Publication

Hierarchical wavelet modelling of environmental sensor data

Anthony Christopher Davison
2007
Working Papers

Abstract

Motivated by the need to smooth and to summarize multiple simultaneous time series arising from networks of environmental monitors, we propose a hierarchical wavelet model for which estimation of hyperparameters can be performed by marginal maximum likelihood. The result is an empirical Bayes thresholding procedure whose results improve on those of wavethresh in terms of mean square error. We apply the approach to data from the SensorScope environmental modelling system, and briefly discuss issues that arise concerning variance estimation in this context.

Official source

https://infoscience.epfl.ch/entities/publication/69ffe057-99a8-4d59-a744-3bf7a191dff6

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Anthony Christopher Davison
2007
Working Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/69ffe057-99a8-4d59-a744-3bf7a191dff6

About this result

Related concepts (32)

Mean squared error

In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures the average of the squares of the errors—that is, the average squared difference between the estimated values and the actual value. MSE is a risk function, corresponding to the expected value of the squared error loss. The fact that MSE is almost always strictly positive (and not zero) is because of randomness or because the estimator does not account for information that could produce a more accurate estimate.

Data

In common usage and statistics, data (USˈdætə; UKˈdeɪtə) is a collection of discrete or continuous values that convey information, describing the quantity, quality, fact, statistics, other basic units of meaning, or simply sequences of symbols that may be further interpreted formally. A datum is an individual value in a collection of data. Data is usually organized into structures such as tables that provide additional context and meaning, and which may themselves be used as data in larger structures.

Likelihood function

In statistical inference, the likelihood function quantifies the plausibility of parameter values characterizing a statistical model in light of observed data. Its most typical usage is to compare possible parameter values (under a fixed set of observations and a particular model), where higher values of likelihood are preferred because they correspond to more probable parameter values.

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Hierarchical wavelet modelling of environmental sensor data

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