âpork, so we have something like y=c1âwelfarerangeofpigs+c2âwelfarerangeofchickens. In this case, treating the welfare ranges of chickens and pigs as correlated will increasethe variance of y. On the flip side, if weâre trying to estimate the welfare impact of switching from eating chicken to eating pork, we have something like y=c3âwelfarerangeofchickensâc4âwelfarerangeofpigs. In that case, treating the welfare ranges of pigs and chickens as correlated will decreasethe variance of y. Trying to address this in an ad-hoc manner seems like itâs pretty challenging.
On the second note, I think thatâs basically treating the welfare capacities of e.g. pigs and chickens as perfectly correlated with one another. That seems extreme to me, since I think a substantial portion of the uncertainty in the welfare rages is coming from uncertainty as to which traits each species has, not which philosophical theory of welfare is correct.
I come away still thinking that the procedure I suggested seems like the most workable of the approaches mentioned so far. To put a little more rigor to things, here are some examples of plotting the welfare range estimates of chickens and pigs against one another with the different methods (uncorrelated sampling from the respective mixture distributions, sampling from the ordered distributions, and pair-wise sampling from the constituent models). In addition, there are some plots showing the impact of the different sampling methods on some toy analyses of the welfare impact of eating chicken/âpork and the impact of switching from eating chicken to eating pork (note that the actual numbers are not intended to be very representative). You can see that the trimming approach only make sense in the second case, and that the paired sampling from constituent models approach produces distributions in between those for the uncorrelated case and those for the ordered case.
Note that when using the pair-wise sampling from constituent models approach, pigs and chickens are more strongly correlated with one another than many other pairs of species are. Here is what the correlation between chickens and shrimp looks like, for example:
Hey, thanks for this detailed reply! When I said âpracticalâ, I more meant âsimple things that people can do without needing to download and work directly with the code for the welfare ranges.â In this sense, I donât entirely agree that your solution is the most workable of them (assuming independence probably would be). But I agreeâpairwise sampling is the best method if you have the access and ability to manipulate the code! (I also think that the perfect correlation you graphed makes the second suggestion probably worse than just assuming perfect independence, so thanks!)
Thanks, this is great information! The concern you raised regarding distinguishing between philosophical theories and models makes a lot of sense. With that said, I donât currently feel super satisfied with the practical steps you suggested.
On the first note, the impact of the correlation depends on the structure of f. Suppose Iâm trying to estimate the total harms of eating chicken/âpork, so we have something like y=c1âwelfare range of pigs+c2âwelfare range of chickens. In this case, treating the welfare ranges of chickens and pigs as correlated will increase the variance of y. On the flip side, if weâre trying to estimate the welfare impact of switching from eating chicken to eating pork, we have something like y=c3âwelfare range of chickensâc4âwelfare range of pigs. In that case, treating the welfare ranges of pigs and chickens as correlated will decrease the variance of y. Trying to address this in an ad-hoc manner seems like itâs pretty challenging.
On the second note, I think thatâs basically treating the welfare capacities of e.g. pigs and chickens as perfectly correlated with one another. That seems extreme to me, since I think a substantial portion of the uncertainty in the welfare rages is coming from uncertainty as to which traits each species has, not which philosophical theory of welfare is correct.
I come away still thinking that the procedure I suggested seems like the most workable of the approaches mentioned so far. To put a little more rigor to things, here are some examples of plotting the welfare range estimates of chickens and pigs against one another with the different methods (uncorrelated sampling from the respective mixture distributions, sampling from the ordered distributions, and pair-wise sampling from the constituent models). In addition, there are some plots showing the impact of the different sampling methods on some toy analyses of the welfare impact of eating chicken/âpork and the impact of switching from eating chicken to eating pork (note that the actual numbers are not intended to be very representative). You can see that the trimming approach only make sense in the second case, and that the paired sampling from constituent models approach produces distributions in between those for the uncorrelated case and those for the ordered case.
Note that when using the pair-wise sampling from constituent models approach, pigs and chickens are more strongly correlated with one another than many other pairs of species are. Here is what the correlation between chickens and shrimp looks like, for example:
Hey, thanks for this detailed reply!
When I said âpracticalâ, I more meant âsimple things that people can do without needing to download and work directly with the code for the welfare ranges.â In this sense, I donât entirely agree that your solution is the most workable of them (assuming independence probably would be). But I agreeâpairwise sampling is the best method if you have the access and ability to manipulate the code! (I also think that the perfect correlation you graphed makes the second suggestion probably worse than just assuming perfect independence, so thanks!)
Yeah that makes complete sense, it was a pain to get the pairwise sampling working.