Numerical estimation of densities
[Abridged] We present a novel technique, dubbed FiEstAS, to estimate the underlying density field from a discrete set of sample points in an arbitrary multidimensional space. FiEstAS assigns a volume to each point by means of a binary tree. Density is then computed by integrating over an adaptive ke...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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2004
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| _version_ | 1797061062271434752 |
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| author | Ascasibar, Y Binney, J |
| author_facet | Ascasibar, Y Binney, J |
| author_sort | Ascasibar, Y |
| collection | OXFORD |
| description | [Abridged] We present a novel technique, dubbed FiEstAS, to estimate the underlying density field from a discrete set of sample points in an arbitrary multidimensional space. FiEstAS assigns a volume to each point by means of a binary tree. Density is then computed by integrating over an adaptive kernel. As a first test, we construct several Monte Carlo realizations of a Hernquist profile and recover the particle density in both real and phase space. At a given point, Poisson noise causes the unsmoothed estimates to fluctuate by a factor ~2 regardless of the number of particles. This spread can be reduced to about 1 dex (~26 per cent) by our smoothing procedure. [...] We conclude that our algorithm accurately measure the phase-space density up to the limit where discreteness effects render the simulation itself unreliable. Computationally, FiEstAS is orders of magnitude faster than the method based on Delaunay tessellation that Arad et al. employed, making it practicable to recover smoothed density estimates for sets of 10^9 points in 6 dimensions. |
| first_indexed | 2024-03-06T20:25:43Z |
| format | Journal article |
| id | oxford-uuid:2f542b2d-5cd5-4eae-bf4b-c260919fc6dd |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T20:25:43Z |
| publishDate | 2004 |
| record_format | dspace |
| spelling | oxford-uuid:2f542b2d-5cd5-4eae-bf4b-c260919fc6dd2022-03-26T12:54:38ZNumerical estimation of densitiesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:2f542b2d-5cd5-4eae-bf4b-c260919fc6ddEnglishSymplectic Elements at Oxford2004Ascasibar, YBinney, J[Abridged] We present a novel technique, dubbed FiEstAS, to estimate the underlying density field from a discrete set of sample points in an arbitrary multidimensional space. FiEstAS assigns a volume to each point by means of a binary tree. Density is then computed by integrating over an adaptive kernel. As a first test, we construct several Monte Carlo realizations of a Hernquist profile and recover the particle density in both real and phase space. At a given point, Poisson noise causes the unsmoothed estimates to fluctuate by a factor ~2 regardless of the number of particles. This spread can be reduced to about 1 dex (~26 per cent) by our smoothing procedure. [...] We conclude that our algorithm accurately measure the phase-space density up to the limit where discreteness effects render the simulation itself unreliable. Computationally, FiEstAS is orders of magnitude faster than the method based on Delaunay tessellation that Arad et al. employed, making it practicable to recover smoothed density estimates for sets of 10^9 points in 6 dimensions. |
| spellingShingle | Ascasibar, Y Binney, J Numerical estimation of densities |
| title | Numerical estimation of densities |
| title_full | Numerical estimation of densities |
| title_fullStr | Numerical estimation of densities |
| title_full_unstemmed | Numerical estimation of densities |
| title_short | Numerical estimation of densities |
| title_sort | numerical estimation of densities |
| work_keys_str_mv | AT ascasibary numericalestimationofdensities AT binneyj numericalestimationofdensities |