ciphergoth just asked what the actual value of Quantified Self/self-experimentation is. This finally tempted me into running value of information calculations on my own experiments. It took me all afternoon because it turned out I didn’t actually understand how to do it and I had a hard time figuring out the right values for specific experiments. (I may not have not gotten it right, still. Feel free to check my work!) Then it turned out to be too long for a comment, and as usual the master versions will be on my website at some point. But without further ado!

The value of an experiment is the information it produces. What is the value of information? Well, we can take the economic tack and say value of information is the value of the decisions it changes. (Would you pay for a weather forecast about somewhere you are not going to? No. Or a weather forecast about your trip where you have to make that trip, come hell or high water? Only to the extent you can make preparations like bringing an umbrella.)

Wikipedia says that for a risk-neutral person, value of perfect information is “value of decision situation with perfect information” - “value of current decision situation”. (Imperfect information is just weakened perfect information: if your information was not 100% reliable but 99% reliable, well, that’s worth 99% as much.)

1 Melatonin

http://www.gwern.net/Zeo#melatonin & http://www.gwern.net/Melatonin

The decision is the binary take or not take. Melatonin costs ~$10 a year (if you buy in bulk during sales, as I did). Suppose I had perfect information it worked; I would not change anything, so the value is $0. Suppose I had perfect information it did not work; then I would stop using it, saving me $10 a year in perpetuity, which has a net present value (at 5% discounting) of $205. So the value of perfect information is $205, because it would save me from blowing $10 every year for the rest of my life. My melatonin experiment is not perfect since I didn’t randomize or double-blind it, but I had a lot of data and it was well powered, with something like a >90% chance of detecting the decent effect size I expected, so the imperfection is just a loss of 10%, down to $184. From my previous research and personal use over years, I am highly confident it works - say, 80%. If it works, the information is useless to...

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