Sam Power
@spmontecarlo.bsky.social
Lecturer in Maths & Stats at Bristol. Interested in probabilistic + numerical computation, statistical modelling + inference. (he / him).
Homepage: https://sites.google.com/view/sp-monte-carlo
Seminar: https://sites.google.com/view/monte-carlo-semina
Homepage: https://sites.google.com/view/sp-monte-carlo
Seminar: https://sites.google.com/view/monte-carlo-semina
Exactly, yeah - it's an important perspective to have to hand, and maybe even usually the right one, but there might sometimes be other stuff going on.
November 10, 2025 at 9:19 PM
Exactly, yeah - it's an important perspective to have to hand, and maybe even usually the right one, but there might sometimes be other stuff going on.
I guess it's something to do with whether the qualifier is indicating that you { can, should, must } view the object through this lens. The 'can' and 'should' versions work for me, in a way that the 'must' version doesn't.
November 10, 2025 at 9:12 PM
I guess it's something to do with whether the qualifier is indicating that you { can, should, must } view the object through this lens. The 'can' and 'should' versions work for me, in a way that the 'must' version doesn't.
[ ... ] sequential task, and then demonstrate how to simulate them non-sequentially (which is a great trick when it works). It reads as bizarre to me because it certainly doesn't feel all that 'inherently sequential' once you see the alternative.
November 10, 2025 at 9:10 PM
[ ... ] sequential task, and then demonstrate how to simulate them non-sequentially (which is a great trick when it works). It reads as bizarre to me because it certainly doesn't feel all that 'inherently sequential' once you see the alternative.
I think most would correctly come to the conclusion that there's something meaningfully sequential going on; no contest on that side. For me, the 'inherently' oversteps by confining things a bit too much. I get thrown because people will say that simulation of Markov chains is an inherently [ ... ]
November 10, 2025 at 9:10 PM
I think most would correctly come to the conclusion that there's something meaningfully sequential going on; no contest on that side. For me, the 'inherently' oversteps by confining things a bit too much. I get thrown because people will say that simulation of Markov chains is an inherently [ ... ]
To poorly lampshade one of the inciting examples, I think that "Markov chains are canonically sequential objects" sits okay with me (a bit imprecise, but plausible that it could be made precise), whereas I find the "inherently" version less agreeable.
November 10, 2025 at 9:00 PM
To poorly lampshade one of the inciting examples, I think that "Markov chains are canonically sequential objects" sits okay with me (a bit imprecise, but plausible that it could be made precise), whereas I find the "inherently" version less agreeable.
I think that I'm normally on board with "canonically", since there's somehow a slightly stronger sense that it's about convention? "Inherently" seems to carry something a bit stronger to me (maybe like "unavoidably" / "categorically", if I understand those well), which may be what bothers me here.
November 10, 2025 at 8:58 PM
I think that I'm normally on board with "canonically", since there's somehow a slightly stronger sense that it's about convention? "Inherently" seems to carry something a bit stronger to me (maybe like "unavoidably" / "categorically", if I understand those well), which may be what bothers me here.
glad to see it's not just me
November 10, 2025 at 8:03 PM
glad to see it's not just me
This makes a bit of sense; the examples which I have in mind do have this flavour of "but with this trick, we see that another way forward is possible".
November 10, 2025 at 7:57 PM
This makes a bit of sense; the examples which I have in mind do have this flavour of "but with this trick, we see that another way forward is possible".
Anyways, this review of modern Kalman filtering is broadly pretty good.
November 10, 2025 at 7:56 PM
Anyways, this review of modern Kalman filtering is broadly pretty good.
Not inherently nonlinear - born linear, but nonlinear by one's own choice!
November 10, 2025 at 7:55 PM
Not inherently nonlinear - born linear, but nonlinear by one's own choice!
Maybe it could mean "nonlinear in all possible worlds; too far gone, never to again darken the doorstep of linearity". Who's to say?
November 10, 2025 at 7:53 PM
Maybe it could mean "nonlinear in all possible worlds; too far gone, never to again darken the doorstep of linearity". Who's to say?
I'm more critical of this than "highly nonlinear" (and similar), because in those cases, I can at least envision a way of making it precise.
November 10, 2025 at 7:51 PM
I'm more critical of this than "highly nonlinear" (and similar), because in those cases, I can at least envision a way of making it precise.
Is it "inherently nonlinear", or is it just ... nonlinear? Whatever it is, it looks like you've just successfully linearised it, so bearing that in mind, it might even be "relatively linear", in the big picture. [ ...]
November 10, 2025 at 7:49 PM
Is it "inherently nonlinear", or is it just ... nonlinear? Whatever it is, it looks like you've just successfully linearised it, so bearing that in mind, it might even be "relatively linear", in the big picture. [ ...]
Read literally, there is a big gap between "it is natural to think of X as being Y" and "X is inherently Y"; people often seem to mean the first and write the second.
November 10, 2025 at 7:47 PM
Read literally, there is a big gap between "it is natural to think of X as being Y" and "X is inherently Y"; people often seem to mean the first and write the second.
It's also true of graphs, but to a lesser extent (because I do know a couple of things about graphs, though mostly phrased in other terms). The abstraction is such a strong one (as are some of the definitions like trees, degree, connectedness, etc) that the specifics of 'graph theory' are sidelined.
November 9, 2025 at 11:32 PM
It's also true of graphs, but to a lesser extent (because I do know a couple of things about graphs, though mostly phrased in other terms). The abstraction is such a strong one (as are some of the definitions like trees, degree, connectedness, etc) that the specifics of 'graph theory' are sidelined.
Maybe another good example would be manifolds. I have all sorts of reasons to be interested in doing various things on manifolds, and I have almost no idea what is proven in a first course on manifolds (beyond giving definitions and checking that they're reasonable, etc.).
November 9, 2025 at 11:28 PM
Maybe another good example would be manifolds. I have all sorts of reasons to be interested in doing various things on manifolds, and I have almost no idea what is proven in a first course on manifolds (beyond giving definitions and checking that they're reasonable, etc.).
That's super fun! I certainly still get this sort of internal glee upon wheeling out things which are "out of scope" within my community, but potentially pedestrian on home turf. Maybe the most fun one for me is to talk about things in intuitive physicist-type language.
November 9, 2025 at 11:27 PM
That's super fun! I certainly still get this sort of internal glee upon wheeling out things which are "out of scope" within my community, but potentially pedestrian on home turf. Maybe the most fun one for me is to talk about things in intuitive physicist-type language.
I guess basic algebra is a good baseline. It's good that I know enough about groups, posets, etc., since they're very useful abstractions that come up a lot. On the other hand, it would be rare for me to need to know anything advanced about their structure.
November 9, 2025 at 11:14 PM
I guess basic algebra is a good baseline. It's good that I know enough about groups, posets, etc., since they're very useful abstractions that come up a lot. On the other hand, it would be rare for me to need to know anything advanced about their structure.
Probably it's just the softer point of why "general mathematical culture" etc. is a valuable exercise, but in some specific contexts.
November 9, 2025 at 11:02 PM
Probably it's just the softer point of why "general mathematical culture" etc. is a valuable exercise, but in some specific contexts.
It certainly narrows the gap between prediction, estimation, and inference, though interestingly, the implication is closer to "predicting well lets you form smaller uncertainty sets" rather than "by predicting well, you can read off a good parameter estimate".
November 9, 2025 at 10:35 PM
It certainly narrows the gap between prediction, estimation, and inference, though interestingly, the implication is closer to "predicting well lets you form smaller uncertainty sets" rather than "by predicting well, you can read off a good parameter estimate".
I suppose the only thing which it suggests is (perhaps indirectly, though it's not hard to see it when you read around the topic a bit) that if you have strategies for predicting effectively (in a certain observable and quantitative sense), then these are unquestionably useful (big shock!).
November 9, 2025 at 10:35 PM
I suppose the only thing which it suggests is (perhaps indirectly, though it's not hard to see it when you read around the topic a bit) that if you have strategies for predicting effectively (in a certain observable and quantitative sense), then these are unquestionably useful (big shock!).
[...] but not that it is the whole story. In this regard, it is compelling as to what to reject, but a bit quieter as to what to focus on. This is also okay, but requires again reckoning with the asymmetry of various statistical tasks.
November 9, 2025 at 10:15 PM
[...] but not that it is the whole story. In this regard, it is compelling as to what to reject, but a bit quieter as to what to focus on. This is also okay, but requires again reckoning with the asymmetry of various statistical tasks.