I am back from the IMACS conference on Monte Carlo methods and the QMC people do achieve this O(n^{1-ε}) rate. Maybe not immensely practical for our problems though as the coefficient in front of the rate may be humongous… But this made me ponder whether we should not have QMC steps in our codes at some point or another. Thanks for the discussion, I am playing devil’s advocate about utility as I also think I/we should get more involved at the data level…

]]>The flip side is “how do you judge utility”?

Well, let’s imagine someone proved something that required an MCMC-type scheme with asymptotic MSE of O(n^{3/4}). I would say that’s useless. SUch things don’t exist etc etc.

But indications are I’m wrong. People like Ian Sloan and Francis Kuo etc have made dimension independent, unbiased randomised QMC schemes that have MSE O(n^{1-delta}), which suggests that it could be possible to construct posterior sampling schemes with a similar error rate. (Also – that pure Monte Carlo is finally dead!)

So, I don’t know.

]]>I’m not sure i meant to say that things should not be published until proven useful. By that metric I would have no papers! But I do think that mathematical statisticians (and journals like AoS) should be concerned with applicability.

I actually think that it’s the connection to data and practical problem classes that should be watched and nurtured. (ML is an example of this, but not the only one) That doesn’t mean that I think everyone should be doing data-driven research, but “data-driven”-driven research may not be a bad aim.

There are only a (relatively) small number of people who can do these things and, as you said, statistics is an enormous field, so surely they should be deployed in the most “useful” manner. (I think the way people have latched onto ABC is a successful example of this)

Maybe the response to his lecture is not to take the maths out, but to “double down” and start blurring the lines between the vanguard of stats as a data science and that of stats as a mathematical discipline.

And, incidentally, if you want to watch a smaller version of the machine learning thing happen, wander over to inverse problems and uncertainty quantification. Massive models (cf big data) beyond, but not far beyond, the classical GLM-type framework. We should be on top of this as a community, but it’s actually the applied and comp maths people who are pushing it ahead (mostly). They have their own journals, conferences etc.

]]>Hmmm, you seem to be falling into the utilitarian fallacy: don’t publish until you prove (or even better a scientist from a field applying statistics) that it is useful (or already used). I do not think papers published in AoS have to be stamped “useful” before being accepted, no more than papers published in Annals of Probability or Annals of Mathematics… The field has grown considerably in the past decenies and allows for a spectrum that ranges from mathematics to computer science. While I agree that we have to keep and nurture connections with machine learning at “all” costs, this does not mean banishing mathematical statistics to one of the circles of Dante’s Hell…

]]>I think that we need to work to prove that our community’s love of maths mirrors the needs of the discipline lest we find ourselves faced with another “machine learning”-shaped debacle. (Ie a situation where a new field springs up around questions that we should be answering)

To Mis-quote David Cox (at a future of mathematical statistics session at the last ISI), the future of mathematical statistics is to stop thinking of mathematical statistics as an actual field. (NB: my memory of what he said possilble reflects me more than him)

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