Statistical methods for paleovector analysis

Abstract

Our concern is with the statistical description of paleomagnetic vectors and the estimation of their mean and variance. These vectors may come from a number of different rock units or archeological samples, representing a range of acquisition times, and be useful for studies of the mean paleomagnetic field and paleosecular variation ; alternatively, the vectors may come from individual measurements taken from a given rock unit or archeological sample, representing the same moment of acquisition, and be useful for studying the acquisition process itself. Directional data of a particular polarity are usually analyzed with a Fisher distribution (1953), and data of mixed polarities are usually analyzed with a Bingham distribution (1964). Occasionally, other directional distributions are used. For example, Bingham ( 1983 ) considered the projection of a three‐dimensional (3D), scalar‐variance Gaussian distribution onto the unit sphere, something he called the “angular‐Gaussian” distribution. More recently, Khokhlov et al. ( 2001 ) considered a generalization of the angular‐Gaussian distribution, one with a covariance matrix, which they used to analyze directional data from a number of sites. With respect to intensity data, they have traditionally been treated separately from paleodirections, analyzed with normal, log‐normal, or gamma distributions. Here, for data of either a particular polarity or of mixed polarities, we summarize these works, and that of Love and Constable ( 2003 ), who developed a full‐vector, scalar‐variance, Gaussian‐statistical framework for treating directional and intensity data simultaneously and self‐consistently.