Before cell can regulate it's DNA repair due to radiation, it has to detect the radiation, which at low levels in question (say, up to ~10x natural background, that's ~ 1..5 microsievert/hour, 2 000 .. 10 000 times less than centigray of gamma per hour) means detecting the probability before anything happens.
The issue with radiation is that people don't understand the units. You read the study you linked, you see, 1 centigray of x-rays, that's a 'low dose' they say, in god knows what context (Radiation therapy? Sure it's a low dose there). That's a 10 milliSieverts, okay? The average background dose a human receives per year, is http://en.wikipedia.org/wiki/Background_radiation , or 1/4 of that. Nobody's been proposing that 4 years worth of normal dose in a hour are going to still be linear.
edit: or actually, we do. We interpolate the low dose effects from the doses of somewhere around 0.1 Sv and up, based on various real world human data. Meaning that, if the effect outlined in your link is real, and there are some defence mechanisms activating at 0.01 Sv which prevent some of the DNA damage (at some other expense) - then we are underestimating the carcinogenicity of radiation at the low (near background) level, at which those defence mechanisms are not active. That is kind of scary to think about, in terms of potential extra cancer deaths.
Okay, I was misunderstanding what you were saying, and it makes sense now.
To paraphrase: Cancer risk in response to radiation levels can only be non-linear when the cell sees past radiation damage signaling it to mount a response. At low doses a given cell is unlikely to see any DNA ionization events, and therefore the risk must be linear.
That's a great point about the potential problem with extrapolating low doses from high dose data. That should really be investigated more carefully... if true "minor" radiation exposures could be a lot more risky than existing estimates suggest.
Nutrition is a case where we have to try to make the best possible use of the data we have no matter how terrible, because we have to eat something now to sustain us while we plan and conduct more experiments.
I want to apply Bayes theorem to make rational health decisions from relatively weak data. I am generally wondering how one can synthesize historical human experiences with incomplete scientific data, in order to make risk-adverse and healthy decisions about human nutrition given limited research.
Example question/hypothesis: Does gluten cause health problems (ie exhibit chronic toxicity) in non-coeliac humans? Is there enough evidence to suggest that avoiding gluten might be a prudent risk-adverse decision for non-coeliacs?
We have some (mostly in vitro) scientific data suggesting that gluten may cause health problems in non-coeliac humans (such as these articles http://evolvify.com/the-case-against-gluten-medical-journal-references/). Let's say for the sake of arguing, that I can somehow convert these studies into a non-unity likelihood ratio for gluten toxicity in humans (although suggestions are welcome here too).
However, we also have prior information that a population of humans has been consuming gluten containing foods for at least 10,000 years, without any blatantly obvious toxic effects. Is there some way to convert this observation (and observations like this) into a prior probability distribution?