In science, a parameter space is the set of all possible combinations of values for all the different parameters contained in a particular mathematical model. The ranges of values the parameters can take may form the axes of a plot, and particular outcomes of the model may be plotted against these axes to illustrate how different regions of the parameter space produce different types of behaviour in the model.
Often the parameters are inputs of a function, in which case the technical term for the parameter space is domain of a function.
Parameter spaces are particularly useful for describing families of probability distributions that depend on parameters. More generally in science, the term parameter space is used to describe experimental variables. For example, the concept has been used in the science of soccer in the article "Parameter space for successful soccer kicks." In the study, "Success rates are determined through the use of four-dimensional parameter space volumes."
In the context of statistics, parameter spaces form the background for parameter estimation. As Ross (1990) describes in his book:
- Parameter space is a subset of p-dimensional space consisting of the set of values of Θ which are allowable in a particular model. The values may sometimes be constrainted, say to the positive quadrant or the unit square, or in case of symmetry, to the triangular region where, say
The idea of intentionally truncating the parameter space has also been advanced elsewhere.
Famous quotes containing the word space:
“The peculiarity of sculpture is that it creates a three-dimensional object in space. Painting may strive to give on a two-dimensional plane, the illusion of space, but it is space itself as a perceived quantity that becomes the peculiar concern of the sculptor. We may say that for the painter space is a luxury; for the sculptor it is a necessity.”
—Sir Herbert Read (1893–1968)