Statistics for analysis in Physics

Question

While I am well aware of the branch of physics called statistical physics my question does not pertain to this. My background is bioinformatics which very rarely uses causal modelling instead we tend to use linear regression and machine learning to gain insights into experimental manipulations. My guess is this approach would not work well for situations where you are testing for a specific mathematical hypothesis rather than just if we change X we think it will affect Y (which is what most of the reasoning in biology boils down to). Physics has a set of much more complex mathematical models and I am curious how actual statistical analysis is performed to show that validity of a hypothesis? I am guessing it would be different for each field.

In quantum mechanics I guess that statistics would just fall right out of the theory but in for instance astronomy how are models validated and how do they reach statistical significance? How do you build null models?

Answer 1

I know some Data Analyst and Data Scientist colleagues that build this career. being physicist, skilled with Monte Carlo Methods.

When I was taking physics on my university. a teacher. told me that a multiple particle system with ( n > 100 ) particles can be solved using probabilities.

The Statistics approach in Physics is more related to Stochastic Processes ( Markov Process, Ergodic Property, Random Walk, Extinction Process, Wiener-Khinchin Theorem) especially used for measure thermodynamics and quantum quantities.

In Kinetic Theory is used Maxwell-Boltzmann Distribution for calculate the speed of a ideal gas ( the Maxwell-Boltzmann distribution is the chi distribution with three degrees of freedom )

In Statistical Mechanics is used Boltzmann Distribution, Equipartition theorem, Bose-Einstein Statistics or Fermi–Dirac Statistics. In Particle statistics we have Spin–statistics theorem, Parastatistics, Anyonic statistics, Braid statistics. The Models are Debye model for thermodynamic, Einstein sold model, Ising model (atomic spin), Potts (generalization of Ising model) There are more models, distributions, theorems and statistics methods but this is the starting point for analyze physics elements.