Abstract:
Global climate models (GCM) offer synoptic scale weather data under different climate scenarios, but often times the grid on which data is available is too sparse to be of real use. The goal of this talk is to introduce the field of climate downscaling, and present a few downscaling techniques (both spatial and temporal), focusing on my work at Environment Canada with exponential dispersion models and PCA. Specifically, I'll be discussing some of the aspects of the Tweedie family of distributions which make them a straightforward choice for temporal downscaling with semi-continuous data, some techniques for scoring different stochastically simulated weather series, and a method for producing air temperature data at fine resolutions on complex terrains.

There are many issues remaining to be addressed, or even formulated,
at the interface of statistics and computation.  One way to capture
the current state of affairs is the following:  If we view data as a
resource, how can it be that in many practical problems of interest
we find ourselves embarassed by being given too much data?  The issue 
is both statistical and computational---on a fixed computational budget 
we are unable to guarantee that the statistical risk decreases as the
number of data points grows (without bound).  A general theory not
yet being available, I present two initial forays into the problem
domain.  The first is an exploration of the bootstrap in the regime 
of very large data sets, where it is computationally infeasible to 
obtain bootstrap resamples.  I present a new procedure, the ``bag of 
little bootstraps,'' which inherits the favorable theoretical properties 
of the bootstrap but is also scalable.  The second is an exploration of 
divide-and-conquer strategies for matrix completion.  Here the theoretical 
support is provided by concentration theorems for random matrices, and I
present a new approach to this problem based on Stein's method. 
 
[Joint work with Ariel Kleiner, Lester Mackey, Purna Sarkar, Ameet 
Talwalkar, Richard Chen, Brendan Farrell and Joel Tropp].

Complex deterministic and stochastic models are often used to
describe dynamic systems in climate science, ecology and biology. Inferring
unknown parameters of these models is of interest, both for understanding the
underlying scientific processes as well as for making valid predictions. Some
of the challenges typically involved in inference for these models are:
likelihood functions that are intractable or only implicitly specified by a
computer model; computationally expensive model simulations; and high-
dimensional, multivariate observations and model output.

I will outline computationally expedient Gaussian process-based inferential
approaches in the context of two very different models, a deterministic Earth-
system model used in climate science, and a stochastic spatial model for
infectious diseases. I will point out some of the common features between the
two, but also highlight significant differences in the modeling frameworks
and inferential goals.

This talk is based on joint work with K. Sham Bhat (Los Alamos National
Labs), Roman Jandarov (Dept. of Statistics, Penn State University [PSU]),
Roman Tonkonojenkov (Dept. of Geosciences, PSU), Klaus Keller (Dept. of
Geosciences, PSU), Ottar Bjornstad (Center for Infectious Disease
Dynamics, PSU), and Bryan Grenfell (Ecology and Evolutionary Biology, Princeton University)

If atmospheric, agricultural, and other environmental systems share one underlying theme it is complex spatial structures, being influenced by such features as topography and weather. For example, the air quality characteristics of cities are likely to be more similar than that of rural areas irrespective of their geographic proximity. Ideally we might model these effects directly; however, information on the underlying causes is often not routinely available. Hence, when modeling environmental systems there exists a need for a class of models that are more complex than those which rely on the assumption of stationarity.

In this talk, we propose a novel approach to modeling nonstationary spatial fields. The proposed method works by expanding the geographic plane over which these processes evolve into higher dimensional spaces, transforming and clarifying complex patterns in the physical plane. By combining aspects of multi-dimensional scaling, group lasso, and latent variables models, a dimensionally sparse projection is found in which the originally nonstationary field exhibits stationarity. Following a comparison with existing methods in a simulated environment, dimension expansion is studied on a classic test-bed data set historically used to study nonstationary models. Following this, we explore the use of dimension expansion in modeling air pollution in the United Kingdom, a process known to be strongly influenced by rural/urban effects, amongst others, which gives rise to a nonstationary field.