Maximum likelihood estimation of the size distribution of liver cell nuclei from the observed distribution in a plane section.
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Maximum likelihood estimation of the size distribution of liver cell nuclei from the observed distribution in a plane section. / Keiding, Niels; Jensen, Søren Tolver; Ranek, Leo.
In: Biometrics, Vol. 28, No. 3, 09.1972, p. 813-829.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Maximum likelihood estimation of the size distribution of liver cell nuclei from the observed distribution in a plane section.
AU - Keiding, Niels
AU - Jensen, Søren Tolver
AU - Ranek, Leo
PY - 1972/9
Y1 - 1972/9
N2 - From sections of liver biopsies, the distribution of the radii of sectioned nuclei is recorded. Under the assumption that the nuclei are spherical, the problem of inferring the real size distribution of the nuclei in the liver from the observed distribution of the profile radii in the section is studied. This is an example of the 'corpuscle problem' first studied by Wicksell. A parametric model for the distribution of the nucleus radii is proposed and ordinary maximum likelihood estimation is discussed. The small sections are clearly under-represented in the profile distribution. This problem which seems to be common in like situations, is here approached by the idea that the unrecorded nucleus sections come from nuclei whose angle of intersection with the microtome is less than some fixed angle p. It is also possible to estimate p and to test the important hypothesis that p = 27r, i.e. that the nucleus size distribution is directly observed in the section. The theory is supplemented by detailed numerical investigations.
AB - From sections of liver biopsies, the distribution of the radii of sectioned nuclei is recorded. Under the assumption that the nuclei are spherical, the problem of inferring the real size distribution of the nuclei in the liver from the observed distribution of the profile radii in the section is studied. This is an example of the 'corpuscle problem' first studied by Wicksell. A parametric model for the distribution of the nucleus radii is proposed and ordinary maximum likelihood estimation is discussed. The small sections are clearly under-represented in the profile distribution. This problem which seems to be common in like situations, is here approached by the idea that the unrecorded nucleus sections come from nuclei whose angle of intersection with the microtome is less than some fixed angle p. It is also possible to estimate p and to test the important hypothesis that p = 27r, i.e. that the nucleus size distribution is directly observed in the section. The theory is supplemented by detailed numerical investigations.
UR - http://www.scopus.com/inward/record.url?scp=0015395598&partnerID=8YFLogxK
U2 - 10.2307/2528765
DO - 10.2307/2528765
M3 - Journal article
C2 - 5073254
AN - SCOPUS:0015395598
VL - 28
SP - 813
EP - 829
JO - Biometrics
JF - Biometrics
SN - 0006-341X
IS - 3
ER -
ID: 202486760