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心理·认知
12
engines
信号检测论 · d′、判断标准、ROC
Signal detection theory · d′, criterion, ROC
噪声/信号分布 · d'=z(H)−z(FA) · 判断标准 + ROC
Two overlapping Gaussians · move the criterion, read hits & false alarms, trace the ROC
韦伯–费希纳定律 · 最小可觉差与感觉量
Weber–Fechner law · JND and sensation
JND ΔI=k·I · 感觉 S=k·ln(I/I0) · 韦伯比
Constant Weber fraction gives a linear JND · integrating it gives a logarithmic sensation scale
希克定律 · 选择反应时
Hick's law · choice reaction time
RT=a+b·log2(n+1) · 选择反应时 · 信息量
RT = a + b·log₂(n+1): each extra bit of choice-uncertainty adds a fixed slice of time
经典条件反射 · Rescorla-Wagner 模型
Classical conditioning · Rescorla-Wagner
Rescorla-Wagner ΔV=αβ(λ−V) · 习得/消退 · 阻断
Associative strength grows by the prediction error λ − V · acquisition, extinction, blocking
操作性条件反射 · 强化程式
Operant conditioning · schedules of reinforcement
FR/VR/FI/VI · 累积记录 · 反应率
FR / VR / FI / VI cumulative records · reinforcement ticks · response-rate comparison
练习的幂律 · 学习曲线
Power law of practice · learning curve
T=a·N^−b · 学习曲线 · log-log 直线
T = T∞ + a·N^(−b): rapid early gains, diminishing returns · straight on log-log
艾宾浩斯遗忘曲线 · 间隔重复
Ebbinghaus forgetting curve · spaced repetition
R=e^(−t/S) · 间隔重复 · 记忆保持
R(t) = e^(−t/S); each review boosts strength S, flattening the curve
漂移扩散模型 · 决策反应时
Drift-diffusion model · decision reaction time
证据累积→边界 · 反应时分布 · 速度-准确性
Noisy evidence accumulates to a boundary; first passage = choice + RT
前景理论 · 价值函数与损失厌恶
Prospect theory · value function & loss aversion
价值函数 S 形 · 损失厌恶 λ · 参照点
v(x)=x^α for gains, −λ(−x)^β for losses, measured from a reference point
感知机 · 线性分类器
Perceptron · linear classifier
w←w+η(t−y)x · 决策边界 · 收敛
The learning rule rotates the decision boundary until the two classes are separated
标准分与正态曲线
Standard scores & the normal curve
z=(x−100)/15 · 百分位 Φ(z) · 68-95-99.7
Convert a raw IQ score to z-score, percentile rank and T-score on N(100, 15²)
语义网络 · 激活扩散
Semantic network · spreading activation
概念节点 + 联结 · 激活扩散 · 启动效应
Activate one concept; activation spreads to associated concepts, decaying with distance