EARLY HISTORY OF GEOMETRIC PROBABILITY AND STEREOLOGY
نویسندگان
چکیده
منابع مشابه
Stereology.
1.1 組織標本を使用する定量解析が抱える諸問題 組織標本の解析は定性的な所見から始まる.顕微鏡を用いた丁寧な観察によって初めて得られる検体の 大きさや分布,形態などについての詳細な情報は,全ての研究の基礎となるべき重要なものである.しか しながら,定性的なデータだけでは,統計学的な検討が難しく,結果が主観的なものになりやすい.この ため,生理的組織と病的組織の比較など,さらなる研究を行う際には,定量的なデータが必要になる.定 量解析の基本的な命題は,いかにして検体の正確な数を客観的に求めることができるか,ということであ る.組織標本に基づく定量解析は単純に思われるが,正確なデータを得ることは実は容易ではない. 最大の問題は,サンプリングバイアスである(図1).これは,標本抽出の際に母集団を代表していない 検体が選ばれるために生じる偏りのことであり,2次元的な切片を使って定量解析を行...
متن کاملPre-history of probability
It has been common to begin histories of probability with the calculations of Fermat and Pascal on games of chance in 1654. Those calculations were the first substantial mathematical results on stochastic phenomena, which, according to a frequentist philosophy of probability, are the true subject-matter of the field. But there is great philosophical interest in studying earlier ideas. That is b...
متن کاملGeometric Inference for Probability Measures
Data often comes in the form of a point cloud sampled from an unknown compact subset of Euclidean space. The general goal of geometric inference is then to recover geometric and topological features (e.g., Betti numbers, normals) of this subset from the approximating point cloud data. It appears that the study of distance functions allows to address many of these questions successfully. However...
متن کاملWeak laws in geometric probability
Using a coupling argument, we establish a general weak law of large numbers for functionals of binomial point processes in d-dimensional space, with a limit that depends explicitly on the (possibly non-uniform) density of the point process. The general result is applied to the minimal spanning tree, the k-nearest neighbors graph, the Voronoi graph, and the sphere of influence graph. Functionals...
متن کاملNormal Approximation in Geometric Probability
Statistics arising in geometric probability can often be expressed as sums of stabilizing functionals, that is functionals which satisfy a local dependence structure. In this note we show that stabilization leads to nearly optimal rates of convergence in the CLT for statistics such as total edge length and total number of edges of graphs in computational geometry and the total number of particl...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Image Analysis & Stereology
سال: 2012
ISSN: 1854-5165,1580-3139
DOI: 10.5566/ias.v31.p1-16