Welcome back to the AI Bayeslab Statistics series.

Taking into account all the impactful themes, values, and constraints we discussed in the last three posts, let’s turn our focus back to the theory itself. As previously mentioned, noise permeates everything, and the primary goal of signal detection theory is to separate the signal from the noisy backdrop. So that we can separate the subjective response tendency from objective sensitivity.

1.The Signal and the Noise

The two key concepts of Signal Detection Theory are Signal and Noise.

Signal (S):

We see it as the information we want to convey to others.

Noise (N):

All distractions, interruptions, and similar factors may hinder the effective conveyance of information. Moreover, this issue can never be minimized and always exists within the system.

2.The Relationship Between Signal and Noise

Refer to the visualization below. Imagine we are sending a message, with the recipient being referred to as the subject. Due to the random factors influencing the intensity of both the signal and noise, neither Signal (S) nor Noise (N) can be received by the subjects; consequently, the response value will not be a unique value. Instead, two distributions arise based on “Sensation Intensity”: the signal plus noise (SN) distribution and the noise (N) distribution. The first is referred to as signal distribution.

The signal distribution (SN) consistently overlaps with the noise distribution. Consequently, the signal distribution (SN) typically produces a stronger psychological sensation than the noise distribution (N). The distance between the two distributions indicates the intensity of this psychological sensation from the signal.

3.Visualization for Signal Detection Theory

Below are three distinct representations of how signal and noise are distributed. The overlapping areas of the two curves imply that the same psychological experience could stem from either noise or a signal. This overlap reveals the subject’s sensitivity, or their capacity to distinguish between noise and signal. As previously indicated, random factors can affect the intensity of sensations from both signals and noise, which means a subject’s reaction to a signal may vary.

4.d’(D prime) vs the Report Criterion

However, when a subject makes a decision, they are guided by a presumed judgment criterion. If they assess the stimulus intensity surpassing that criterion, they categorize it as “SN” for a signal. Conversely, if it falls below that mark, it is labeled as “N” for a noise.

This decision-making criterion is shaped by factors like the prior probability of the signal and the potential consequences of the decision, influencing the subject’s response bias and subjective response tendency. A stricter criterion leads the subject to lean towards reporting “no”; conversely, a more lenient criterion encourages the subject to lean towards reporting “yes.” Referring to scenario two from the previous article, “Three scenarios to illustrate the core value of signal detection theory,” a stricter judgment criterion means the subject is more prone to report no sound. In contrast, a more lenient criterion increases the likelihood of reporting that a sound is heard.

In the visualization above, the blue curve illustrates noise, and the red curve depicts the signal. The three graphs show varying overlapping areas between the signal and noise distributions. From left to right, they represent S1 < S2 < S3. This indicates that distinguishing objective sensitivity between noise and signal is most difficult in S1, while S3 exhibits the least overlap, facilitating easier recognition of objective sensitivity.

With a grasp of the objective sensitivity and subjective judgment criteria discussed earlier, along with the visualization examples, we will present two independent metrics in the upcoming post to clarify the calculation formulas and the significance of the statistical values associated with various signals and noise.

Stay tuned, subscribe to Bayeslab, and let everyone master the wisdom of statistics at a low cost with AI Agent Online tool.

About Bayeslab

Bayeslab: Website

The AI First Data Workbench

X: @BayeslabAI

Documents: https://bayeslab.gitbook.io/docs

Blogs:https://bayeslab.ai/blog