View source for Strong and weak sampling

{{Orphan|date=January 2021}}

'''Strong and weak sampling''' are two sampling approach<ref>{{cite web |last1=Xu |first1=Fei |title=Bayesian word learning Sensitivity to sampling in Bayesian word learning |url=https://web.mit.edu/cocosci/Papers/devsci07_xu_tenenbaum.pdf |website=MIT |publisher=Developmental Science}}</ref> in Statistics, and are popular in computational cognitive science and language learning.<ref>{{cite web |last1=Hsu |first1=Anne |title=Sampling assumptions in language learning 1 Running head: SAMPLING ASSUMPTIONS IN LANGUAGE LEARNING Sampling assumptions affect use of indirect negative evidence in language learning |url=https://www.researchgate.net/figure/Two-different-sampling-assumptions-for-language-learning-a-Under-the-weak-sampling_fig11_267829053 |website=ResearchGate}}</ref> In strong sampling, it is assumed that the data are intentionally generated as positive examples of a concept,<ref>{{cite web |last1=Navarro |first1=Danielle |title=Lecture 20: Strong vs weak sampling |url=https://compcogsci-3016.djnavarro.net/lecture20.pdf |website=Computational Cognitive Science}}</ref> while in weak sampling, it is assumed that the data are generated without any restrictions.<ref>{{cite journal |last1=Navarro |first1=Daniel |title=Sampling assumptions in inductive generalization |journal=Cognitive Science |year=2012 |volume=36 |issue=2 |pages=187–223 |doi=10.1111/j.1551-6709.2011.01212.x |pmid=22141440 |url=https://pubmed.ncbi.nlm.nih.gov/22141440/|doi-access=free }}</ref>

==Formal Definition==
In '''strong sampling''', we assume observation is randomly sampled from the true hypothesis:

<math>P(x|h) = \begin{cases} \frac{1}{|h|} & \text{, if } x \in h \\ 0 & \text{, otherwise} \end{cases}</math>

In '''weak sampling''', we assume observations randomly sampled and then classified:

<math>P(x|h) = \begin{cases} 1 & \text{, if } x \in h \\ 0 & \text{, otherwise} \end{cases}</math>

==Consequence: Posterior computation under Weak Sampling==

<math>P(h|x) = \frac{P(x|h) P(h)}{\sum\limits_{h'} P(x|h') P(h')} = \begin{cases} \frac{P(h)}{\sum\limits_{h': x \in h'} P(h')} & \text{, if } x \in h \\ 0 & \text{, otherwise} \end{cases} </math>

Therefore the likelihood <math>P(x|h')</math> for all hypotheses <math>h'</math> will be "ignored".

==References==
{{reflist}}

==External links==
*[https://compcogsci-3016.djnavarro.net/lecture20.pdf Lecture 20: Strong vs weak sampling]

[[Category:Sampling (statistics)]]


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