Optimal matching and deterministic sampling

2021 ◽  
Author(s):  
Jeff Abrahamson
2016 ◽  
Vol 2 (1) ◽  
pp. 4-23
Author(s):  
Samuel D. Pimentel
Keyword(s):  

Author(s):  
Hongping Wu ◽  
Yi Yan ◽  
Danfeng Sun ◽  
Huifeng Wu ◽  
Peng Liu
Keyword(s):  

2020 ◽  
Vol 26 (1) ◽  
pp. 1-16
Author(s):  
Kevin Vanslette ◽  
Abdullatif Al Alsheikh ◽  
Kamal Youcef-Toumi

AbstractWe motive and calculate Newton–Cotes quadrature integration variance and compare it directly with Monte Carlo (MC) integration variance. We find an equivalence between deterministic quadrature sampling and random MC sampling by noting that MC random sampling is statistically indistinguishable from a method that uses deterministic sampling on a randomly shuffled (permuted) function. We use this statistical equivalence to regularize the form of permissible Bayesian quadrature integration priors such that they are guaranteed to be objectively comparable with MC. This leads to the proof that simple quadrature methods have expected variances that are less than or equal to their corresponding theoretical MC integration variances. Separately, using Bayesian probability theory, we find that the theoretical standard deviations of the unbiased errors of simple Newton–Cotes composite quadrature integrations improve over their worst case errors by an extra dimension independent factor {\propto N^{-\frac{1}{2}}}. This dimension independent factor is validated in our simulations.


2006 ◽  
Vol 8 (2) ◽  
pp. 229-233
Author(s):  
Su Jiancang ◽  
Sun Jian ◽  
Liu Guozhi ◽  
Liu Chunliang ◽  
Ding Zhenjie

2015 ◽  
Vol 46 (6) ◽  
pp. 785-810 ◽  
Author(s):  
Rachel M. McLaren ◽  
Andrew C. High

Although the supportive communication people receive from others during stressful times can be helpful, it can also result in negative outcomes. One explanation for these different effects might be how closely the support people receive matches their desires. This study extends optimal matching theory and examines how the discrepancy between the support people want and what they receive (called support gaps) corresponds with hurt feelings, perceived negative relational consequences, and esteem improvement. People can either receive less support than the desire (i.e., be under-benefited) or receive more support than they desire (i.e., be over-benefited), and these different types of support gaps produce distinct patterns of results. Specifically, action-facilitating support, which includes informational and tangible support, and nurturant support, which includes emotional, esteem, and network support, were studied. Results showed that being over-benefited in informational support and being under-benefited in emotional and esteem support is hurtful, and hurt corresponded with negative relational consequences and reduced esteem improvement. Implications for research on support gaps and hurt feelings are discussed.


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