# Bayesian statistics in science

• I
• Sunil
In summary: This is not the standard meaning of 'model'. A model is a template in which the parameters are not fixed but to be determined by experiment. In the case of quantum tomography, the model is the Hilbert space chosen to model the quantum system - nothing else. The state is a matrix of parameters that are not determined by the model but by experiments, using the traditional objective, universally agreed statistical techniques. (Unless you think that the publications of the particle data group are not objective but subjective mind content. Then we do not need to discuss further.)So, a quantum model is just a template in which the parameters are not fixed, while
gentzen said:
Basically, I expect a fundamental limitation of achievable accuracy.
What does "accuracy" mean here? Do you think there can be some ultimate truth concerning the value of a probability? Even with dice, the value ## \frac 1 6 ## can be "exact" as a prior, but in the real world it can only be "approximate", valid as long as it agrees with observations.
gentzen said:
And I expect that this enables you to include some preferred properties in your model, for example that there exists only a single world.
That there exists only a single world agrees with my gut feeling. :-)

This whole search of some logical justification of which method if inference that is "optimal", as in as that would be a mathematical or logical problem for a "general inference problem" seems to me like a misguided mess. All the references here reminds my of how different this is from how I prefer to think of this, and that there are a couple of parallell and intermixed issues here, that for ME is entangled, but which for some are independent.

(1) The quest for the "optimal" mathematical theory of making quantiative inference from quantiative evidence, this involes defining measures and update rules. And the quest for pure logical argument for which is the best one.

(2) The quest for the physical interactions nature, between it's parts, this involes the physics and measures of matter and how it evolves, relative to other parts, and the quest for natural explanations for natures choices.

(2) is my interest, but cast in the form of (1), and the question is which one is best fit for physics? I see that some of the references are mainly about (1) intermixed with philosophy, in a sense that has little to do with foundations of physics, or with physical constraints on inferences made by physical observers, and how this relates to BH information paradoxes, quantum weirdness etc. IF one forgets this perspective, and mixes arguments from the casre of pure (1), I think there will be misunderstnadings due to the different goals of discussions. This is why I picture the "agent" and a physical version of the "prior information", and that the physical basis of "information" is in the mictrostructure of matter.

/Fredrik

AlexCaledin said:
- do you mean, in the quantum state of the universe?
I mentioned it just as to illustrate that discussions here regarding the foundations of science and probability may be discussed in itself, within the realm of logic or mathematics, or in relation to foundations of physics (and then i specifically mean the foundations of physical law). The goals and issues are different. Philosophers of mathematics and philosopers of physics are related by may still have different goals.

(The way I happe to think of it, by "information" in this case, i mean what the agent knows about the rest of the universe, this information or more than just the "quantum state", or the "prior probability", it contains also the "prior information" the defines say hilbert spaces or probability spaces etc. But as the agent is a subsystem, this can not be compared to the "quantum state of the whole" in the sense of Wheeler-deWitt, which is more a non-physical fiction. This fiction is thus rejected in my thinking. Not on grounds of mathematics but on other admittedly murky grounds. But as one ties mathematics ot reality, it's bound to get murky somewhere. But these arguments are usually beyond what you see in many math/logic discussions, which is my point)

/Fredrik

gentzen said:
But my gut feeling expects something worse than just insufficient data per parameter. Something like

from an abstract of Christopher Fuchs and Ruediger Schacks. (I didn't read their paper yet, even so it is short. But I saw their abstract a long time ago, and it did influence my gut feeling.) Basically, I expect a fundamental limitation of achievable accuracy. And I expect that this enables you to include some preferred properties in your model, for example that there exists only a single world.
If one has some dream about finding and optimal objective learning algorithm that is guaranteed to find the truth, this may be a "problem", but that seems like a fantasy.

But if in instead (that i was suggesting) is trying to just predict the dynamics of a system of interacting agents, that this is not a problem; it's a trait that can help explain non trivial selforganisation. If all agents, ultimately converge to the same thing, its seems one would only be able to find decay kind of phenomena there, similary to entropic flows. With multiple attractors, we will get more interesting phenomenology.

/Fredrik

Related abstractions exists for models of the brain and social interactions.

For example the "bayesian brain hypothesis"

"This is the first crucial point in understanding the Bayesian brain hypothesis. It is a profound point: the internal model of the world within the brain suggests that processes in the brain model processes in the physical world. In order to successfully predict the future, the brain needs to run simulations of the world on its own hardware. These processes need to follow a causality similar to that of the external world, and a world of its own comes alive in the brain observing it."
-- https://towardsdatascience.com/the-bayesian-brain-hypothesis-35b98847d331

Unless one takes is too litteraly(!), and understandn that there are differences, this is similar to the agent view, except - think of matter om gemeral - instead of brains. It is an intuitive way to understand the concepts.

Edit: Also an arxiv ref would have been better i suppose. One related us here.. they label it predictive coding.. which is conceptually the way prior information are "coded"...

https://arxiv.org/abs/2107.12979

/Fredrik

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Fra said:
as the agent is a subsystem, this can not be compared to the "quantum state of the whole" in the sense of Wheeler-deWitt, which is more a non-physical fiction
- very well, suppose you make the whole universe consisting of those agent subsystems - and then, they request the universe quantum state to correlate and "objectively" record all their observations, because otherwise it's not fun. ( - Just like two fellows having nothing to do and asking for a chessboard)

Have you read Enrico Fermi's assertion, that the description of reality ought to be dualistic, physical + mental? Sorry, I forgot where to find it.

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AlexCaledin said:
- very well, suppose you make the whole universe consisting of those agent subsystems - and then, they request the universe quantum state to correlate and "objectively" record all their observations, because otherwise it's not fun. ( - Just like two fellows having nothing to do and asking for a chessboard)

Have you read Enrico Fermi's assertion, that the description of reality ought to be dualistic, physical + mental? Sorry, I forgot where to find it.
I take it you mean, "not fun" = an inconsisteny between views?

My counter questions would then be: Record where? Also note that observerations has to be "communicated" as well; exactly wo where is this communicated?

The argument is that the inconsistency is not a physical one. It's a logical inconsistency which just means that it's the existence of a logically motivated objectivity, that is inconsistent. The inconsistency is arrived at an fictional level, and thus iis not actually a problem excepct for their own way of thinking!

No I haven't read Fermi's description of that. The word "mental" rejects me though So I am guess I didn't miss anything.

The analogy with a learning brain can be a loose source of insight into abstractions only, but that's where it ends. I am not suggesting that matter has "human properties", I am rather saying the opposite, that even human brains follow the same physics as anything else. What's impressive about human brain lies not in some divine religious dimensions(except there are those who may thing so, but this is not even close to what i am talking about), but soley in it's complexity, and it's exactly how effective laws evolve at different layers in a complex system that we apparently are far from understanding and beeing able to "capture" in models. This is also why laws at complexity levels orders of magnitudes apart appear "unrelated.

/Fredrik

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