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Machine Interval Experiments - Sainudiin Raazesh
A statistical experiment provides a
framework for statistical inference, including hypothesis
testing and parameter estimation, from observations of an
empirical phenomenon. When observations in the continuum of
real numbers are not empirically measurable to infinite
precision and when conventional floating-point computations
used in the inference procedure are not exact, the
statistical experiment can become epistemologically invalid.
The family of measures of the conventional statistical
experiment indexed by a compact finite-dimensional continuum
is extended to the complete metric space of all compact
subsets of the index set by the natural interval extension
of the likelihood function. The extended experiment allows a
statistical decision made with the aid of a computer to be
equivalent to a numerical proof. From the integrative
interface of pure mathematics, computer science and
statistics this work solves three open problems in
computational statistics: (1) parametric bootstraps for
mixture models, (2) rigorous maximum likelihood estimates
of the branch lengths of a phylogenetic tree and (3) Monte
Carlo sampling from a challenging densities.
EAN: 9783838315997Potrzebujesz pomocy? Masz pytania?Zadaj pytanie a my odpowiemy niezwłocznie, najciekawsze pytania i odpowiedzi publikując dla innych. 
