Dataset Information

The Weighted-Average Lagged Ensemble.

ABSTRACT: A lagged ensemble is an ensemble of forecasts from the same model initialized at different times but verifying at the same time. The skill of a lagged ensemble mean can be improved by assigning weights to different forecasts in such a way as to maximize skill. If the forecasts are bias corrected, then an unbiased weighted lagged ensemble requires the weights to sum to one. Such a scheme is called a weighted-average lagged ensemble. In the limit of uncorrelated errors, the optimal weights are positive and decay monotonically with lead time, so that the least skillful forecasts have the least weight. In more realistic applications, the optimal weights do not always behave this way. This paper presents a series of analytic examples designed to illuminate conditions under which the weights of an optimal weighted-average lagged ensemble become negative or depend nonmonotonically on lead time. It is shown that negative weights are most likely to occur when the errors grow rapidly and are highly correlated across lead time. The weights are most likely to behave nonmonotonically when the mean square error is approximately constant over the range forecasts included in the lagged ensemble. An extreme example of the latter behavior is presented in which the optimal weights vanish everywhere except at the shortest and longest lead times.

SUBMITTER: DelSole T

PROVIDER: S-EPMC5784419 | biostudies-literature | 2017 Nov

REPOSITORIES: biostudies-literature

ACCESS DATA

Publications

The Weighted-Average Lagged Ensemble.

DelSole T T Trenary L L Tippett M K MK

Journal of advances in modeling earth systems 20171129 7

A lagged ensemble is an ensemble of forecasts from the same model initialized at different times but verifying at the same time. The skill of a lagged ensemble mean can be improved by assigning weights to different forecasts in such a way as to maximize skill. If the forecasts are bias corrected, then an unbiased weighted lagged ensemble requires the weights to sum to one. Such a scheme is called a weighted-average lagged ensemble. In the limit of uncorrelated errors, the optimal weights are pos ...[more]

PMID: 29399270

Similar Datasets

Project description:BACKGROUND:The body-bar Pebble Game (PG) algorithm is commonly used to calculate network rigidity properties in proteins and polymeric materials. To account for fluctuating interactions such as hydrogen bonds, an ensemble of constraint topologies are sampled, and average network properties are obtained by averaging PG characterizations. At a simpler level of sophistication, Maxwell constraint counting (MCC) provides a rigorous lower bound for the number of internal degrees of freedom (DOF) within a body-bar network, and it is commonly employed to test if a molecular structure is globally under-constrained or over-constrained. MCC is a mean field approximation (MFA) that ignores spatial fluctuations of distance constraints by replacing the actual molecular structure by an effective medium that has distance constraints globally distributed with perfect uniform density. RESULTS:The Virtual Pebble Game (VPG) algorithm is a MFA that retains spatial inhomogeneity in the density of constraints on all length scales. Network fluctuations due to distance constraints that may be present or absent based on binary random dynamic variables are suppressed by replacing all possible constraint topology realizations with the probabilities that distance constraints are present. The VPG algorithm is isomorphic to the PG algorithm, where integers for counting "pebbles" placed on vertices or edges in the PG map to real numbers representing the probability to find a pebble. In the VPG, edges are assigned pebble capacities, and pebble movements become a continuous flow of probability within the network. Comparisons between the VPG and average PG results over a test set of proteins and disordered lattices demonstrate the VPG quantitatively estimates the ensemble average PG results well. CONCLUSIONS:The VPG performs about 20% faster than one PG, and it provides a pragmatic alternative to averaging PG rigidity characteristics over an ensemble of constraint topologies. The utility of the VPG falls in between the most accurate but slowest method of ensemble averaging over hundreds to thousands of independent PG runs, and the fastest but least accurate MCC.

Project description:In real physical systems the underlying spatial components might not have crisp boundaries and their interactions might not be instantaneous. To this end, we propose δ-MAPS; a method that identifies spatially contiguous and possibly overlapping components referred to as domains, and identifies the lagged functional relationships between them. Informally, a domain is a spatially contiguous region that somehow participates in the same dynamic effect or function. The latter will result in highly correlated temporal activity between grid cells of the same domain. δ-MAPS first identifies the epicenters of activity of a domain. Next, it identifies a domain as the maximum possible set of spatially contiguous grid cells that include the detected epicenters and satisfy a homogeneity constraint. After identifying the domains, δ-MAPS infers a functional network between them. The proposed network inference method examines the statistical significance of each lagged correlation between two domains, applies a multiple-testing process to control the rate of false positives, infers a range of potential lag values for each edge, and assigns a weight to each edge reflecting the magnitude of interaction between two domains. δ-MAPS is related to clustering, multivariate statistical techniques and network community detection. However, as we discuss and also show with synthetic data, it is also significantly different, avoiding many of the known limitations of these methods.We illustrate the application of δ-MAPS on data from two domains: climate science and neuroscience. First, the sea-surface temperature climate network identifies some well-known teleconnections (such as the lagged connection between the El Nin\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\tilde {o}$\end{document}õ Southern Oscillation and the Indian Ocean). Second, the analysis of resting state fMRI cortical data confirms the presence of known functional resting state networks (default mode, occipital, motor/somatosensory and auditory), and shows that the cortical network includes a backbone of relatively few regions that are densely interconnected.

Dataset Information

The Weighted-Average Lagged Ensemble.

Publications

The Weighted-Average Lagged Ensemble.

Similar Datasets

OmicsDI is part of the ELIXIR infrastructure

Tweets