Program: Montana Chapter of ASA 2005 Fall Meeting

Butte-Highlands Room, Student Union Building
Montana Tech, Butte, Montana

September 20, 2005

Time	Topic	Speaker	Affiliation
8:45 - 9:30	*Coffee and Doughnuts*
9:30 - 10:10	Space-Filling Designs for Highly-Constrained Mixture Experiments	John Borkowski	Montana State University - Bozeman
10:15 - 10:50	Modeling Map Positional Error to infer about True Feature Location	Jarrett Barber	Montana State University - Bozeman
10:55 - 11:30	A Brief Introduction to Functional Data Analysis	Mark Greenwood	Montana State University - Bozeman
11:30 - 1:15	*No-host Lunch*
1:15 - 2:00	The Two-component Error Model: Applications and Goodness-of-fit	Machelle D. Wilson	University of Montana - Missoula
2:00 - ?	*MT Chapter ASA Business Meeting*	Susan Hinkins, President	Minutes

ABSTRACTS

Space-Filling Designs for Highly-Constrained Mixture Experiments
- The goal of a space-filling design is uniform scatter of the design points in the experimental region of interest. For mixture designs of reasonable size, as the dimension of the experimental region increases, space-filling design criteria (such as maximin an minimax) place most, if not all, design points at or near the boundary of the constrained region. In this presentation, several number theoretic (NT) methods for generating space-filling mixture designs for highly-constrained mixture experiments will be implemented for an eight-component mixture problem. The uniform scatter of the points in these designs will be evaluated using distance-based criteria.
Modeling Map Positional Error to infer about True Feature Locations
- We address the issue of positional error, or the difference between location as represented in a spatial database and the corresponding (but unobservable) true location, in the presence of reference location information of higher accuracy than the map locations. Our data consist of feature locations on one or more maps as well as control points (so-called ground-truthing) associated with a subset of the features. The control points are either Global Position System (GPS) measured locations or locations on our highest quality map.
  
  In practice, given GPS measurements, map location is transformed by a global (or registration) transformation to a first stage estimate of location. This estimate is then revised to a second stage estimate by so-called rubber-sheeting (which for some locations, may be Òforced" to agree with the associated GPS measurements). And, finally, there is the measurement error associated with the the GPS location. We present a fully model-based approach to capture all of these aspects. With all of these pieces, positional error can be estimated. In fact, the modeling enables us to attach uncertainty to each component as well as to the overall inference. A key feature of our formulation is to model the true location as varying in a specified way around the observed location.
  
  Often, for a region, we have multiple maps of varying accuracy along with ground truthing data. A natural strategy would be to use all of the maps to learn about true locations, true features. But this suggests a context for some type of model averaging since true location means the same thing across all maps (models). In fact, the "data" changes across maps but we clarify that this may be viewed as specifying regression models with different covariate sets.
  
  Finally, we illustrate our approach using three maps of a residential neighborhood in Durham, North Carolina. In particular, we infer about true location for point features (road intersections) and for linear features (roads and city blocks).
A Brief Introduction to Functional Data Analysis
- Functional Data Analysis (FDA) is a relatively new area of statistics that seeks to exploit the structure of data that are generated by continuous processes over time or space. The methods are especially useful for problems where data are recorded at high resolution, where all the variables are not measured at the same times, or where derivatives may be of interest. A couple of examples of situations where FDA provides unique results are discussed as well as some aspects of performing FDA using Matlab, R and S-PLUS.
The Two-component Error Model: Applications and Goodness-of-fit
- The talk will introduce a two-component error model for use in analytical chemistry and will show applications and two goodness-of-fit statistics, one for testing overall error structure and one for testing lack-of-fit due to poor experimental design.