I’ve been thinking of doing more things like this, however, I wonder about this part:
P(E | H1) = 0.2 (if 150g is enough, poor recovery is unlikely)
P(E | H2) = 0.7 (if 170g is needed, poor recovery is likely if you only ate 150g)
Any reason why these particular conditional probabilities are chosen here -- 0.2 and 0.7?
Would there be any principled way to update these probabilities while new evidence rolls in, and maybe even start both from 0.5? I think for simple observation our set of formulae might be under-constrained, so maybe we’d need to incorporate other stream of evidence to constrain it enough?
Yeah, the 0.2 and 0.7 aren’t meant to be special, they’re just encoding how plausible the “poor recovery” evidence is under each protein hypothesis. In a real-life scenario, you’d have no idea what those numbers should be at first, so starting both hypotheses at 0.5 and updating as you collect experience would make more sense. Over time, you could even adjust the likelihoods themselves (empirical Bayes style) if you notice your model consistently over- or under-predicts fatigue.
You’re also right that the setup’s under-constrained, real protein needs depend on stress, sleep, calorie intake, etc., and those should all be treated as separate evidence streams. You would need more diverse and semi-independent evidence streams. A few useful ones could be:
Sleep quality: Poor sleep often amplifies soreness and fatigue unrelated to protein, so tracking it helps disambiguate causes.
Training performance metrics: E.g., strength progression, endurance, or rep quality. These are lagging but objective signals of recovery adequacy (as in the table).
Subjective appetite/hunger: Often correlates with energy balance and protein sufficiency.
Body composition trends: Slow, medium-term evidence, muscle gain or loss tells you if your intake supports growth.
Resting heart rate or HRV: Physiological recovery indicators that help separate systemic fatigue from nutritional deficits.
But in general, the Bayesian framing is still useful, though: it turns “how much protein should I eat?” from a static rule into a dynamic inference problem that refines itself with experience. If you have any other evidence streams feel free to let me know.
I’ve been thinking of doing more things like this, however, I wonder about this part:
Any reason why these particular conditional probabilities are chosen here -- 0.2 and 0.7?
Would there be any principled way to update these probabilities while new evidence rolls in, and maybe even start both from 0.5? I think for simple observation our set of formulae might be under-constrained, so maybe we’d need to incorporate other stream of evidence to constrain it enough?
Hey Dalmert,
Yeah, the 0.2 and 0.7 aren’t meant to be special, they’re just encoding how plausible the “poor recovery” evidence is under each protein hypothesis. In a real-life scenario, you’d have no idea what those numbers should be at first, so starting both hypotheses at 0.5 and updating as you collect experience would make more sense. Over time, you could even adjust the likelihoods themselves (empirical Bayes style) if you notice your model consistently over- or under-predicts fatigue.
You’re also right that the setup’s under-constrained, real protein needs depend on stress, sleep, calorie intake, etc., and those should all be treated as separate evidence streams. You would need more diverse and semi-independent evidence streams. A few useful ones could be:
Sleep quality: Poor sleep often amplifies soreness and fatigue unrelated to protein, so tracking it helps disambiguate causes.
Training performance metrics: E.g., strength progression, endurance, or rep quality. These are lagging but objective signals of recovery adequacy (as in the table).
Subjective appetite/hunger: Often correlates with energy balance and protein sufficiency.
Body composition trends: Slow, medium-term evidence, muscle gain or loss tells you if your intake supports growth.
Resting heart rate or HRV: Physiological recovery indicators that help separate systemic fatigue from nutritional deficits.
But in general, the Bayesian framing is still useful, though: it turns “how much protein should I eat?” from a static rule into a dynamic inference problem that refines itself with experience. If you have any other evidence streams feel free to let me know.
Thanks for asking.