Robert Noble writes:
I’m curious as to whether you’ve any thoughts on the term ‘non-stochastic probability’, which appears in the title of a recent paper in Nature Cancer. It doesn’t make any sense to me but then again I’m only a mathematician, not a statistician, and the paper’s 26 authors, several peer reviewers, and professional editors clearly disagree with me. I’m curious because the paper’s been published in a big journal and I can see the term catching on among biologists.
The paper’s senior author explained to me on twitter: ‘We demonstrated that each cell is ‘born’ with a fixed probability to persist therapy which we named CTP. The CTP is highly stable over time and is inherited rather than being stochastically determined when a cell is created. This is what we mean by ‘non-stochastic probability’’
I [Noble] replied: ‘So you showed that the probability of a cell persisting depends on its ancestry. I don’t see a need for the term “non-stochastic probability”. The title could be “IRS1 phosphorylation underlies the inherited propensity …” My null hypothesis wouldn’t be that every cell is assigned a stochastic probability of persisting. You couldn’t test that hypothesis because you can observe only one event per cell. Rather it would be that the probability of persisting is independent of ancestry.’
Am I wrong? Does it matter?
I’m in no way questioning the quality of the work or the validity of the conclusions; it’s just the terminology that I find strange, especially given that it’s in the title, which the authors must have given careful consideration.
I replied that I don’t think “non-stochastic probability” is a thing. But I guess if their method works, it doesn’t matter what they call it. I think I mangle computer science terminology all the time.
Stochastic probability of the cell being a “persister”
Lineage 1
Generation 0: p
G1: p
G2: p
Lineage 2
Generation 0: p
G1: p
G2: p
*Non*-stochastic probability of the cell being a “persister”
Lineage 1
Generation 0: p1
G1: p1
G2: p1
Lineage 2
Generation 0: p2
G1: p2
G2: p2
Where p1, p2, … are samples from a uniform distribution. Since they are claiming non-genetic heritability, another term for this could be “Lamarkian probability”.
That’s how the authors see it. But why use the term “non-stochastic probability”? Why not just say that persistence propensity has an inherited component? For example, breast cancer risk in humans partly depends on ancestry, yet we don’t say that people are born with a non-stochastic probability of developing breast cancer. The same terminology can apply whether the mechanism is genetic or epigenetic.
I think they were already using “stochastic” to describe a “random” daughter cell becoming a persister. Then they went to “non-stochastic” to describe the inherited alternative.
I also agree it is a poor choice of words.
I’ve noticed “stochastic” being used in biology to specify random outcomes during development which are not determined by genetics. See, for example, the discussion of stochasticity in this thread:
https://www.metafilter.com/185207/How-much-of-us-is-just-random
In the case of this paper, I think they’re trying to emphasize that this is a random outcome during development which *is* determined by genetics, therefore not “stochastic” in the way that biologists use the term.
I should point out that I’m not Andrew Gelman… if a moderator wants to change my name to Andrew K that would probably reduce confusion.
“But I guess if their method works, it doesn’t matter what they call it”
I don’t think that’s true. It *is* true that their method will work (or not) regardless of what it’s named (a rose by any other name…). But that doesn’t mean the name doesn’t matter. Communication is important! The title seems unfortunate to me. Regardless of whether “non-stocastic probability” exists, I don’t think it clearly communicates what they’ve found.
For me it makes sens. A time-indexed random variable can refer to stochastic probability whereas a random variable can’t.
I’m not finding a definition of “stochastic” here. The problem might be that different people are using different definitions of that term.
I’ve always thought that “stochastic” means random. My Ph.D. advisor was a probabilist, but maybe I don’t know what it means, and just assumed it means random.
“Persist therapy” is another mouthful. Is that a term of art, or just strange English?
Yes, persistence has a specific biological meaning, distinct from resistance. For example, see https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1449587/.
I think that the term “non-stochastic probability” makes sense. The probability of the event is not determined probabilistically. You could imagine that the probability of an event occurring is drawn from say a beta distribution, and then the event occurs with that probability. This would be an example of “stochastic probability”. As opposed to an event that occurs with a fixed probability, say the value p which never changes. This would be an example of “non-stochastic probability”.
However, one thing that I think everyone can agree on is that the term “stochastic probability” is an unfortunate term. English can be very imprecise this way, which is why we (generally) like to rigorously define terms.
Though the authors you mention meant something else, the term “non-stochastic randomness” makes sense. It’s a quite important discovery. The term “stochastically random” -if we follow Kolmogorov -means random and “statistically stable”, where frequencies converge to limits. While the term “non-stochastically random” means random and “statistically unstable”, where frequencies do not converge to limits. It turns out that even this statistcally unstable random phenomena have statistical laws – families of finitely-additive probablities, to whch the distributions of frequencies converge in the sense of limit points ( or cluster points) in weak-* topology. Main ref is https://link.springer.com/book/10.1007/978-1-4419-5548-7 .
The man is here https://www.researchgate.net/profile/Victor-Ivanenko/research
This may be more rreal-world, than traditional probabilistic concepts. As a matter of fact, this result is the only available frequentist justification (not interpretation) of the idealised probability axioms of Kolmogorov.