Parameter space refers to the multidimensional space formed by all the possible values that parameters can take in a given model or system. Each parameter corresponds to a dimension within this space, and the combination of values defines a point in that space. In various fields, the concept of parameter space is used as follows: 1. **Mathematics and Statistics**: In statistical modeling, the parameter space may refer to all possible configurations of parameters that define a statistical model.
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The parameter space of a statistical model is the set of allowed statistical parameter values indexing its probability distributions. For an exponential distribution parametrized by its mean, ; for a Bernoulli distribution, . Intersecting a confidence interval with the known parameter space cannot remove the true statistical parameter and therefore preserves its coverage probability.