# Detection theory
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## Microsims — p5.js
### Detection theory (p5.js) · `H₀ vs H₁`
<div class="microsim-player">
<iframe src="https://editor.p5js.org/sciencenibber/full/6Bp-_b4MG" width="100%" height="480" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Detection theory — p5.js microsim"></iframe>
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*Decide whether a signal is present in noise, trading missed detections against false alarms.*
**Open in the editor:** [▶ fork this sketch](https://editor.p5js.org/sciencenibber/sketches/6Bp-_b4MG) · movement *VI · Control theory & estimation* · library `p5js`
### Related microsims
Live sims on neighbouring articles — 6 of them inside this article's own Wikipedia link tree:
- [[Digital_image_processing]] *(in tree)*
- [[Digital_signal_processing]] *(in tree)*
- [[Discrete_cosine_transform]] *(in tree)*
- [[Discrete_time_and_continuous_time]] *(in tree)*
- [[Estimation_theory]] *(in tree)*
- [[Integral_transform]] *(in tree)*
*Sim hosted off-article; the article owns the reference, not the runtime (WIKI_RULES §10.4). Placed by `g08_place_microsims.py`.*
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## Links (Wikipedia order)
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> Signal Processing concept · part of the Signal Processing Portal · movement VI · !01 制御 seigyo.svg
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*Rendered from the live microsim (▶ motion).*
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## See it next
[](Estimation_theory)
*→ [[Estimation_theory|Estimation theory]]*
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Back to Signal Processing Portal · the room · Semiotic gateway
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## What it is
Detection theory is the statistical framework for deciding whether a signal is present in noisy observations, formalizing the trade-off between correctly detecting signals and raising false alarms.
## How it works / why it matters
An observation is modeled as arising from one of two hypotheses — noise alone, or signal-plus-noise — and a decision rule compares a test statistic against a threshold, accepting the signal when it is exceeded. Moving the threshold trades the probability of detection against the probability of false alarm, a relationship traced by the receiver operating characteristic (ROC) curve; the Neyman–Pearson lemma shows the likelihood ratio is the optimal statistic for a fixed false-alarm rate. Detection theory governs radar, digital communication receivers, medical diagnostics, and psychophysics.
## Signs & universals
Instantiates the semiotic universals: threshold · probability · signal.
## Related
The decision counterpart of parameter [[Estimation_theory]] within Statistical signal processing; both reason over a stochastic process. See [[Kalman_filter]].
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## From the Real GENERATIVE library
> Detection theory or signal detection theory is a means to measure the ability to differentiate between information-bearing patterns (called stimulus in living organisms, signal in machines) and random patterns that distract from the information (called noise, consisting of background stimuli and random activity of the detection machine and of the nervous sys ([Wikipedia](https://en.wikipedia.org/wiki/Detection_theory))
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*Built to the [[WT!P5_js_Microsim_Master_Class|p5.js Master Class]].*
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## Wikipedia : Wikitube
**Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Detection_theory) : [Wikitube](https://en.wikitube.io/wiki/Detection_theory)
## Previous hub tags
Tree parents: [[Decision_theory]] · [[Information_theory]].
Legacy hubs: none.
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*Sources: 1 legacy note. Minted wave 1, 2026-07-30 (v1.6 order).*