3 thoughts on “5-3 Madhur Mangalam. Is non-ergodicity a cause of the reproducibility crises?”
Ole Peters
Very nice. The Thirumalai-Mountain metric can be used to assess when correlations begin to be washed out. Under fairly general conditions, this metric decays inversely proportionally to time, and one use of it is to check that we can treat something as ergodic on sufficiently long time scales, namely when we see the 1/T decay.
If I understand your talk correctly, you find that in many systems of interest the metric indicates that we’re not in a regime where ergodicity is a reasonable assumption. Nice!
I was wondering if you knew our work, with Max Werner, on ergodicity breaking as a recipe for irreproducible results? https://arxiv.org/abs/1706.07773
The basic idea is the same: averaging data of a non-ergodic observable over time can easily lead to a different result every time you run the experiment. Your result may look perfectly stable and solid in any one realization, but the next realization will look just as solid and give a totally different result.
I am open to ergodicity being the exception, but going back to the very first talk we can break from the binary to consider how ergodic or non-ergodic a phenomena is.
1. So when I think of general physiological state data, things like systemic body temperature, pH, magnesium levels, whatever. Having qualitatively looked at trajectories of these within individuals, and ensemble measures of these, the distributions look very similar, assuming you condition on similar healthy populations. So my hunch was that these coarse-grain phenomena are fairly ergodic. So you are saying this is very unlikely to be true? And this could be demonstrated by your EB-metric?
2. You assert that almost everything is a cascading fluctuation, or can be modelled as such. It’s only a 12 minute talk so I know you can’t defend every assumption but can you elaborate on this assertion? Why is it true of almost all physiological phenomena? And where can I find evidence for this?
3. I am curious if cascading fluctuations on one spatial-scale, when coarse-grained at a higher scale can masquerade as ergodic, even if at the lower level they are not.
I’d love to hear more about your views on the ergodicity assumptions underlying free energy theory. I have always thought that was quite a mystical assumption. Apparently they have recently relaxed those assumptions but I haven’t dug into it. Have you engaged with that community on these issues at all?
Very nice. The Thirumalai-Mountain metric can be used to assess when correlations begin to be washed out. Under fairly general conditions, this metric decays inversely proportionally to time, and one use of it is to check that we can treat something as ergodic on sufficiently long time scales, namely when we see the 1/T decay.
If I understand your talk correctly, you find that in many systems of interest the metric indicates that we’re not in a regime where ergodicity is a reasonable assumption. Nice!
I was wondering if you knew our work, with Max Werner, on ergodicity breaking as a recipe for irreproducible results?
https://arxiv.org/abs/1706.07773
The basic idea is the same: averaging data of a non-ergodic observable over time can easily lead to a different result every time you run the experiment. Your result may look perfectly stable and solid in any one realization, but the next realization will look just as solid and give a totally different result.
Lots to talk about here… Thank you!
Very interesting indeed thank you.
I am open to ergodicity being the exception, but going back to the very first talk we can break from the binary to consider how ergodic or non-ergodic a phenomena is.
1. So when I think of general physiological state data, things like systemic body temperature, pH, magnesium levels, whatever. Having qualitatively looked at trajectories of these within individuals, and ensemble measures of these, the distributions look very similar, assuming you condition on similar healthy populations. So my hunch was that these coarse-grain phenomena are fairly ergodic. So you are saying this is very unlikely to be true? And this could be demonstrated by your EB-metric?
2. You assert that almost everything is a cascading fluctuation, or can be modelled as such. It’s only a 12 minute talk so I know you can’t defend every assumption but can you elaborate on this assertion? Why is it true of almost all physiological phenomena? And where can I find evidence for this?
3. I am curious if cascading fluctuations on one spatial-scale, when coarse-grained at a higher scale can masquerade as ergodic, even if at the lower level they are not.
Cheers,
O
I’d love to hear more about your views on the ergodicity assumptions underlying free energy theory. I have always thought that was quite a mystical assumption. Apparently they have recently relaxed those assumptions but I haven’t dug into it. Have you engaged with that community on these issues at all?