## Stats

**Authors@Google: Nate Silver **

http://www.youtube.com/watch?v=mYIgSq-ZWE0&feature=em-uploademail

**Probablistic Programming & Bayesian Methods for Hackers**

http://camdavidsonpilon.github.io/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/

## Model Thinking Part 2 – Coarsera

**Model thinking – Scoot E. Page – U. of Michigan
**

**Modeling People**

3 types of models: rational actor, behavioral, and rule based

- Rational Actor: maximize some function, object, optimized
- Behavior: observe what people do, neuroscience supports this view
- Rule base _ e.g. Schelling model, people follow rule(s)

Rational Actor

- An objective
- Optimize the objective

Value is to establish benchmark to be used because: (also can determine how far people from rational choice)

- Objective decision – reduced bias
- Easy to mathematically solve for
- People learn by repeating, hence closer to good result
- Mistakes cancel out, eliminating bias

**Behavior Model**

Daniel Kahnemen says people have slow process (rational) and fast process (emotional) thinking

Bias examples

- Prospect theory – bird in hard worth two in the bush
- Hyperbolic – take immediate reward and discount future pain
- Status Quo — stick with current situation
- Bias Rate — first rate estimate will have a second rate estimate be make similar

Some people say above biases are WEIRD — essentially only happens in developed countries

Approach to take in modeling: look at rational then introduce bias, then look at potential rules.

**Rule Based**

Follow a rule(s), e.g. Schelling. Rules can be easy to understand, capture main effort, can be ad hoc, can be exploitable, may note be optimal

Two types in two contexts which are Decision and Game

Fixed — might be random, tit for tat, grime trigger

Adaptive — in Decision context might be gradient (take something that works and extend), in Decision might be Best Response, mimicry (copy other’s that work)

**Impact of 3 models**

- Market — type of model does not matter much since market forces drive towards a mean. Zero Intelligence Agent will bid randomly lower (if buyer) and randomly higher (if seller) and than average to actual cleared price.
- Race to Bottom (game) — type of model can matter as follows — (1) Rational bid would b zero since rational person would always assume some number and quote a number 2/3’s from the mean (goal of the game). He would continue to iterate this quoted number down since he would assume that everyone is rational and hence will be eventually iterating down to. (2) Biased (behavior model) would probably just pick 50. (3) Rule (best response) – will guess 50, some will then take 2/3 of 50 (33), then some will take 2/3 of 33 (22), then over the long run, down to zero — rule is a mix of rational and biased. If all people in game are rational, then new irrational person enters game, will cause rational people to be influence by what the rational person perceives the irrational person will do.

**Categorical and Linear Models**

- Categorical Models — group sample and analyze sub-groups to see how well the grouping covers (reduces variance) the data — see r_squared.py for detailed explanation. R-Squared indicates how much of the data variance was explained by the model — Correlation indicates a relationship between variables, BUT Causation means that one variable is actually dependent an another — Or X (independent) entails Y (dependent) check this last statement

- Linear mode – draw a line through the data — Y depends on X, Y = F(X), Y is a function of X
- Non-linear model – curve, some similarities to linear model
- Big Coefficient – shows how important X is in Y = a1 x1 + a2 x2 — useing Big Coefficient as a guide only makes sense in world where there is lots of data

## Model Thinking Part 1- Coarsera

**Model thinking – Scoot E. Page – U. of Michigan**

**Reasons to Model**

- Predict points
- Understand data
- Understand patterns — class of outcome
- Design solutions

**Shelling Segregation Model**

- Sorting (be with people you like) and peer influence (homophily) (act like people you are with) on behavior
- model is agent based, consisting of agent, behavior, and aggregation
- Shelling threshold based — tipping (move tipping: exodus tip (move out), genesis (move in)
- micro behavior is not the same as macro aggregation, hence people individually may be tolerant (micro) but resulting population movement (macro may produce segregation.

**Granovettor’s Model**

Model is N individuals, Each N has a threshold: T (j) for person j, join if T (j) other join e.g.: 0,1,2,3,4 — all will join since 0 for sure joins

This tells us that lower thresholds and more variation in thresholds can have large effects.

**Standing Ovation Model**

extension to** Granovettor’s Model**

partially caused by peer effect (homophily) and information

Model rules:

- Threshold to stand: T
- Quality: Q
- Signal S=Q+E (error of diversity)
- Initial Rule: S > TG; Subsequent rule standup if more X% (E) stand up

Why standing ovation:

- higher quality
- lower threshold\larger peer effect
- more variation (E)
- Celebrity
- group size

This model (and others) is a way to determining results in situations.

Note that deciding if a sorting effect or peer effect from a snap shoot of state is difficult to determine, hence additional dynamic data to see what was major cause — hence more dynamic data meed in model to explain what movement (sorting) or neighbor influence (peer) caused change.

**Aggregation**

Philip Anderson – “More is Different” – emergent properties at macro level

Aggregation of data

Independent decisions

Central Limit Theorem

Assumes independent events and finite (limited range) variance

Probability is a normal (Gaussian) distribution (looks like a bell curve) with likely outcome at the mean

plus/minus 1 Standard deviation (sigma) cover 68% in a normal curve; plus/minus 2 standard deviations cover 95%; plus/minus 3 standard deviations cover 99.75% of possible outcomes

Binomial Theorem example if N/2 is the mean, then SD is (square root of N / 2), so N = 100 = 100/ 2 = 50, SD is 10/2 (sq root of 100) / 2) = 5

6Sigma = 3.4 errors out of 1,000,000 events

Cellular Automaton– self organization, emergence — some level of functionality such as glider; get logic right

Game of Life — Rules: If off, turn on if 3 neighbors on; if on, stay on if 2 or 3 neighbors on

**Preferences**

Transitive Preference order, rational preferences, collective preferences – social sense this is called rational

all individual are rational but the aggregate can be non-transitive — this is called *Condorcet’s paradox*

**Decision Making**

For multidimensional decision making:

- Qualitative – use matrix
- Quantitative – use matrix plus weights

For Spatial Chose models: select ideal point (single or multidimensional) for a good, then determine values for each decision point possibility , than a see difference from ideal point and add up the differences. The difference between the ideal points and the computed points determines which is the closest decision point possibility. Come back to this and clarify.

**Probability**

- outcome is a set of things that can happen
- event is a subset of outcomes.

3 axions

- probability of an event is between 0 and 1 — could also be 0 or 1
- Sum of all possible outcomes = 1
- If A is subset of B, then p(A) is less than or equal to p(B) or p(B) is greater than or equal to p(A)

3 types of statistics:

- Classical (e.g., dice and coin flips — can prove mathematically
- Frequency (estimating frequency by counting data – how often has something happend? – assumes stationarity (nothing has changed),
- Subjective (estimate but base on model)