Editing Detection theory (section)

== Applications ==

Signal Detection Theory has wide application, both in humans and [[Comparative psychology|animals]].  Topics include [[memory]], stimulus characteristics of schedules of reinforcement, etc.

=== Sensitivity or discriminability ===

Conceptually, sensitivity refers to how hard or easy it is to detect that a target stimulus is present from background events. For example, in a recognition memory paradigm, having longer to study to-be-remembered words makes it easier to recognize previously seen or heard words. In contrast, having to remember 30 words rather than 5 makes the discrimination harder.  One of the most commonly used statistics for computing sensitivity is the so-called [[sensitivity index]] or ''d'''.  There are also [[non-parametric]] measures, such as the area under the [[Receiver operating characteristic|ROC-curve]].<ref name="Green&Swets"/>

=== Bias ===

Bias is the extent to which one response is more probable than another, averaging across stimulus-present and stimulus-absent cases. That is, a receiver may be more likely overall to respond that a stimulus is present or more likely overall to respond that a stimulus is not present. Bias is independent of sensitivity. Bias can be desirable if false alarms and misses lead to different costs. For example, if the stimulus is a bomber, then a miss (failing to detect the bomber) may be more costly than a false alarm (reporting a bomber when there is not one), making a liberal response bias desirable. In contrast, giving false alarms too often ([[The Boy Who Cried Wolf|crying wolf]]) may make people less likely to respond, a problem that can be reduced by a conservative response bias.

=== Compressed sensing ===
Another field which is closely related to signal detection theory is called '''''[[compressed sensing]]''''' (or compressive sensing). The objective of compressed sensing is to recover high dimensional but with low complexity entities from only a few measurements. Thus, one of the most important applications of compressed sensing is in the recovery of high dimensional signals which are known to be sparse (or nearly sparse) with only a few linear measurements. The number of measurements needed in the recovery of signals is by far smaller than what Nyquist sampling theorem requires provided that the signal is sparse, meaning that it only contains a few non-zero elements. There are different methods of signal recovery in compressed sensing including '''''[[basis pursuit]]''''', '''''expander recovery algorithm'''''<ref>{{cite journal |last1=Jafarpour |first1=Sina |last2=Xu |first2=Weiyu |last3=Hassibi |first3=Babak |last4=Calderbank |first4=Robert |title=Efficient and Robust Compressed Sensing Using Optimized Expander Graphs |journal=IEEE Transactions on Information Theory |date=September 2009 |volume=55 |issue=9 |pages=4299–4308 |doi=10.1109/tit.2009.2025528 |s2cid=15490427 |url=https://authors.library.caltech.edu/15653/1/Jafarpour2009p5830Ieee_T_Inform_Theory.pdf }}</ref>''''', CoSaMP'''''<ref>{{Cite journal|last1=Needell|first1=D.|last2=Tropp|first2=J.A.|title=CoSaMP: Iterative signal recovery from incomplete and inaccurate samples|journal=Applied and Computational Harmonic Analysis|volume=26|issue=3|pages=301–321|doi=10.1016/j.acha.2008.07.002|year=2009|arxiv=0803.2392|s2cid=1642637 }}</ref> and also '''''fast''''' '''''non-iterative algorithm'''''.<ref>Lotfi, M.; Vidyasagar, M."[[arxiv:1708.03608|A Fast Noniterative Algorithm for Compressive Sensing Using Binary Measurement Matrices]]".</ref> In all of the recovery methods mentioned above, choosing an appropriate measurement matrix using probabilistic constructions or deterministic constructions, is of great importance. In other words, measurement matrices must satisfy certain specific conditions such as '''''[[Restricted isometry property|RIP]]''''' (Restricted Isometry Property) or '''''[[Nullspace property|Null-Space property]]''''' in order to achieve robust sparse recovery.