hw2 problem 5

HW02/calculateHW2P5.py

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+import numpy as np
+
+# SIMULATION CALCULATIONS
+def simulate_culprit(N, pSuperman):
+    return np.random.rand(N) < pSuperman
+
+def simulate_crumbs(N, supermanProb, batmanProb, culprit):
+    randomDraw = np.random.rand(N, 3)
+    supermanCrumbs = (randomDraw < supermanProb)
+    batmanCrumbs = (randomDraw < batmanProb)
+    return np.where(culprit[:, None], supermanCrumbs, batmanCrumbs)
+
+def combination(crumbResults, culprit):
+    combinations = {}
+    for couch in [False, True]:
+        for kitchen in [False, True]:
+            for gym in [False, True]:
+                for culprit_label, culprit_val in [("Superman", True), ("Batman", False)]:
+                    mask = (crumbResults[:, 0] == couch) & (crumbResults[:, 1] == kitchen) & (crumbResults[:, 2] == gym) & (culprit == culprit_val)
+                    combinations[(couch, kitchen, gym, culprit_label)] = np.sum(mask)
+    return combinations
+
+def print_probabilities(combinations, N):
+    print("Couch:\t Kitchen:  Gym:\t  Culprit:")
+    for k, v in combinations.items():
+        couch, kitchen, gym, culprit_label = k
+        #formatting
+        couch_str = 'True ' if couch else 'False'
+        kitchen_str = 'True ' if kitchen else 'False'
+        gym_str = 'True ' if gym else 'False'
+        if culprit_label == 'Batman': culprit_label = 'Batman  '
+
+        print(f"{couch_str}\t {kitchen_str}\t   {gym_str}  {culprit_label}: {(v / N) * 100:.2f}%")
+
+# ANALYTIC CALCULATIONS
+def analytic_probabilities(pSuperman, pBatman, supermanProb, batmanProb):
+    combinations = {}
+    for couch in [False, True]:
+        for kitchen in [False, True]:
+            for gym in [False, True]:
+                #Superman
+                prob_superman = pSuperman
+                prob_superman *= supermanProb[0] if couch else (1 - supermanProb[0])
+                prob_superman *= supermanProb[1] if kitchen else (1 - supermanProb[1])
+                prob_superman *= supermanProb[2] if gym else (1 - supermanProb[2])
+                combinations[(couch, kitchen, gym, "Superman")] = prob_superman
+
+                #Batman
+                prob_batman = pBatman
+                prob_batman *= batmanProb[0] if couch else (1 - batmanProb[0])
+                prob_batman *= batmanProb[1] if kitchen else (1 - batmanProb[1])
+                prob_batman *= batmanProb[2] if gym else (1 - batmanProb[2])
+                combinations[(couch, kitchen, gym, "Batman")] = prob_batman
+
+    return combinations
+
+def print_analytic_probabilities(combinations):
+    print("Couch:\t Kitchen:  Gym:\t  Culprit:")
+    for k, v in combinations.items():
+        couch, kitchen, gym, culprit_label = k
+
+        #formatting
+        couch_str = 'True ' if couch else 'False'
+        kitchen_str = 'True ' if kitchen else 'False'
+        gym_str = 'True ' if gym else 'False'
+        if culprit_label == 'Batman': culprit_label = 'Batman  '
+        print(f"{couch_str}\t {kitchen_str}\t   {gym_str}  {culprit_label}: {v * 100:.2f}%")

HW02/mainHW2P5.py

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+from calculateHW2P5 import simulate_culprit, simulate_crumbs, combination, print_probabilities, analytic_probabilities, print_analytic_probabilities
+import numpy as np
+
+if __name__ == "__main__":
+    #N = 100000 #used while testing
+    NSize = [1000, 10000, 100000]
+    #Priors for each suspect
+    pSuperman = 0.5
+    pBatman = 0.5
+
+    #Likelihoods of crumbs on each location
+    supermanProb = np.array([0.3, 0.7, 0.2])
+    batmanProb = np.array([0.4, 0.6, 0.3])
+
+    #Simulate
+    '''
+    culprit = simulate_culprit(N, pSuperman)
+    crumbResults = simulate_crumbs(N, supermanProb, batmanProb, culprit)
+
+    print("Simulation:")
+    print_probabilities(combination(crumbResults, culprit), N)
+    '''
+    print("Simulation:")
+    for N in NSize:
+        print(f"N = {N}")
+        # Simulate culprit and crumbs
+        culprit = simulate_culprit(N, pSuperman)
+        crumbResults = simulate_crumbs(N, supermanProb, batmanProb, culprit)
+
+        # Count combinations and print probabilities
+        print("Simulated Probabilities:")
+        print_probabilities(combination(crumbResults, culprit), N)
+        print("\n")
+
+    #Analytic
+    print("Analytic:")
+    print_analytic_probabilities(analytic_probabilities(pSuperman, pBatman, supermanProb, batmanProb))
+
+'''
+As the value of N increases, the simulated probabilities get closer to the analytic probabilities. 
+'''