Predictive Distribution

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Carl Edward Rasmussen - One of the best experts on this subject based on the ideXlab platform.

  • bayesian inference and learning in gaussian process state space models with particle mcmc
    arXiv: Machine Learning, 2013
    Co-Authors: Roger Frigola, Thomas B. Schön, Fredrik Lindsten, Carl Edward Rasmussen
    Abstract:

    State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference \emph{and learning} (i.e. state estimation and system identification) in nonlinear nonparametric state-space models. We place a Gaussian process prior over the state transition dynamics, resulting in a flexible model able to capture complex dynamical phenomena. To enable efficient inference, we marginalize over the transition dynamics function and infer directly the joint smoothing Distribution using specially tailored Particle Markov Chain Monte Carlo samplers. Once a sample from the smoothing Distribution is computed, the state transition Predictive Distribution can be formulated analytically. Our approach preserves the full nonparametric expressivity of the model and can make use of sparse Gaussian processes to greatly reduce computational complexity.

  • propagation of uncertainty in bayesian kernel models application to multiple step ahead forecasting
    International Conference on Acoustics Speech and Signal Processing, 2003
    Co-Authors: Joaquin Quinonero Candela, A Girard, Jan Larsen, Carl Edward Rasmussen
    Abstract:

    The object of Bayesian modelling is Predictive Distribution, which, in a forecasting scenario, enables evaluation of forecasted values and their uncertainties. We focus on reliably estimating the Predictive mean and variance of forecasted values using Bayesian kernel based models such as the Gaussian process and the relevance vector machine. We derive novel analytic expressions for the Predictive mean and variance for Gaussian kernel shapes under the assumption of a Gaussian input Distribution in the static case, and of a recursive Gaussian Predictive density in iterative forecasting. The capability of the method is demonstrated for forecasting of time-series and compared to approximate methods.

T R R Pearman - One of the best experts on this subject based on the ideXlab platform.

  • improving the Predictive capability of benthic species Distribution models by incorporating oceanographic data towards holistic ecological modelling of a submarine canyon
    Progress in Oceanography, 2020
    Co-Authors: T R R Pearman, Katleen Robert, Alexander Callaway, Rob A Hall, Lo C Iacono, Veerle A I Huvenne
    Abstract:

    Submarine canyons are associated with increased biodiversity, including cold-water coral (CWC) colonies and reefs which are features of high conservation value that are under increasing anthropogenic pressure. Effective spatial management and conservation of these features requires accurate Distribution maps and a deeper understanding of the processes that generate the observed Distribution patterns. Predictive Distribution modelling offers a powerful tool in the deep sea, where surveys are constrained by cost and technological capabilities. To date, Predictive Distribution modelling in canyons has focussed on integrating groundtruthed acoustically acquired datasets as proxies for environmental variables thought to influence faunal patterns. Physical oceanography is known to influence faunal patterns but has rarely been explicitly included in Predictive Distribution models of canyon fauna, thereby omitting key information required to adequately capture the species-environment relationships that form the basis of Predictive Distribution modelling. In this study, acoustic, oceanographic and biological datasets were integrated to undertake high-resolution predictions of benthic megafaunal diversity and CWC Distribution within Whittard Canyon, North-East Atlantic. The main aim was to investigate which environmental variables best predict faunal patterns in canyons and to assess whether including oceanographic data improves Predictive modelling. General additive models, random forests and boosted regression trees were used to build Predictive maps for CWC occurrence, megafaunal abundance, species richness and biodiversity. To provide more robust predictions, ensemble techniques that summarise the variation in predictions and uncertainties between modelling approaches were applied to build final maps. Model performance improved with the inclusion of oceanographic data. Ensemble maps identified areas of elevated current speed that coincided with steep ridges and escarpment walls as the areas most likely to harbour CWCs and increased biodiversity, probably linked to local hydrodynamics interacting with topography to concentrate food resources. This study shows how incorporating oceanographic data into canyon models can broaden our understanding of processes generating faunal patterns and improve the mapping of features of conservation, supporting effective procedures for spatial ecosystem management.

Veerle A I Huvenne - One of the best experts on this subject based on the ideXlab platform.

  • improving the Predictive capability of benthic species Distribution models by incorporating oceanographic data towards holistic ecological modelling of a submarine canyon
    Progress in Oceanography, 2020
    Co-Authors: T R R Pearman, Katleen Robert, Alexander Callaway, Rob A Hall, Lo C Iacono, Veerle A I Huvenne
    Abstract:

    Submarine canyons are associated with increased biodiversity, including cold-water coral (CWC) colonies and reefs which are features of high conservation value that are under increasing anthropogenic pressure. Effective spatial management and conservation of these features requires accurate Distribution maps and a deeper understanding of the processes that generate the observed Distribution patterns. Predictive Distribution modelling offers a powerful tool in the deep sea, where surveys are constrained by cost and technological capabilities. To date, Predictive Distribution modelling in canyons has focussed on integrating groundtruthed acoustically acquired datasets as proxies for environmental variables thought to influence faunal patterns. Physical oceanography is known to influence faunal patterns but has rarely been explicitly included in Predictive Distribution models of canyon fauna, thereby omitting key information required to adequately capture the species-environment relationships that form the basis of Predictive Distribution modelling. In this study, acoustic, oceanographic and biological datasets were integrated to undertake high-resolution predictions of benthic megafaunal diversity and CWC Distribution within Whittard Canyon, North-East Atlantic. The main aim was to investigate which environmental variables best predict faunal patterns in canyons and to assess whether including oceanographic data improves Predictive modelling. General additive models, random forests and boosted regression trees were used to build Predictive maps for CWC occurrence, megafaunal abundance, species richness and biodiversity. To provide more robust predictions, ensemble techniques that summarise the variation in predictions and uncertainties between modelling approaches were applied to build final maps. Model performance improved with the inclusion of oceanographic data. Ensemble maps identified areas of elevated current speed that coincided with steep ridges and escarpment walls as the areas most likely to harbour CWCs and increased biodiversity, probably linked to local hydrodynamics interacting with topography to concentrate food resources. This study shows how incorporating oceanographic data into canyon models can broaden our understanding of processes generating faunal patterns and improve the mapping of features of conservation, supporting effective procedures for spatial ecosystem management.

Lo C Iacono - One of the best experts on this subject based on the ideXlab platform.

  • improving the Predictive capability of benthic species Distribution models by incorporating oceanographic data towards holistic ecological modelling of a submarine canyon
    Progress in Oceanography, 2020
    Co-Authors: T R R Pearman, Katleen Robert, Alexander Callaway, Rob A Hall, Lo C Iacono, Veerle A I Huvenne
    Abstract:

    Submarine canyons are associated with increased biodiversity, including cold-water coral (CWC) colonies and reefs which are features of high conservation value that are under increasing anthropogenic pressure. Effective spatial management and conservation of these features requires accurate Distribution maps and a deeper understanding of the processes that generate the observed Distribution patterns. Predictive Distribution modelling offers a powerful tool in the deep sea, where surveys are constrained by cost and technological capabilities. To date, Predictive Distribution modelling in canyons has focussed on integrating groundtruthed acoustically acquired datasets as proxies for environmental variables thought to influence faunal patterns. Physical oceanography is known to influence faunal patterns but has rarely been explicitly included in Predictive Distribution models of canyon fauna, thereby omitting key information required to adequately capture the species-environment relationships that form the basis of Predictive Distribution modelling. In this study, acoustic, oceanographic and biological datasets were integrated to undertake high-resolution predictions of benthic megafaunal diversity and CWC Distribution within Whittard Canyon, North-East Atlantic. The main aim was to investigate which environmental variables best predict faunal patterns in canyons and to assess whether including oceanographic data improves Predictive modelling. General additive models, random forests and boosted regression trees were used to build Predictive maps for CWC occurrence, megafaunal abundance, species richness and biodiversity. To provide more robust predictions, ensemble techniques that summarise the variation in predictions and uncertainties between modelling approaches were applied to build final maps. Model performance improved with the inclusion of oceanographic data. Ensemble maps identified areas of elevated current speed that coincided with steep ridges and escarpment walls as the areas most likely to harbour CWCs and increased biodiversity, probably linked to local hydrodynamics interacting with topography to concentrate food resources. This study shows how incorporating oceanographic data into canyon models can broaden our understanding of processes generating faunal patterns and improve the mapping of features of conservation, supporting effective procedures for spatial ecosystem management.

Raimundo Real - One of the best experts on this subject based on the ideXlab platform.

  • AUC: A misleading measure of the performance of Predictive Distribution models
    Global Ecology and Biogeography, 2008
    Co-Authors: Jennifer M Lobo, Alberto Jiménez-valverde, Raimundo Real
    Abstract:

    The area under the receiver operating characteristic (ROC) curve, known as the AUC, is currently considered to be the standard method to assess the accuracy of Predictive Distribution models. It avoids the supposed subjectivity in the threshold selection process, when continuous probability derived scores are converted to a binary presence–absence variable, by summarizing overall model performance over all possible thresholds. In this manuscript we review some of the features of this measure and bring into question its reliability as a comparative measure of accuracy between model results. We do not recommend using AUC for five reasons: (1) it ignores the predicted probability values and the goodness-of-fit of the model; (2) it summarises the test performance over regions of the ROC space in which one would rarely operate; (3) it weights omission and commission errors equally; (4) it does not give information about the spatial Distribution of model errors; and, most importantly, (5) the total extent to which models are carried out highly influences the rate of well-predicted absences and the AUC scores.