Stereology for Statisticians

by Baddeley; Adrian

• ISBN13: 9781584884057
• ISBN10: 1584884053
• Edition: 1st
• Format: Hardcover
• Copyright: 2004-11-29
• Publisher: Chapman & Hall/

Summary

Stereology, or quantitative microscopy, is a basic research tool in science and technology. The emergence of design-based methods has greatly increased the power, flexibility, adaptability, and scope of stereology applications, establishing a closer connection between statistics and quantitative microscopy. Despite its scientific importance, modern stereology remains largely unknown to the statistical community, with valuable information either widely scattered or inaccessible to newcomers to the field. Now is the perfect time for a book that enables biostatisticians and statistical consultants to give beneficial advice to researchers in microscopy.Stereology for Statisticians sets out the principles of stereology from a statistical viewpoint, focusing on both basic theory and practical implications. This book discusses ways to effectively communicate statistical issues to clients, draws attention to common methodological errors, and provides references to essential literature.The first full text on design-based stereology, it opens with a review of classical and modern stereology, followed by a treatment of mathematical foundations such as geometry, probability, and statistical inference. The book then presents core techniques, including estimation of absolute geometrical quantities, relative quantities, and statistical inference for populations of discrete objects. The final chapters discuss implementing techniques in practical sampling designs, summarize understanding of the variance of stereological estimators, and describe open problems for further research.

Table of Contents

1 Introduction	1	(8)
2 Classical stereology	9	(46)
2.1 Volume fraction	9	(8)
2.2 Surface area density and length density	17	(8)
2.3 Particles	25	(7)
2.4 Particle size	32	(6)
2.5 Thick sections	38	(3)
2.6 Counting profiles in two dimensions	41	(1)
2.7 Projections	42	(4)
2.8 Statistical critique of classical stereology	46	(2)
2.9 Advice to consultants	48	(2)
2.10 Exercises	50	(2)
2.11 Bibliographic notes	52	(3)
3 Overview of modern stereology	55	(32)
3.1 Motivation	55	(1)
3.2 Statistical foundations	56	(7)
3.3 Random sampling designs	63	(8)
3.4 Geometrical identities	71	(4)
3.5 Geometrical probability	75	(3)
3.6 Advice to consultants	78	(4)
3.7 Exercises	82	(1)
3.8 Bibliographic notes	83	(4)
4 Geometrical identities	87	(24)
4.1 Plane sections and line transects	88	(9)
4.2 Quadrats	97	(7)
4.3 Curvature	104	(3)
4.4 Exercises	107	(1)
4.5 Bibliographic notes	108	(3)
5 Geometrical probability	111	(24)
5.1 UR points	112	(2)
5.2 IUR and FUR lines in the plane	114	(3)
5.3 FUR planes	117	(2)
5.4 FUR quadrats in the plane	119	(4)
5.5 Isotropic directions	123	(3)
5.6 IUR planes	126	(3)
5.7 IUR quadrats	129	(1)
5.8 Advice to consultants	129	(1)
5.9 Exercises	130	(3)
5.10 Bibliographic notes	133	(2)
6 Statistical formulations of stereology	135	(20)
6.1 Terminology	135	(2)
6.2 Generic models	137	(2)
6.3 Parameters	139	(3)
6.4 Reference spaces	142	(2)
6.5 Estimation in the Random case	144	(3)
6.6 Estimation in the Restricted case	147	(2)
6.7 Estimation in the Extended case	149	(2)
6.8 Advice to consultants	151	(1)
6.9 Exercises	152	(1)
6.10 Bibliographic notes	153	(2)
7 Uniform and isotropic uniform designs	155	(20)
7.1 Estimation of volume and area	155	(7)
7.2 Length and surface area estimation	162	(6)
7.3 Exercises	168	(4)
7.4 Bibliographic notes	172	(3)
8 Vertical and local designs	175	(34)
8.1 Vertical sections	176	(12)
8.2 Vertical slices and vertical projections	188	(4)
8.3 Local lines	192	(7)
8.4 Local vertical sections	199	(3)
8.5 Local isotropic sections	202	(2)
8.6 Variance comparisons of local estimators	204	(1)
8.7 Exercises	205	(1)
8.8 Bibliographic notes	206	(3)
9 Ratio estimation	209	(20)
9.1 Ratio estimation in finite populations	209	(4)
9.2 Stereological estimation via ratios	213	(3)
9.3 Estimation of stereological ratios	216	(8)
9.4 Data modelling	224	(3)
9.5 Exercises	227	(1)
9.6 Bibliographic notes	228	(1)
10 Discrete sampling and counting	229	(26)
10.1 Basic principles	229	(4)
10.2 Unbiased sampling rules for particles	233	(9)
10.3 Decomposition	242	(2)
10.4 Reweighting	244	(4)
10.5 Variance reduction	248	(1)
10.6 Fractionator	249	(1)
10.7 Exercises	250	(2)
10.8 Bibliographic notes	252	(3)
11 Inference for particle populations	255	(22)
11.1 Strategies for particle stereology	255	(2)
11.2 The design-based case	257	(12)
11.3 Model-based case	269	(6)
11.4 Exercises	275	(1)
11.5 Bibliographic notes	276	(1)
12 Design of stereological experiments	277	(18)
12.1 Design constraints	277	(1)
12.2 Parameters and estimators	278	(3)
12.3 Design strategies	281	(3)
12.4 Implementation	284	(5)
12.5 Sources of non-sampling error	289	(1)
12.6 Optimal design	290	(5)
13 Variance of stereological estimators	295	(34)
13.1 Variances in model-based stereology	296	(6)
13.2 Variances in design-based stereology	302	(12)
13.3 Variance comparisons and Rao-Blackwell	314	(3)
13.4 Prediction variance	317	(1)
13.5 Nested ANOVA	318	(3)
13.6 Particle number	321	(3)
13.7 Advice to consultants	324	(2)
13.8 Exercises	326	(1)
13.9 Bibliographic notes	327	(2)
14 Frontiers and open problems	329	(4)
14.1 Variances	329	(1)
14.2 Inhomogeneous materials and tissues	330	(1)
14.3 Anisotropy and digital stereology	330	(1)
14.4 Spatial arrangement	331	(1)
14.5 Stereology of extremes	331	(1)
14.6 Fractal behaviour of surfaces	331	(1)
14.7 Non-recognition artefacts	331	(1)
14.8 Reconciliation with other areas	332	(1)
14.9 Shape models	332	(1)
A Sampling theory	333	(8)
A.1 Population and sample	333	(2)
A.2 Estimation from a sample	335	(1)
A.3 Sampling designs	336	(2)
A.4 Nonuniform sampling designs	338	(1)
A.5 Variances of estimators	339	(2)
List of notation	341	(4)
References	345	(32)
Index	377