scholarly journals A novel active learning-based Gaussian process metamodelling strategy for estimating the full probability distribution in forward UQ analysis

2020 ◽  
Vol 84 ◽  
pp. 101937
Author(s):  
Ziqi Wang ◽  
Marco Broccardo
2018 ◽  
Author(s):  
Andrey Chetverikov ◽  
Gianluca Campana ◽  
Arni Kristjansson

Our interactions with the visual world are guided by attention and visual working memory. Things that we look for and those we ignore are stored as templates that reflect our goals and the tasks at hand. The nature of such templates has been widely debated. A recent proposal is that these templates can be thought of as probabilistic representations of task-relevant features. Crucially, such probabilistic templates should accurately reflect feature probabilities in the environment. Here we ask whether observers can quickly form a correct internal model of a complex (bimodal) distribution of distractor features. We assessed observers’ representations by measuring the slowing of visual search when target features unexpectedly match a distractor template. Distractor stimuli were heterogeneous, randomly drawn on each trial from a bimodal probability distribution. Using two targets on each trial, we tested whether observers encode the full distribution, only one peak of it, or the average of the two peaks. Search was slower when the two targets corresponded to the two modes of a previous distractor distribution than when one target was at one of the modes and another between them or outside the distribution range. Furthermore, targets on the modes were reported later than targets between the modes that, in turn, were reported later than targets outside this range. This shows that observers use a correct internal model, representing both distribution modes using templates based on the full probability distribution rather than just one peak or simple summary statistics. The findings further confirm that performance in odd-one out search with repeated distractors cannot be described by a simple decision rule. Our findings indicate that probabilistic visual working memory templates guiding attention, dynamically adapt to task requirements, accurately reflecting the probabilistic nature of the input.


Entropy ◽  
2020 ◽  
Vol 22 (8) ◽  
pp. 890
Author(s):  
Sergey Oladyshkin ◽  
Farid Mohammadi ◽  
Ilja Kroeker ◽  
Wolfgang Nowak

Gaussian process emulators (GPE) are a machine learning approach that replicates computational demanding models using training runs of that model. Constructing such a surrogate is very challenging and, in the context of Bayesian inference, the training runs should be well invested. The current paper offers a fully Bayesian view on GPEs for Bayesian inference accompanied by Bayesian active learning (BAL). We introduce three BAL strategies that adaptively identify training sets for the GPE using information-theoretic arguments. The first strategy relies on Bayesian model evidence that indicates the GPE’s quality of matching the measurement data, the second strategy is based on relative entropy that indicates the relative information gain for the GPE, and the third is founded on information entropy that indicates the missing information in the GPE. We illustrate the performance of our three strategies using analytical- and carbon-dioxide benchmarks. The paper shows evidence of convergence against a reference solution and demonstrates quantification of post-calibration uncertainty by comparing the introduced three strategies. We conclude that Bayesian model evidence-based and relative entropy-based strategies outperform the entropy-based strategy because the latter can be misleading during the BAL. The relative entropy-based strategy demonstrates superior performance to the Bayesian model evidence-based strategy.


2015 ◽  
Vol 167 ◽  
pp. 122-131 ◽  
Author(s):  
Jin Zhou ◽  
Shiliang Sun

1986 ◽  
Vol 30 (02) ◽  
pp. 123-126
Author(s):  
A. E. Mansour

Introduction and background - The probability distribution of the peak process of a stationary random process with zero mean was first determined by Rice [1]. 2 Following his basic derivation, Longuet-Higgins [2] and Cartwright and Longuet-Higgins [3] evaluated various wave statistics, first for a narrow-band Gaussian process, then extended the results for a Gaussian process of any spectral width.


2019 ◽  
Vol 76 (2) ◽  
pp. 497-516 ◽  
Author(s):  
Gang Chen ◽  
Jesse Norris ◽  
J. David Neelin ◽  
Jian Lu ◽  
L. Ruby Leung ◽  
...  

Abstract Precipitation changes in a warming climate have been examined with a focus on either mean precipitation or precipitation extremes, but changes in the full probability distribution of precipitation have not been well studied. This paper develops a methodology for the quantile-conditional column moisture budget of the atmosphere for the full probability distribution of precipitation. Analysis is performed on idealized aquaplanet model simulations under 3-K uniform SST warming across different horizontal resolutions. Because the covariance of specific humidity and horizontal mass convergence is much reduced when conditioned onto a given precipitation percentile range, their conditional averages yield a clear separation between the moisture (thermodynamic) and circulation (dynamic) effects of vertical moisture transport on precipitation. The thermodynamic response to idealized climate warming can be understood as a generalized “wet get wetter” mechanism, in which the heaviest precipitation of the probability distribution is enhanced most from increased gross moisture stratification, at a rate controlled by the change in lower-tropospheric moisture rather than column moisture. The dynamic effect, in contrast, can be interpreted by shifts in large-scale atmospheric circulations such as the Hadley cell circulation or midlatitude storm tracks. Furthermore, horizontal moisture advection, albeit of secondary role, is important for regional precipitation change. Although similar mechanisms are at play for changes in both mean precipitation and precipitation extremes, the thermodynamic contributions of moisture transport to increases in high percentiles of precipitation tend to be more widespread across a wide range of latitudes than increases in the mean, especially in the subtropics.


2018 ◽  
Vol 149 (17) ◽  
pp. 174114 ◽  
Author(s):  
Elena Uteva ◽  
Richard S. Graham ◽  
Richard D. Wilkinson ◽  
Richard J. Wheatley

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