第29回統計地震学セミナー

日時(Date)

2012年7月6日（金）/ 6 JUL 2012 (Friday)

場所
(Location)

統計数理研究所 D312A号室 /
Room D312A @ Institute of Statistical Mathematics

講演者 1
(Speaker 1)

D. J. Daley
(Department of Mathematics and Statistics The University of Melbourne)

時間(Time)

14:30〜

講演題目
(Title)

Dimension walks and schoenberg spectral measures for isotropic random fields

概要
(Abstract)

Schoenberg (1938) showed how Bochner's basic representation theorem for positive definite functions (e.g. correlation function of a stationary stochastic process) `simplifies' for spatial processes (d-dimensional random fields) which are isotropic: the standard Fourier kernel function is replaced by the characteristic function of a random direction in d-space and the spectral measure, instead of being on d-space, is on the positive half-line.

The talk describes how Wendland's `dimension walks', which were defined earlier by Matheron as Descente and Montee in studying relations between d-D and either (d+2)-D or (d-2)-D correlation functions, are equivalent to simple modifications of their d-Schoenberg measures.

Another family of dimension walks arises from projections from unit d-spheres to lower dimensional spheres, first via the kernel functions in the Schoenberg representation and then more generally, for d-Schoenberg measures.

講演者 2
(Speaker 2)

Adrian Baddeley
(CSIRO Mathematics, Informatics and Statistics Perth, Australia)

時間(Time)

15:30〜

講演題目
(Title)

Leverage, influence and residual diagnostics for point process models

概要
(Abstract)

For a spatial point process model fitted to spatial point pattern data, we develop diagnostics for model validation, analogous to the classical measures of leverage and influence and residual plots in a generalized linear model. The diagnostics can be characterised as derivatives of basic functionals of the model.

They can also be derived heuristically (and computed in practice) as the limits of classical diagnostics under increasingly fine discretizations of the spatial domain.

We apply the diagnostics to example datasets where there are concerns about model validity.

講演者 3
(Speaker 3)

島谷健一郎 (統計数理研究所)
（Kenichiro Shimatani (ISM)）

時間(Time)

16:30〜

講演題目
(Title)

inferring parameters in inhomogeneous Neyman-Scott processes using the Palm likelihood

概要
(Abstract)

Plant populations often exhibit spatially clustering distributions, in which the two processes, limited seed dispersal and limited safe sites, are primary mechanisms. The inhomogeneous Neyman-Scott process can combine and model these two ecological processes. Estimating the model parameters allows evaluation of the relative effects of dispersal and safe sites retrospectively from spatial individual distribution data along environmental gradients. Here we propose a likelihood-based method for this spatial point process by extending the recently developed method, the Palm likelihood. Our approach was applied to even-aged black spruce forests in Canada. We obtained a set of model parameters that well reproduced the observed spatial patterns, and the fitted point processes predicted the reassembly pathway of the boreal forests.