Statistical Analysis of Rock Fabric
Point Estimation, Smoothing and Regression
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Statistical tools for analyzing distributions of rockfabric orientations are limited to point estimatorsand graphical plots. Inapplicability of conventionalstatistics is a result of directional nature of theseobservations. This book presents new techniquesexpanding arsenal of orientational analysis andapplicable in statistics for directional data ingeneral. In the introductory chapter, discussion ofdirectional data is given together with its relationto observations in structural geology. Next chapterpresents the tools themselves, starting with pointestimation on Stiefel and Grassman manifolds ...
Statistical tools for analyzing distributions of rock
fabric orientations are limited to point estimators
and graphical plots. Inapplicability of conventional
statistics is a result of directional nature of these
observations. This book presents new techniques
expanding arsenal of orientational analysis and
applicable in statistics for directional data in
general. In the introductory chapter, discussion of
directional data is given together with its relation
to observations in structural geology. Next chapter
presents the tools themselves, starting with point
estimation on Stiefel and Grassman manifolds using
incomplete data. Following it, a nonlinear regression
model of directions on linear (spatial) data is
presented. Finally, modification of kernel smoothing
for directional data is discussed. Last chapter is a
case study of a structurally complex metamorphic
terrane in which, besides applying the above tools,
use of bootstrap for the purpose of inference is
shown. This book should be especially useful for
structural geologists specializing in orientational
analysis, but may also fit interests of others
working with directional data.
fabric orientations are limited to point estimators
and graphical plots. Inapplicability of conventional
statistics is a result of directional nature of these
observations. This book presents new techniques
expanding arsenal of orientational analysis and
applicable in statistics for directional data in
general. In the introductory chapter, discussion of
directional data is given together with its relation
to observations in structural geology. Next chapter
presents the tools themselves, starting with point
estimation on Stiefel and Grassman manifolds using
incomplete data. Following it, a nonlinear regression
model of directions on linear (spatial) data is
presented. Finally, modification of kernel smoothing
for directional data is discussed. Last chapter is a
case study of a structurally complex metamorphic
terrane in which, besides applying the above tools,
use of bootstrap for the purpose of inference is
shown. This book should be especially useful for
structural geologists specializing in orientational
analysis, but may also fit interests of others
working with directional data.
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