briefly explain about classical and quantum statistics?
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Before the advent of quantum mechanics, Maxwell, Boltzmann, Gibbs etc, applied statistical methods with the help of classical physics. These methods are collectively known as Classical statistics or Maxwell-Boltzmann (MB) Statistics. Page 3. 3. These statistics were successful in explaining pressure, temperature etc.
classical statistics : Classical statistics uses techniques such as Ordinary Least Squares and Maximum Likelihood – this is the conventional type of statistics that you see in most textbooks covering estimation, regression, hypothesis testing, confidence intervals, etc. ... In fact Bayesian statistics is all about probability calculations!
quantum statistics : Quantum statistical mechanics is statistical mechanics applied to quantum mechanical systems. In quantum mechanics a statistical ensemble is described by a density operator S, which is a non-negative, self-adjoint, trace-class operator of trace 1 on the Hilbert space H describing the quantum system.