Part 1: Measuring neurons and the brain¶

What do we learn from studying perception?¶

Basic science: explains how mental representations arise from the physical world.
Quantitative data: measures human abilities (normal range, age differences, impairments) with applications.
Neuroscience: shows how perception links neural processes with mental functions.
Broader understanding: perception underlies almost all behavior (action, emotion, thought).

Neurons and Neural Firing¶

Neuron structure: dendrites, soma, axon, terminals; many structural variations exist.![[Screenshot 2025-08-27 at 6.53.47 PM.png]]
Neural firing (spikes):
- Triggered by chemical stimulation at receptors (感觉器官).
- Positive ions enter, neuron reaches threshold, fires an action potential.
- Brief electrical signal travels down axon; ions pumped out to reset.
Information flow between neurons: Electrical signals produce chemical changes that allows them to cross the synapse (gap) between neurons, creating neural networks.![[Screenshot 2025-08-27 at 7.16.04 PM.png]]

How does neural firing signal perceptual information?¶

Neurons communicate information through action potentials (spikes).

Two types of information are conveyed (Two main coding strategies):

Total spike activity
- count of spikes within a time window.
- Stronger stimulus → more spikes, faster accumulation. ![[Screenshot 2025-08-27 at 7.23.44 PM.png]]
  - Top Graph (weak vs strong stimulus, spikes over time):
    - Weak stimulus → few spikes, spaced out.
    - Strong stimulus → many spikes, closely packed.
    - Shows stimulus strength is encoded in spike frequency.
  - Bottom Graph (summed spikes):
    - Y-axis: total spike number.
    - X-axis: time.
    - Strong stimulus curve rises steeply → more spikes accumulate faster.
    - Weak stimulus curve is shallower → fewer spikes over same period.
    - Interpretation: stimulus intensity is reflected in how quickly spike counts build up.
Precise spike timing
- Timing patterns of firing relative to input. Rate of firing over time.
- Example: auditory neurons fire in sync with sound wave frequency (“neural entrainment”).![[Screenshot 2025-08-27 at 7.39.51 PM.png]]
Spike count encodes intensity: more spikes = stronger stimulus.
Spike timing encodes rhythm/frequency: neurons lock onto temporal patterns, especially in auditory and touch systems.
Both mechanisms work together: intensity (how much) + timing (when) → richer encoding of perception.

Methods to Study Perception¶

Controlled behavior: accuracy, speed
- e.g., visual search → response time differences for target present vs absent
- It takes longer to find the target (red triangle) in conjunction search.
Natural observational measures: eye fixation, body/eye/face movements
Neural measures:
- Invasive: single neuron recordings
- Noninvasive: fMRI (BOLD signal), DTI (white matter tracts), EEG, fNIRS, MEG

Psychophysics: Linking Physical & Psychological¶

Vary physical stimulus, measure psychological response
Two types:
- Threshold (responses just at the limits of perception)
- Supra-threshold (responses to clearly perceivable events)

Measuring thresholds: absolute and difference¶

Fundamental Abilities Measured
- Detection threshold: is something there?
- Discrimination threshold: minimal detectable difference (JND)
- Binary choice: A vs A’ discrimination
- Identification: accuracy of identifying a stimulus

Thresholds¶

Absolute threshold: How much input do we need to tell something is happening?
Difference threshold (JND): How much of a diﬀerence do we need to tell one input from another?
Methods to measure absolute threshold:
- Method of Limits (ascending/descending series)
- Method of Adjustment (subject freely adjusts stimulus)
- Method of Constant Stimuli (fixed set, % detection across trials, fit function for threshold)
Methods to measure difference threshold:
- JND = “just noticeable difference”
- The Weber fraction = $\frac{JND value}{standard value}$
- Weber’s Law: JND is a constant fraction of baseline stimulus; smaller Weber fraction = greater sensitivity
- Applications: measure perceptual ability, effects of age/impairment, practical uses (hearing loss, interface design)

Supra-threshold Measures: Magnitude estimation¶

Focus on stimuli clearly detectable
Questions: How does perceived intensity scale with physical variation? Does scaling differ by dimension (brightness, weight, taste, etc.)?
Magnitude Estimation
- Subjects assign numbers proportional to perceived intensity (free scale, above threshold)
- Produces power functions:
  - Perceived magnitude = $$K \times Stimulus^{n}$$
  - n < 1: means that each increase in stimulus magnitude counts less - diminishing returns (e.g., brightness, loudness)
  - n > 1: means that each increase in stimulus magnitude counts more - increasing returns (e.g., shock, heaviness)![[Screenshot 2025-09-02 at 2.32.20 AM.png]]
- Different dimensions have characteristic exponents (e.g., brightness ≈ 0.5, heaviness ≈ 1.45, shock ≈ 3.5)
- Data normalization needed due to individual scaling differences
- Log-log transformation linearizes data, slope = exponent (n)

Binary Discrimination (Supra-threshold)¶

Different from threshold discrimination
Signal detection approach: measure accuracy distinguishing between two above-threshold stimuli
Vary stimulus differences to find % accuracy at target level (not 100%)
Applications of Psychophysics
- Provides core sensory metrics (e.g., Weber fractions)
- Assesses sensory function and decline (aging, disease)
- Tests human–computer interfaces and VR systems
- Goals: maximize detection/discrimination, ensure wide perceptual range

Signal Detection Basics¶

Signal detection theory measures how well people discriminate between two conditions (signal vs. noise).
On each trial, a signal or no-signal is presented, and the observer responds “signal” or “no signal.”
Four possible outcomes: Hit, Miss, False Alarm, Correct Rejection.

Outcomes and Measures¶

Outcomes can be expressed as proportions (% hit, % miss, % false alarm, % correct rejection).
Key measures:
- d′ (sensitivity): Distance between signal and noise distributions in SD units.
- Criterion (c or β): The threshold for deciding “signal.” ![[Screenshot 2025-09-02 at 10.06.18 AM.png]]

Theoretical Model¶

Internal responses to signal and noise are modeled as normal distributions.
Mean response is higher for signal than for noise.
Criterion determines boundary between “signal” and “no signal” judgments.
d′ increases → distributions separate more → better sensitivity.
Shifting criterion changes trade-off between hits and false alarms.

Visualizations¶

Probability curves illustrate how hits and false alarms depend on distributions and criterion. ![[Screenshot 2025-09-02 at 10.11.07 AM.png]]
Examples:
- High d′ → high hits.
- Liberal criterion → more hits but also more false alarms.
- Conservative criterion → fewer hits, fewer false alarms.
$d'= z_1 + z_2$

ROC Curves (Receiver Operating Characteristic)¶

Moving criterion shifts point along the curve.
Higher sensitivity (larger d′) shifts the ROC curve away from the diagonal.
Area under the curve (AUC) is another measure of sensitivity (A = 0.5 = chance, A close to 1 = high sensitivity).
ROC slope relates to β (criterion).
confidence???

Extensions to Machine Learning¶

ML classifiers also make binary decisions (e.g., cancer detection).
Similar measures apply:
- Precision: Hits / (Hits + False Alarms).
- Recall: Same as hit rate.
- Specificity: Correct rejection rate.
- Accuracy: Overall proportion correct.
Precision/Recall curves are especially useful when signals are rare.

Computation¶

d’ (sensitivity in terms of distance between curves) =NORMSINV(HIT_PROP)-NORMSINV(FA_PROP)
Beta (criterion expressed by ratio of height of curves) =EXP((NORMSINV(FA_PROP)^2)- NORMSINV(HIT_PROP)^2)/2)
C (criterion expressed by x axis position, relative to point where curves cross, ie c = 0 where beta = 1) =-(NORMSINV(HIT_PROP)+NORMSINV(FA_PROP))/2
A (area under ROC curve measure of sensitivity) =NORMSDIST(D_PRIME/SQRT(2))
Example worksheet shows calculations with given hit/false alarm rates.