As a part of exploring spatial distribution of particles/objects, not to approximate via Poisson process or Gaussian process (parametric), nor to impose hypotheses such as homogenous, isotropic, or uniform, various nonparametric methods somewhat dragged my attention for data exploration and preliminary analysis. Among various nonparametric methods, the one that I fell in love with is tessellation (state space approaches are excluded here). Computational speed wise, I believe tessellation is faster than kernel density estimation to estimate level sets for multivariate data. Furthermore, conceptually constructing polygons from tessellation is intuitively simple. However, coding and improving algorithms is beyond statistical research (check books titled or key-worded partially by computational geometry). Good news is that for computation and getting results, there are some freely available softwares, packages, and modules in various forms. Continue reading ‘[ArXiv] Voronoi Tessellations’ »
Posts tagged ‘spatial statistics’
I decide to discuss Kalman Filter a while ago for the slog after finding out that this popular methodology is rather underrepresented in astronomy. However, it is not completely missing from ADS. I see that the fulltext search and all bibliographic source search shows more results. Their use of Kalman filter, though, looked similar to the usage of “genetic algorithms” or “Bayes theorem.” Probably, the broad notion of Kalman filter makes it difficult my finding Kalman Filter applications by its name in astronomy since often wheels are reinvented (algorithms under different names have the same objective). Continue reading ‘[MADS] Kalman Filter’ »
Kriging is the first thing that one learns from a spatial statistics course. If an astronomer sees its definition and application, almost every astronomer will say, “Oh, I know this! It is like the 2pt correlation function!!” At least this was my first impression when I first met kriging.
There are three distinctive subjects in spatial statistics: geostatistics, lattice data analysis, and spatial point pattern analysis. Because of the resemblance between the spatial distribution of observations in coordinates and the notion of spatially random points, spatial statistics in astronomy has leaned more toward the spatial point pattern analysis than the other subjects. In other fields from immunology to forestry to geology whose data are associated spatial coordinates of underlying geometric structures or whose data were sampled from lattices, observations depend on these spatial structures and scientists enjoy various applications from geostatistics and lattice data analysis. Particularly, kriging is the fundamental notion in geostatistics whose application is found many fields. Continue reading ‘[MADS] Kriging’ »
I was questioned by two attendees, acquainted before the AAS, if I can suggest them clustering methods relevant to their projects. After all, we spent quite a time to clarify the term clustering. Continue reading ‘my first AAS. IV. clustering’ »
Because of the extensive works by Prof. Peebles and many (observational) cosmologists (almost always I find Prof. Peeble’s book in cosmology literature), the 2 (or 3) point correlation function is much more dominant than any other mathematical and statistical methods to understand the structure of the universe. Unusually, this week finds an astro-ph paper written by a statistics professor addressing the K-function to explore the mystery of the universe.
[astro-ph:0804.3044] J.M. Loh
Estimating Third-Order Moments for an Absorber Catalog