# State Space

#### Statistical Glossary

State Space:

State space is an abstract space representing possible states of a system. A point in the state space is a vector of the values of all relevant parameters of the system.

It is often assumed that the system is dynamic – that is, its state at time t + dt can be predicted from its state at time t through a differential equation.

For example, an object moving in 3D space, e.g. a ball or a stone, can be represented as a point in 6-dimensional state (x, y, z, vx, vy, vz) . Here x,y,z are ordinary 3D coordinates of the object, vx, vy, vz are the three components of its velocity in those dimensions.

State space is usually not directly observable. The goal of some statistical techniques is to estimate or predict the state of a system (a point in its state space) from observed data.

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