A Bayesian approach for convex combination of two Gumbel-Barnett copulas

2013 ◽  
Author(s):  
M. Fernández ◽  
V. A. González-López
Keyword(s):  
Bayesian Approach ◽  
Convex Combination

Verbal statistical learning: Prior knowledge impacts word identification but not metacognition

2020 ◽  
Author(s):  
Laetitia Zmuda ◽  
Charlotte Baey ◽  
Paolo Mairano ◽  
Anahita Basirat
Keyword(s):  
Task Performance ◽  
Prior Knowledge ◽  
Statistical Learning ◽  
Cognitive Processes ◽  
Bayesian Approach ◽  
Word Identification ◽  
Artificial Language ◽  
Artificial Languages ◽  
Transitional Probabilities ◽  
Fully Bayesian

It is well-known that individuals can identify novel words in a stream of an artificial language using statistical dependencies. While underlying computations are thought to be similar from one stream to another (e.g. transitional probabilities between syllables), performance are not similar. According to the “linguistic entrenchment” hypothesis, this would be due to the fact that individuals have some prior knowledge regarding co-occurrences of elements in speech which intervene during verbal statistical learning. The focus of previous studies was on task performance. The goal of the current study is to examine the extent to which prior knowledge impacts metacognition (i.e. ability to evaluate one’s own cognitive processes). Participants were exposed to two different artificial languages. Using a fully Bayesian approach, we estimated an unbiased measure of metacognitive efficiency and compared the two languages in terms of task performance and metacognition. While task performance was higher in one of the languages, the metacognitive efficiency was similar in both languages. In addition, a model assuming no correlation between the two languages better accounted for our results compared to a model where correlations were introduced. We discuss the implications of our findings regarding the computations which underlie the interaction between input and prior knowledge during verbal statistical learning.

A Class of Harmonic Starlike Functions defined by Multiplier Transformation

2020 ◽  
pp. 455-469
Author(s):  
Deepali Khurana ◽  
Raj Kumar ◽  
Sibel Yalcin
Keyword(s):  
Convex Combination ◽  
Univalent Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Harmonic Mappings ◽  
Distortion Bounds ◽  
Radius Of Convexity ◽  
Univalent Harmonic Mappings ◽  
Harmonic Starlike ◽  
Multiplier Transformation

We define two new subclasses, $HS(k, \lambda, b, \alpha)$ and \linebreak $\overline{HS}(k, \lambda, b, \alpha)$, of univalent harmonic mappings using multiplier transformation. We obtain a sufficient condition for harmonic univalent functions to be in $HS(k,\lambda,b,\alpha)$ and we prove that this condition is also necessary for the functions in the class $\overline{HS} (k,\lambda,b,\alpha)$. We also obtain extreme points, distortion bounds, convex combination, radius of convexity and Bernandi-Libera-Livingston integral for the functions in the class $\overline{HS}(k,\lambda,b,\alpha)$.

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