1,131 research outputs found
Regression with Distance Matrices
Data types that lie in metric spaces but not in vector spaces are difficult
to use within the usual regression setting, either as the response and/or a
predictor. We represent the information in these variables using distance
matrices which requires only the specification of a distance function. A
low-dimensional representation of such distance matrices can be obtained using
methods such as multidimensional scaling. Once these variables have been
represented as scores, an internal model linking the predictors and the
response can be developed using standard methods. We call scoring the
transformation from a new observation to a score while backscoring is a method
to represent a score as an observation in the data space. Both methods are
essential for prediction and explanation. We illustrate the methodology for
shape data, unregistered curve data and correlation matrices using motion
capture data from an experiment to study the motion of children with cleft lip.Comment: 18 pages, 7 figure
Does Data Splitting Improve Prediction?
Data splitting divides data into two parts. One part is reserved for model
selection. In some applications, the second part is used for model validation
but we use this part for estimating the parameters of the chosen model. We
focus on the problem of constructing reliable predictive distributions for
future observed values. We judge the predictive performance using log scoring.
We compare the full data strategy with the data splitting strategy for
prediction. We show how the full data score can be decomposed into model
selection, parameter estimation and data reuse costs. Data splitting is
preferred when data reuse costs are high. We investigate the relative
performance of the strategies in four simulation scenarios. We introduce a
hybrid estimator called SAFE that uses one part for model selection but both
parts for estimation. We discuss the choice to use a split data analysis versus
a full data analysis
The Exact and Asymptotic Distributions of Cramérù Von Mises Statistics
Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/146839/1/rssb02077.pd
Time series forecasting with neural networks: a comparative study using the air line data
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73285/1/1467-9876.00109.pd
Attribution of long-term changes in peak river flows in Great Britain
We investigate the evidence for changes in the magnitude of peak river flows in Great Britain. We focus on a set of 117 near-natural "benchmark" catchments to detect trends not driven by land use and other human impacts, and aim to attribute trends in peak river flows to some climate indices such as the North Atlantic Oscillation (NAO) and the East Atlantic (EA) index. We propose modelling all stations together in a Bayesian multilevel framework to be better able to detect any signal that is present in the data by pooling information across several stations. This approach leads to the detection of a clear countrywide time trend. Additionally, in a univariate approach, both the EA and NAO indices appear to have a considerable association with peak river flows. When a multivariate approach is taken to unmask the collinearity between climate indices and time, the association between NAO and peak flows disappears, while the association with EA remains clear. This demonstrates the usefulness of a multivariate and multilevel approach when it comes to accurately attributing trends in peak river flows
Shape change along geodesics with application to cleft lip surgery
Continuous shape change is represented as curves in the shape space. A method for checking the closeness of these curves to a geodesic is presented. Three large databases of short human motions are considered and shown to be well approximated by geodesics. The motions are thus approximated by two shapes on the geodesic and the rate of progress along the path. An analysis of facial motion data taken from a study of subjects with cleft lip or cleft palate is presented that allows the motion to be considered independently from the static shape. Inferential methods for assessing the change in motion are presented. The construction of predicted animated motions is discussed
Variability in measurements of micro lengths with a white light interferometer
The effect of the discretionary setâup parameters scan length and initial scanner position on the measurements of length performed with a white light interferometer microscope was investigated. In both analyses, two reference materials of nominal lengths 40 and 200â”m were considered. Random effects and mixed effects models were fitted to the data from two separate experiments. Punctual and interval estimates of variance components were provided
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