4.1 Signal and Noise

The challenges of finding the information we want amidst messy data.

Useful Links

• Guess the Message Game Handout
• Three Column Overview of the Week
• Lesson Slides (2023 Master)
• Website Page

Learning Goals

After this lesson, students should

1. Be able to explain what scientists mean by "signal," "noise," and "signal-to-noise ratio."
2. Be able to identify examples of "signal" and "noise," recognizing that these examples are context-dependent.
3. Be able to roughly compare measurement techniques in terms of their resultant signal-to-noise ratios.
4. Be able to describe examples of techniques and tools to suppress noise and/or amplify signal.

Definitions

• Signal

  Aspects of observations or stimuli that provide useful information about the target of interest, as opposed to noise.

• Noise

  The aspects of observations that get confused with signal but do not provide the same useful information about the target of interest. Noise is frequently, but not always, the result of random measurement fluctuations.

• Signal-to-noise Ratio

  The relative strength of signal compared to the relative strength of noise in a given context. Obtaining meaningful information from the world requires distinguishing signal from noise. Therefore, human cognition (both scientific and otherwise) relies on techniques and tools to suppress noise and/or amplify signal (i.e., increase signal-to-noise ratio). It is possible to design filters to increase the signal-to-noise ratio, if you know where the noise is going to appear.

Examples

• As a member of the Bajau people of Southeast Asia, you are diving to collect shellfish for food. While the shellfish themselves are the signal, there are several sources of noise: rocks and other creatures resembling shellfish, waving sunlight patterns on the seafloor. The signal-to-noise ratio may be low if the water is murky (higher noise), the shellfish are camouflaged (lower signal), or if the light is dim (lower signal). BBC article
• Detecting fish jumps (signal) on a lake on a day when the wind is causing waves (noise). Some splashing waves may be misidentified as fish jumps.
• Getting the words of a radio personality through static.
• Hearing your conversational partner at a party where lots of conversations are happening.
• Figuring out if there's a meaningful difference between the control condition and experimental condition in an RCT. Random fluctuations in the chosen experimental sample may cause a spurious difference between the two groups; this is a source of noise.
• Finding the facts on a topic where there's a lot of disinformation floating around.
• Saul's story of an exoplanet around a pulsar, when it was not really there.
• Palette cleansing with water or crackers between tasting different wines. The subtle differences between wines are the signal, while lingering flavours and scents from the previous wine are the noise.
• Covid symptom screening, where the signal is the actual Covid infection, and the noise is all the other illnesses/allergies/etc causing similar symptoms.
• Smoke detectors detect the presence of smoke from a fire (signal) by measuring the opacity of air. Steam is a possible source of noise.

Context

We introduce the concept of signal and noise in "detection problems" and teach students how to identify the signal and various sources of noise in diverse scenarios. This foreshadows the ethical considerations in deciding how strong a signal must be to be counted as a "positive" (5.1 False Positives and Negatives).

Before

2.2 Systematic and Statistical Uncertainty

Both systematic and statistical uncertainties introduce noise to every measurement.

3.1 Probabilistic Reasoning

The presence of noise, which sometimes disguises as a signal, is inevitable in any measurement. The identification of a signal always comes with a roughly quantifiable level of confidence.

After

4.2 Finding Patterns in Random Noise

In addition to the signal-to-noise ratio, there are other statistical tools (e.g. p-value) to quantify the strength of the signal amidst all the noise.

5.1 False Positives and Negatives

"Positive" and "negative" refer to whether we identify what we detect as a signal or not. The decision of any "threshold" of strength for a signal to be counted as positive inevitably involves human values judgment in a trade-off between the rates of false positives and false negatives.

5.2 Scientific Optimism

Some signals in nature seem hopelessly too weak to detect, such as the tiny fluctuations in the distance between two mirrors as a result of the gravitational waves from faraway black holes, but scientists spend decades to develop new instruments to increase the strength of the signal, as well as new analysis techniques to filter out the noise.

6.1 Correlation and Causation

The detection of a "statistically significant" difference between conditions in an RCT is the identification of a signal. The random variations that exist between experimental subjects are a source of noise.

Recommended Outline

Before Class

• Review PlayPosit and discussion questions and ask faculty, Gabriel, or Emlen any questions you have.
• Print the handouts for Guess the Message Game.

During Class

• (5 min) Come up with some fun way to assign the roles of spokesperson and notetaker (e.g. earliest birthday in the year, lives furthest from campus). Remind them of the responsibilities of these roles.
• (5 min) Opening clicker question.
• (20 min) Go through several scenarios in the scenario analysis activity.
• (30 min) Play the guess the message game.
• (5 min) Teach a little about signal-to-noise ratio.
• (5 min) Collect questions for plenary.

After Class

• [Any essential logistical things that need to be done as followup for this class]
• Collect answers from notetakers for the forum / plenary.

Lesson Content

Warmup Poll

1. How can we definitely tell if a single stimulus is signal or noise?
   1. By improving the sensitivity of the instrument.
   2. The stimulus is definitely a signal if it is stronger than most of the previous stimuli.
   3. It is impossible to tell for sure if a single stimulus is a signal or noise.
2. Any single supposed signal might be a rare (or not-so-rare) spike in noise.

Scenario Analysis

For each of the following scenarios, answer the following questions about signal and noise.

1. What is the sense/instrument that you are using?
2. What does the sense/instrument actually measure?
3. What is the signal from the sense/instrument you are expecting?
4. What sources of noise do you anticipate in this measurement? List two or more if you can.
5. (Optional) How would you reduce these sources of noise?

Example: Bajau Divers

Members of the Bajau people of Southeast Asia collecting shellfish for food.

1. What is the sense/instrument that you are using?
2. What does the sense/instrument actually measure?
3. What is the signal from the sense/instrument you are expecting?
4. What sources of noise do you anticipate in this measurement? List two or more if you can.
5. (Optional) How would you reduce these sources of noise?

Scenarios

• Catching gossip about you from across the room at a party. What about understanding what the person you're talking to is saying?
• Detecting a metal knife in the luggage of someone boarding an airplane.
• Detecting an ongoing earthquake in Berkeley.
• Determining if your arch nemesis put cyanide in your almond milk.
• Determining whether there are birds around you on your weekly birding expedition, then determining whether owls are in the mix.
• Is that a creepy crawly on your neck right now?
• Identifying a budding new wave of COVID in the US. (Suppose you're a health official provided with daily updates of the following data from hospitals across the country: rates of people coming into the ER with fever, coughs, broken bones, wounds, diarrhea, and cardiac arrest...)

Signal and Noise Game

In this game the students will write a message and corrupt it to varying degrees. Each student will have a partner with whom they shared the corrupted messages. Each student will try and decode the messages from the other student from most to least corrupted. Full instructions are available here.

Instructions

1. Hand out the students a copy of the worksheet. It has the full instructions in it.
2. (2 min) Explain the game as per the instructions linked above. Make sure the students know not to share their uncorrupted messages with each other until the game is complete.
3. (10 min) Have students pair up and play the game.
4. (3 min) Ask the discussion questions below.

Discussion Questions

1. What was the highest corruption level at which you could understand the message?
2. What are the factors affecting the signal-to-noise ratio?

Takeaway

• The ratio of signal to noise determines how easy it is to distinguish between true signal and the noise that "pretends" to be signal.
• We could have a poor ratio because the signal is very low or because the noise is very high.
• Example: Why is it hard to have a conversation at a cocktail party?
  • Signal: Increase the sound of your voice.
  • Noise: Go outside to get away from the background conversations.

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4.2 Finding Patterns in Random Noise