Extensible grids: uniform sampling on a space filling curve
نویسندگان
چکیده
منابع مشابه
Extensible grids: uniform sampling on a space-filling curve
We study the properties of points in [0, 1]d generated by applying Hilbert’s space-filling curve to uniformly distributed points in [0, 1]. For deterministic sampling we obtain a discrepancy of O(n−1/d) for d ≥ 2. For random stratified sampling, and scrambled van der Corput points, we get a mean squared error of O(n−1−2/d) for integration of Lipshitz continuous integrands, when d ≥ 3. These rat...
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In mathematics classes where the natural numbers are studied, several surprising results can be shown about the relative “sizes” of infinite sets, such as the fact the there is a oneto-one mapping between the natural numbers N and the even numbers, showing that they are both countably infinite, with the “same size”. Similar logic also shows that there is a mapping from the natural numbers N ont...
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ژورنال
عنوان ژورنال: Journal of the Royal Statistical Society: Series B (Statistical Methodology)
سال: 2015
ISSN: 1369-7412,1467-9868
DOI: 10.1111/rssb.12132