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<<TableOfContents>> == A Random Walk == by William Stein {{{#!sagecell html('<h1>A Random Walk</h1>') vv = []; nn = 0 @interact def foo(pts = checkbox(True, "Show points"), refresh = checkbox(False, "New random walk every time"), steps = (50,(10..500))): # We cache the walk in the global variable vv, so that # checking or unchecking the points checkbox doesn't change # the random walk. html("<h2>%s steps</h2>"%steps) global vv if refresh or len(vv) == 0: s = 0; v = [(0,0)] for i in range(steps): s += random() - 0.5 v.append((i, s)) vv = v elif len(vv) != steps: # Add or subtract some points s = vv[-1][1]; j = len(vv) for i in range(steps - len(vv)): s += random() - 0.5 vv.append((i+j,s)) v = vv[:steps] else: v = vv L = line(v, rgbcolor='#4a8de2') if pts: L += points(v, pointsize=10, rgbcolor='red') show(L, xmin=0, figsize=[8,3]) }}} {{attachment:randomwalk.png}} == 3D Random Walk == {{{#!sagecell @interact def rwalk3d(n=(50,1000), frame=True): pnt = [0,0,0] v = [copy(pnt)] for i in range(n): pnt[0] += random()-0.5 pnt[1] += random()-0.5 pnt[2] += random()-0.5 v.append(copy(pnt)) show(line3d(v,color='black'),aspect_ratio=[1,1,1],frame=frame) }}} {{attachment:randomwalk3d.png}} == Hidden Markov Model: The Occasionally Dishonest Casino == by Marshall Hampton Based on the classic example in "Biological Sequence Analysis" by Durbin et al. To get the dice picture you need to download this [[http://wiki.sagemath.org/interact/stats?action=AttachFile&do=get&target=dishonest_casino.sws|dishonest_casino.sws]] {{{#!sagecell m = hmm.DiscreteHiddenMarkovModel([[0.8,0.2],[0.1,0.9]], [[1/10,1/10,1/10,1/10,1/10,1/2],[1/6,1/6,1/6,1/6,1/6,1/6]], [.2,.8],emission_symbols=[1,2,3,4,5,6]) @interact def dishonest_casino(auto_update=False): test = list(m.generate_sequence(80)) a = os.system('cp '+DATA+'dice_sm.png ./dice.png') vit_test = list(m.viterbi(test[0])[0]) html('<h3>The Occasionally Dishonest Casino</h3>') html('<img src="'+DATA+'dice_sm.png">') html('Emissions:'+str(test[0]).replace(',','').replace(' ','')[1:-1]) vit_str = str(vit_test).replace(',','').replace(' ','') vit_str = vit_str.replace('1','F').replace('0','<font color="#FF0000">L</font>')[1:-1] html('Viterbi: '+vit_str) actual_str = str(list(test[1])).replace(',','').replace(' ','') actual_str = actual_str.replace('1','F').replace('0','<font color="#FF0000">L</font>')[1:-1] html('Actual: '+ actual_str) }}} {{attachment:hmm_casino.png}} |
Sage Interactions - Statistics and Probability
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Contents
A Random Walk
by William Stein
3D Random Walk
Hidden Markov Model: The Occasionally Dishonest Casino
by Marshall Hampton
Based on the classic example in "Biological Sequence Analysis" by Durbin et al.
To get the dice picture you need to download this dishonest_casino.sws
