# Advanced data analysis in Physics experiments

Before answering, please see our policy on resource recommendation questions. Please try to give substantial answers that detail the style, content, and prerequisites of the book or paper (or other resource). Explain what the resource is like as much as you can; that way the reader can decide which one is most suited for them rather than relying on the suggestions of others. Answers which just suggest a book or paper will be deleted.

I know that regression, chi-distribution, covariance, error propagation, etc. are frequent tools for experimental physicists.

So, I'd like to know if advanced statistics topics are used in data analysis in Physics (bootstrapping, frequentist vs bayesian approach, Montecarlo, etc)?

I've found many articles about this in particle physics, but not in other fields (classical mechanics, EM...). So, could they be applied to things such as studying the period of a pendullum (although it might be overkill)?

Is there any statistics book with physical applications? Something like Taylor's "Error analysis" but more advanced.

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This sounds like a list question. Any way you could make it more focused? –  David Z Nov 20 '13 at 23:44
To clarify, book questions are allowed by the policy, but list questions .. not so much. I suggest you rearrange your question to make the primary point about books –  Manishearth Nov 21 '13 at 11:20
@Manishearth My question is if advanced statistics is worth studying for non particle physics (not about the particular tools, so no list wanted)? And if yes, statistics books with physical examples. If something is off-topic I'll edit it or delete it altogether. –  jinawee Nov 21 '13 at 11:31
@jinawee Oh, it's not off topic, from what I see. I'm just saying that it would be better if the primary emphasis of the question was books. –  Manishearth Nov 21 '13 at 11:51
There's no book (yet) so I can't write an answer, but in fluid dynamics there is all kinds of statistics used. Forgetting the whole field of turbulence, there's a huge quantity of work being done in uncertainty quantification in experiments and numerics; PCA and POD are used to analyze results; reduced-order modeling is used to generate simplified systems from complex ones... etc –  tpg2114 Nov 21 '13 at 11:51

I think that your question is one of many answers and interpretations, making it a good question, but very hard to answer. Thus, my response will be very vague and simple, yet I am willing to expand if needed.

Classical mechanics has the advantage of being deterministic, Statistical Mechanics (although it is in theory classical), and Quantum Mechanics are not deterministic, they are statistical, as you have noted. Hence, they employ several statistical methods. With that been said, some are more efficient than others, thus, physics uses this methods in order to come up with methods (namely, equations) of its own to solve particular problems.

For example the Montecarlo Method would not be very productive when studying the behavior of several particles on a closed space (imagine running so many computations!), on the other hand the Maxwell-Boltzmann Distribution, which is derived from a series of analytical statistical methods, is very productive. Another example of how physics applies statistics to make its own methods, perhaps a more commonly known one, is the fact that the probability amplitude of finding a particle described by $\Psi (x, t)$ on time $t$, is $\Psi*\Psi$, a concept widely used in Quantum Mechanics and particle physics.

In conclusion, physics does not use only one statistical method, it analyzes several methods to come up with methods of its own. Also, the "type" of statistics used depends upon the field, particularly upon how deterministic the area is. Thus, when speaking QM one speaks in an statistical way, but when speaking about Classical Mechanics (a pendulum's period, for example :p) one speaks in a more deterministic way, hence employing little, if any, statistical methods.

Let me know if you have any other questions, I hope this is of some help to you!

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