Bayesian Statistics Seminar
North Carolina State University
presents
Souparno Ghosh
Duke University
"Inference for Size Demography from Point Pattern Data using Integral
Projection Models"
ABSTRACT
Population dynamics with regard to evolution of traits has typically
been studied using matrix projection models (MPMs). Recently, to work with
continuous traits, integral projection models (IPMs) have been
proposed. Imitating the path with MPMs, IPMs are handled first with a
fitting stage, then
with a projection stage. Fitting these models has so far been done only with
individual-level transition data which is used to estimate the demographic
functions that comprise the kernel of the IPM specification. Then, the
estimated kernel is iterated from an initial trait distribution to project
steady state population behavior under this kernel. When trait distributions
are observed over time, such an approach fails to align projected
distributions
with these observed temporal benchmarks.
The contribution here, focusing on size distributions, is to address
this issue.
We view the observed size distribution at a given time as a point pattern over
a bounded interval. We build a three-stage Bayesian hierarchical model to
infer about the dynamic intensities used to explain the observed point
patterns. This model is driven by a latent deterministic IPM and we introduce
uncertainty by having the operating IPM vary around this deterministic
specification. Further uncertainty arises in the realization of the point
pattern given the operating IPM. Such modeling enables full posterior
inference about all features of the model. Such dynamic modeling,
optimized by
fitting data observed over time, is better suited to projection.
Exact model fitting is very computationally challenging; we offer approximate
strategies to facilitate computation. We illustrate with simulated data
examples as well as well as a set of annual tree growth data from Duke Forest
in North Carolina. A further example shows the benefit of our approach, in
terms of projection, compared with the foregoing individual level fitting.
This is based on a joint work with Alan E. Gelfand and James S. Clark
Thursday, November, 10, 2011
4:00 - 5:00 pm
1216 SAS Hall
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