• hypothesis testing
• paired t-test
• bootstrapping
• p-value
• t-test
• parametric test
• gaussian distribution
• confidence interval
• chi squared test
• convex
• concave
• gradient descent
• gradient ascent
• time series analysis
• hyperplane
• half-space

Null Hypothesis

Statistically Significant

The result is probably not due to random luck.

Vector norm

The vector norm is denoted

$$\Vert \mathbf{x}\Vert$$

and may represent any vector norm.

Absolute-value norm

$$\Vert \mathbf{x}\Vert =\Vert \mathbf{x}{\Vert }_1=\sum _{j=1}^n|x_j|$$

Euclidean norm

$$\Vert \mathbf{x}\Vert =\Vert \mathbf{x}{\Vert }_2=\sqrt{\sum _{j=1}^n{x}_j^2}$$

Probability space

The probability space consists of three elements: the sample space, the event space and a probability function. The probability function assigns each event in the event space a probability between 0 and 1 where each event maps to a set of outcomes in the sample space.

Parametric family

A parametric family is a family whose differences only depend in the set of parameters used.

Point process

A spatial Poisson process is a special case of a point process.

Stochastic calculus

Stochastic calculus is a branch of mathematics that operates on stochastic processes.

Hoeffding's inequality

Hoeffding's inequality is an upper bound on the probability that the sum of independent random variables differs by a certain amount with regards to its expected value.

Boole's inequality

Boole's inequality is also known as the union bound. It states that for any finite set of events the probability that at least one of the events happens is no greater than the sum of the probabilities of the individual events.