這周是期中考試，前面近兩個月所學有些遺忘，這邊記錄一下。
課程入口
module thinking
沒學過的可以去看一下，老師語速略快，一開始可能不適應，幸好有字幕。
Segregation / Peer Effects
通過不同的模型，而不是個人的情感來模擬(mimic)真實世界，會更準確。同時，也能將複雜的問題簡單化。
模型在時間變量的作用下，產出結果的規律分爲四大類：
* Equilibrium
* Cycle
* Random
* Complex
Schelling’s Segregation Model
基於紐約住宅區人口結構的分佈調查，有明顯的人種和收入的區塊劃分。這是自主選擇的結果。
建立了一個基於鄰居情況與自己匹配程度達不到x%是否決定搬家的模型，軟件自動模擬的結果是：
* x = 40, 最終整體統計在 79.5%
* x = 52, 最終整體統計在 93.8%
* x = 80, 最終軟件模擬無解，人們一直在搬家
結論是：Observed macrobehavior does not automatically imply biased micromotives!
Index of Dissimilarity:
吐槽：嘗試了LaTeX語句未正確顯示，這裏的markdown不支持數學公式？ 主要是判斷某一個區域混雜性的指標，0的話就是完全混雜，1是完全對立。
如下圖中，藍色是純富人區，每個block住10人，綠色爲混住，每個block 5窮5富，黃色都是窮人，每個block住10人，分別計算每個block的Ri，就行了。（計算方式見下面）
ID’= ½ { 6(1/45) + 6(1/9) + 12(1/15)} =
½{72/45} = ½ {1.60} = 0.8 for normalized metric
Ri = distortion metric i, |b/B – y/Y|
b=# blue in block, B=# blue total (150)
y=#yellow in block, Y=#yellow total (90)
Ni = number of blocks with Ri value
Peer Effect
簡單地說，就是從衆心理
Model: N individuals, Each with a Threshold
(Tj for person j), Rule: join if Tj others join
The Standing Ovation Model
簡言之，俺是有原則的
Builds off of Granovettor’s Model: people may optimize when they have time to think about it, but also may just follow simple rules when they don’t – as in a standing ovation.
Assumptions: (a) Peer Effect, (b) Information – assume other’s competence
Model:
* Threshold to Stand (T),
* Quality of show (Q),
* Signal (S = Q + E) where E = error (noise)
* Initial Rule: If S > T => Stand
* Subsequent Rule: Stand if > X% stand
Aggregation
引入一個game of life的遊戲，簡單的規則和行爲，最後生成的結果（環境）卻是複雜的。
正太分佈下的標準方差 = N*P(1-P)的平方根
\pm1 \delta = 68%, \pm2 \delta = 95%, \pm3 \delta = 99.75%.
所以，一般6個標準方差外的事情，就不要多慮了。
衆口難調的例子：
Each Person is RATIONAL but the Collective is IRRATIONAL. The consequence is that in social policy, voting, and group decisions their is opportunity to have strategic preferences to bias the ‘collective preferences’
Decision Models
決策過程建模
Multi-Criterion Decision Making：每項設置比重，看誰佔得多。
Spatial Choice Models：在一個範圍內的選擇，看和誰觀點近了，比如黨派之爭等
決策樹，列出每個分支的預期收益，找最大收益即可
信息價值計算：Value of Information Calculation Steps:
(1) Calculate value without the information
(2) Calculate value with the information(change tree, solve as if you knew the answer)
(3) Calculate the difference
第二步略微有點搞，就是信息100%確定的情況下，信息原本的發生概率轉換爲了你是否走信息所在決策分支的概率，這樣就生成了新的決策樹，得到不同的值。
對人進行建模
有一個很有意思的遊戲：
Race to the Bottom: Pick a number in [0,100]. The closest to 2/3 of the mean wins. What happens?
我的理解是，別自以爲屌，在社會上混，真實的最佳答案往往不是理論的最佳答案。
Behavioral Model: Observe people are not rational.
- Prospect Theory: （捨不得喫虧理論）People are risk averse over gains and risk loving over losses
- Hyperbolic Discounting: （雙鳥在林不如一鳥在手）Discount the same short period of time difference in the near future more than the same short period of time difference in the far future
- Status Quo Bias: （懶人） Donate organs: UK uses ‘check box to donate’ with 10% marking the box. Europe countries using ‘Not contribute organs’ have only 10% marking the box. Implies strong status quo bias.
- Base Rate Bias: （定錨）Ask year box made then ask what price. The first number influences the estimate of the second number.
Rational Model: Objective function (mathematical) to maximize. People OPTIMIZE the Objective function
Rule Based Model: e.g., Schelling, simple rule that is close to what people actually do.
- Fix Decision
- Fix Strategy: Divide evenly or Tit for Tat Moore Machine
Tit for Tat - change state if opponent switches
Grim Trigger – if defect go to mean and stay there
Decision vs Game:
* Decision: Objective depends only on own action
* Game: Objective depends on actions of others
Categorical and Linear Models
學過Machine Learning的話，這裏沒太多花頭，就是謹記，數據有限，眼界有限，有時會誤入局部最優陷阱 （local maximum trap）
Categorical
R-squared: % variation explained（分類靠譜指數）
1 - （合體後的delta - 各個分類delta之和）/ 合體後的delta
* R-squared near 1 model explains a lot，就是靠譜的意思
* R-squared near 0 model explains little，就是亂來的意思
* Data quality impacts a good model’s R-squared
Linear
Linear Model: Best linear fit to a data set. Offset from line is a measure of variation.
R-squared通過y軸平均值的水平線的均方差爲底，找匹配的
做個專業的看圖手
* R-Squared – how much of the data is explained,
* Observations – how many data points,
* Standard Error – How much variation in the data to begin with
* Linear Model – Intercept (sign and magnitude, SE and probability of sign error)
* Linear Model – Coefficients of independent variables (sign and magnitude, SE & probability of sign error)