Lec22.

• 正态分布
• 均匀分布
• 指数分布

Lec23.

**data enhancement:**extrapolate
Texas sharp shooter fallacy(神射手谬误)

股市模拟:

• efficient market hypothesis:有效性市场假说==>随机漫步模型
  • stock & market
  • adjusted for risk
  • distribution
  • multiplicative vs additive
  • memoryless(Poisson):无记忆性

Lec24.

think computationly

computational thinking:

• identify or invent useful abstractions
• formulate solution to a problem as a computational experiment
• design and construct a sufficiently implementation of experiment
• validate experimental setup
• run experment
• evaluate results of experiment
• repeat as needed

Abstraction:

• choosing the right abstractions
• operating in terms of multiple layers of abstractions simultaneously
• defining the relationships the between

Automation:

• think in terms of machineizing our abstractions
• Mechanization is possible

thinking recursively:

• Reformulating a seemingly difficult problem into one which we know how to solve
• Reduction,cmbedding,transformation,simulation

Take it a step at time:

• understand problem
• think about overall structure and algorithm independently of expression in programming language
• break into small parts
• identify useful abstractions
• code and unit test a part at a time
• first functionality, then efficiency
• start with pseudo code

By systematic:

• when debugging, think scientific method
• ask yourself why program did what it did, not why it didn’t do what you wanted it to do.

Lec19.

biased random walks:有偏好的随机运动 子类继承Drunk并且修改move的规则但是调用父类的move来实现移动.

polymorphism(多态性):继承的优势

在只能在两个相反的方向上走动的随机模拟时,结果不是像想的那样会在原点附近徘徊(其实和四方向同理),所以说在随机事件中,在一系列的随机之后是很难回到初始的状态的,因为当你向某一方向走动一次之后,你的起点就发生了变化,已经不再是原点而是你现在站的点位.

**图像化:**更好的看到结果并且可以对结果进行可视化的分析来判断结果的正确性

**模拟的优势:**生成一个有代表性的样本来进行测试,可以用来模拟真实的问题,但是又比穷举节省了更多的时间和性能.

• generate a simple of representation scenarios
• experimental devices
• description not prescriptive:optimization,描述性

Lec20.

分析问题的分歧:

• stochastic vs deterministic:确定性问题还是非确定性问题
• static vs dynamic:在动态的情况下时间变得很重要
• discrete vs continues:离散 vs 连续

蒙特卡洛:inferential statistics,推论统计(演绎),random smaple tonds to exhisit same properties as the population from which it is drawn:可以从一些简单的样本看到事物中的共同的地方(共性).

Lec21.

如何选择一个合理的样本对于实验很重要.我们需要知道在选择的样本上进行的实验是否能够很好的模拟问题.
一个答案是统计可靠的并不代表是正确的答案.==>检查答案和物理现实是不是符合

• data
• models that explain data
• consequence of models

直线拟合:

• objective function:目标函数
• least squares fit:最小二乘法

Liner regression:线性回归

• 评估一个拟合:R2
• 并不是越高次的多项式永远是拟合更好的.(过拟合?)
• closer != better:我们不需要一个模型解释已经测量的数据都出现在哪里,而是需要模型有更好的预测能力,能够更好的解释未知的数据.

Lec16.

Class:

• template for data type
• cluster data & method
• modularity/abstraction
• data hiding:only acess the parts though a method
• class used to make instances

Encapsulation:(封装)

• data hide
• inheritance:继承
• shadow/override methods
• hierarchy of classes

Lec17.&Lec18.

• Informal problem description to a formal problem statement:把一个非正式的问题转化到一个更加通用的模型上来
• Inventing computational models:创造计算模型
• dealing with & exploiting randomness:探索随机性
• making sense of data:让数据变得有意义,如何理解数据
• evaluating quality of answers:如何来判断和分析程序给出的答案是不是我们所想要的答案

随机走动:

• simolate(模拟) random walk(无规则运动)
• 数据抽象
  • Location
  • compass Pt
  • Field
  • Drunk
• pseudo random(伪随机)

课程使用的代码:

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import mathimport randomimport pylab

class Location(object):    
    def __init__(self, x, y):        
        self.x = float(x)        
        self.y = float(y)    
    
    def move(self, xc, yc):        
        return Location(self.x + float(xc), self.y+float(yc))    
    
    def getCoords(self):        
        return self.x, self.y    
    
    def getDist(self, other):        
        ox, oy = other.getCoords()        
        xDist = self.x - ox        
        yDist = self.y - oy        
        return math.sqrt(xDist**2 + yDist ** 2)


class CompassPt(object):    
    possibles = ('N', 'S', 'E', 'W')    
    def __init__(self, pt):        
        if pt in self.possibles:            
            self.pt = pt        
        else:            
            raise ValueError('in CompassPt.__init__')    
    
    def move(self, dist):        
        if self.pt == 'N':            
            return (0, dist)        
        elif self.pt == 'S':            
            return (0, -dist)        
        elif self.pt == 'E':            
            return (dist, 0)        
        elif self.pt == 'W':            
            return (-dist, 0)        
        else:            
            raise ValueError('in compassPt.move')


class Field(object):    
    def __init__(self, drunk, loc):        
        self.drunk = drunk        
        self.loc = loc    
        
    def move(self, cp, dist):        
        oldLoc = self.loc        
        xc, yc = cp.move(dist)        
        self.loc = oldLoc.move(xc, yc)    
    
    def getLoc(self):        
        return self.loc    
    
    def getDrunk(self):        
        return self.drunk


class Drunk(object):    
    def __init__(self, name):        
        self.name = name    
    
    def move(self, field, time=1):        
        if field.getDrunk() != self:            
            raise ValueError('Drunk.move called with drunk not in field')        
        for i in range(time):            
            pt = CompassPt(random.choice(CompassPt.possibles))            
            field.move(pt, 1)
    
def performTrial(time, f):    
    start = f.getLoc()    
    distances = [0.0]    
    for t in range(1, time+1):        
        f.getDrunk().move(f)        
        newLoc = f.getLoc()        
        distance = newLoc.getDist(start)        
        distances.append(distance)    
    return distances

# assert False
drunk = Drunk('a man')
for i in range(3):    
    f = Field(drunk, Location(0, 0))    
    distances = performTrial(500, f)    
    pylab.plot(distances)
pylab.title('random walk')
pylab.xlabel('time')
pylab.ylabel('distance from origin')

pylab.show()

assert False

perform trial 的解释:

1. inner loop that simolates 1 trial
2. ‘enclose’ inner loop in a loop that conducts appropriate of trials
3. calculate and present statics

随机运动的应用:

• Browning motion:布朗运动
• stock market:预测股票
• kinetics
• evolution