Propagating Non-normally Distributed Uncertainty - The Ljungskile Code

Author(s):  
A. Ödegaard-Jensen ◽  
G. Meinrath ◽  
Ch. Ekberg
Keyword(s):  
1968 ◽  
Vol 78 (2, Pt.1) ◽  
pp. 269-275 ◽  
Author(s):  
Wesley M. DuCharme ◽  
Cameron R. Peterson
Keyword(s):  

1972 ◽  
Vol 28 (03) ◽  
pp. 447-456 ◽  
Author(s):  
E. A Murphy ◽  
M. E Francis ◽  
J. F Mustard

SummaryThe characteristics of experimental error in measurement of platelet radioactivity have been explored by blind replicate determinations on specimens taken on several days on each of three Walker hounds.Analysis suggests that it is not unreasonable to suppose that error for each sample is normally distributed ; and while there is evidence that the variance is heterogeneous, no systematic relationship has been discovered between the mean and the standard deviation of the determinations on individual samples. Thus, since it would be impracticable for investigators to do replicate determinations as a routine, no improvement over simple unweighted least squares estimation on untransformed data suggests itself.


Sensors ◽  
2021 ◽  
Vol 21 (5) ◽  
pp. 1792
Author(s):  
Juan Hagad ◽  
Tsukasa Kimura ◽  
Ken-ichi Fukui ◽  
Masayuki Numao

Two of the biggest challenges in building models for detecting emotions from electroencephalography (EEG) devices are the relatively small amount of labeled samples and the strong variability of signal feature distributions between different subjects. In this study, we propose a context-generalized model that tackles the data constraints and subject variability simultaneously using a deep neural network architecture optimized for normally distributed subject-independent feature embeddings. Variational autoencoders (VAEs) at the input level allow the lower feature layers of the model to be trained on both labeled and unlabeled samples, maximizing the use of the limited data resources. Meanwhile, variational regularization encourages the model to learn Gaussian-distributed feature embeddings, resulting in robustness to small dataset imbalances. Subject-adversarial regularization applied to the bi-lateral features further enforces subject-independence on the final feature embedding used for emotion classification. The results from subject-independent performance experiments on the SEED and DEAP EEG-emotion datasets show that our model generalizes better across subjects than other state-of-the-art feature embeddings when paired with deep learning classifiers. Furthermore, qualitative analysis of the embedding space reveals that our proposed subject-invariant bi-lateral variational domain adversarial neural network (BiVDANN) architecture may improve the subject-independent performance by discovering normally distributed features.


1987 ◽  
Vol 23 (1) ◽  
pp. 70-75
Author(s):  
Yu. M. Kolyano ◽  
I. I. Bernar

Motor Control ◽  
2015 ◽  
Vol 19 (4) ◽  
pp. 253-270 ◽  
Author(s):  
Asger Roer Pedersen ◽  
Peter William Stubbs ◽  
Jørgen Feldbæk Nielsen

The aim was to investigate trial-by-trial response characteristics in the short-latency stretch reflex (SSR). Fourteen dorsiflexion stretches were applied to the ankle joint with a precontracted soleus muscle on 2 days. The magnitude and variability of trial-by-trial responses of the SSR were assessed. The SSR was log-normally distributed and variance heterogeneous between subjects. For some subjects, the magnitude and variance differed between days and stretches. As velocity increased, variance heterogeneity tended to decrease and response magnitude increased. The current study demonstrates the need to assess trial-by-trial response characteristics and not averaged curves. Moreover, it provides an analysis of SSR characteristics accounting for log-normally distributed and variance heterogeneous trial-by-trial responses.


AIChE Journal ◽  
2013 ◽  
Vol 59 (7) ◽  
pp. 2471-2484 ◽  
Author(s):  
Gennady M. Ostrovsky ◽  
Nadir N. Ziyatdinov ◽  
Tatiana V. Lapteva

1978 ◽  
Vol 15 (3) ◽  
pp. 645-649 ◽  
Author(s):  
Svante Janson

This paper gives an elementary proof that, under some general assumptions, the number of parts a convex set in Rd is divided into by a set of independent identically distributed hyperplanes is asymptotically normally distributed. An example is given where the distribution of hyperplanes is ‘too singular' to satisfy the assumptions, and where a different limiting distribution appears.


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