38. Notation and overview of statistics material

“If your result needs a statistician then you should design a better experiment.”

—Ernest Rutherford

The material in this Appendix provides a summary of important concepts and definitions in mathematical statistics plus a guide to working with probability distributions in scipy.stats.

• The probability measure contains the definition of the probability measure and random variables in both discrete and continuous samples spaces. The concepts of expectation values and moments are introduced. There is also a brief discussion on different views on probability.

• Working with probability distributions lists a selection of important probability distributions and explains how scipy.stats can be used when working with distributions. It also contains definitions of relevant point estimates and credible regions.

38.1. Notation

Quantity	General notation
Conditional probability	\(\cprob{A}{B}\)
Covariance	\(\cov{X}{Y}\)
Distribution function	\(P(x)\)
Empty set	\(\emptyset\)
Event	\(A\)
Expectation value	\(\expect{X}\)
Likelihood function	\(\mathcal{L}(\para)\)
Model parameters	\(\para\)
Probability density function	\(\p{x}\)
Probability mass function	\(\p{x}\)
Probability measure	\(\prob\)
Random variable	\(X\)
Sample space	\(S\)
Standard deviation	\(\std{X}\)
Variance	\(\var{X}\)