Climate driven spatiotemporal variations in seabird bycatch hotspots and implications for seabird bycatch mitigation

Bycatch in fisheries is a major threat to many seabird species. Understanding and predicting spatiotemporal changes in seabird bycatch from fisheries might be the key to mitigation. Inter-annual spatiotemporal patterns are evident in seabird bycatch of the U.S. Atlantic pelagic longline fishery monitored by the National Marine Fisheries Service Pelagic Observer Program (POP) since 1992. A newly developed fast computing Bayesian approximation method provided the opportunity to use POP data to understand spatiotemporal patterns, including temporal changes in location of seabird bycatch hotspots. A Bayesian model was developed to capture the inherent spatiotemporal structure in seabird bycatch and reduce the bias caused by physical barriers such as coastlines. The model was applied to the logbook data to estimate seabird bycatch for each longline set, and the mid-Atlantic bight and northeast coast were the fishing areas with the highest fleet bycatch estimate. Inter-annual changes in predicted bycatch hotspots were correlated with Gulf Stream meanders, suggesting that predictable patterns in Gulf Stream meanders could enable advanced planning of fishing fleet schedules and areas of operation. The greater the Gulf Stream North Wall index, the more northerly the seabird bycatch hotspot two years later. A simulation study suggested that switching fishing fleets from the hindcasted actual bycatch hotspot to neighboring areas and/or different periods could be an efficient strategy to decrease seabird bycatch while largely maintaining fishers’ benefit.

Evaluating Dropout Placements in Bayesian Regression Resnet

Deep Neural Networks (DNNs) have shown great success in many fields. Various network architectures have been developed for different applications. Regardless of the complexities of the networks, DNNs do not provide model uncertainty. Bayesian Neural Networks (BNNs), on the other hand, is able to make probabilistic inference. Among various types of BNNs, Dropout as a Bayesian Approximation converts a Neural Network (NN) to a BNN by adding a dropout layer after each weight layer in the NN. This technique provides a simple transformation from a NN to a BNN. However, for DNNs, adding a dropout layer to each weight layer would lead to a strong regularization due to the deep architecture. Previous researches [1, 2, 3] have shown that adding a dropout layer after each weight layer in a DNN is unnecessary. However, how to place dropout layers in a ResNet for regression tasks are less explored. In this work, we perform an empirical study on how different dropout placements would affect the performance of a Bayesian DNN. We use a regression model modified from ResNet as the DNN and place the dropout layers at different places in the regression ResNet. Our experimental results show that it is not necessary to add a dropout layer after every weight layer in the Regression ResNet to let it be able to make Bayesian Inference. Placing Dropout layers between the stacked blocks i.e. Dense+Identity+Identity blocks has the best performance in Predictive Interval Coverage Probability (PICP). Placing a dropout layer after each stacked block has the best performance in Root Mean Square Error (RMSE).

Inferring the basal sliding coefficient field for the Stokes ice sheet model under rheological uncertainty

We consider the problem of inferring the basal sliding coefficient field for an uncertain Stokes ice sheet forward model from synthetic surface velocity measurements. The uncertainty in the forward model stems from unknown (or uncertain) auxiliary parameters (e.g., rheology parameters). This inverse problem is posed within the Bayesian framework, which provides a systematic means of quantifying uncertainty in the solution. To account for the associated model uncertainty (error), we employ the Bayesian approximation error (BAE) approach to approximately premarginalize simultaneously over both the noise in measurements and uncertainty in the forward model. We also carry out approximative posterior uncertainty quantification based on a linearization of the parameter-to-observable map centered at the maximum a posteriori (MAP) basal sliding coefficient estimate, i.e., by taking the Laplace approximation. The MAP estimate is found by minimizing the negative log posterior using an inexact Newton conjugate gradient method. The gradient and Hessian actions to vectors are efficiently computed using adjoints. Sampling from the approximate covariance is made tractable by invoking a low-rank approximation of the data misfit component of the Hessian. We study the performance of the BAE approach in the context of three numerical examples in two and three dimensions. For each example, the basal sliding coefficient field is the parameter of primary interest which we seek to infer, and the rheology parameters (e.g., the flow rate factor or the Glen's flow law exponent coefficient field) represent so-called nuisance (secondary uncertain) parameters. Our results indicate that accounting for model uncertainty stemming from the presence of nuisance parameters is crucial. Namely our findings suggest that using nominal values for these parameters, as is often done in practice, without taking into account the resulting modeling error, can lead to overconfident and heavily biased results. We also show that the BAE approach can be used to account for the additional model uncertainty at no additional cost at the online stage.

Deep Data Assimilation: Integrating Deep Learning with Data Assimilation

In this paper, we propose Deep Data Assimilation (DDA), an integration of Data Assimilation (DA) with Machine Learning (ML). DA is the Bayesian approximation of the true state of some physical system at a given time by combining time-distributed observations with a dynamic model in an optimal way. We use a ML model in order to learn the assimilation process. In particular, a recurrent neural network, trained with the state of the dynamical system and the results of the DA process, is applied for this purpose. At each iteration, we learn a function that accumulates the misfit between the results of the forecasting model and the results of the DA. Subsequently, we compose this function with the dynamic model. This resulting composition is a dynamic model that includes the features of the DA process and that can be used for future prediction without the necessity of the DA. In fact, we prove that the DDA approach implies a reduction of the model error, which decreases at each iteration; this is achieved thanks to the use of DA in the training process. DDA is very useful in that cases when observations are not available for some time steps and DA cannot be applied to reduce the model error. The effectiveness of this method is validated by examples and a sensitivity study. In this paper, the DDA technology is applied to two different applications: the Double integral mass dot system and the Lorenz system. However, the algorithm and numerical methods that are proposed in this work can be applied to other physics problems that involve other equations and/or state variables.

Illustrative Discussion of MC-Dropout in General Dataset: Uncertainty Estimation in Bitcoin

The past few years have witnessed the resurgence of uncertainty estimation generally in neural networks. Providing uncertainty quantification besides the predictive probability is desirable to reflect the degree of belief in the model’s decision about a given input. Recently, Monte-Carlo dropout (MC-dropout) method has been introduced as a probabilistic approach based Bayesian approximation which is computationally efficient than Bayesian neural networks. MC-dropout has revealed promising results on image datasets regarding uncertainty quantification. However, this method has been subjected to criticism regarding the behaviour of MC-dropout and what type of uncertainty it actually captures. For this purpose, we aim to discuss the behaviour of MC-dropout on classification tasks using synthetic and real data. We empirically explain different cases of MC-dropout that reflects the relative merits of this method. Our main finding is that MC-dropout captures datapoints lying on the decision boundary between the opposed classes using synthetic data. On the other hand, we apply MC-dropout method on dataset derived from Bitcoin known as Elliptic data to highlight the outperformance of model with MC-dropout over standard model. A conclusion and possible future directions are proposed.

Assessing local fit by approximating probabilities

Validity evidence for factor structures underlying a set of items can come from how well a proposed model reconstructs, or fits, the observed relationships. Global model fit is limited in that some components of the proposed model fit better than other components. This limitation has lead to the recommendation of examining fit locally within model components. We describe a new probabilistic approach to assessing local fit using a Bayesian approximation and illustrate use with a simulated dataset. We show how the posterior approximation closely approximated the sampling distribution of the true parameter. We discuss potential limitations and possible generalizations.