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# Bayes is BAE

Before programming, before formal probability there was Bayes. He introduced the notion that multiple uncertain estimates which are related could be combined to form a more certain estimate. It turns out that this extremely simple idea has a profound impact on how we write programs and how we can think about life. The applications range from machine learning and robotics to determining cancer treatments. In this talk we'll take an in depth look at Bayses rule and how it can be applied to solve problems in programming and beyond.

May 08, 2017

## Transcript

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11. ### Divine Benevolence, or an Attempt to Prove That the Principal

End of the Divine Providence and Government is the Happiness of His Creatures

13. ### An Introduction to the Doctrine of Fluxions, and a Defence

of the Mathematicians Against the Objections of the Author of The Analyst

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79. ### Probability of \$3.7 mil given Heads P(A ∣ B) =

P(B ∣ A) P(A) P(B)
80. ### Probability of \$3.7 mil given Heads P(A ∣ B) =

P(B ∣ A) P(A) P(B)
81. ### probability of heads P(A ∣ B) = P(B ∣ A)

P(A) P(B) P(B) =

83. ### P(B) = H H H T probability of heads P(B)

= 0.5 * 0.5 + 0.5 * 1 0.75 P(B) =

P(B) = 0.75
85. ### P(A) = P(A ∣ B) = P(B ∣ A) P(A)

P(B) 0.75 probability of \$3.7 million

=
88. ### P(A ∣ B) = P(B ∣ A) P(A) P(B) 0.50

0.75 0.50 P(A) =
89. ### P(A ∣ B) = P(B ∣ A) P(A) P(B) P(B

∣ A) = 0.75 0.50 probability of heads given \$3.7

=
91. ### P(B ∣ A) = 0.5 P(A ∣ B) = P(B

∣ A) P(A) P(B) 0.75 0.5 * 0.5
92. ### \$3.7 mil given Heads P(A ∣ B) = P(B ∣

A) P(A) P(B) 0.75 0.5 * 0.5 P(A ∣ B) = 1 3 = 0.3333

99. ### P(Ai ∣ B) = P(B ∣ Ai ) P(Ai )

∑ j P(B ∣ Aj ) P(Aj )
100. ### P(A ∣ B) = P(B ∣ A) P(A) P(B) P(Ai

∣ B) = P(B ∣ Ai ) P(Ai ) ∑ j P(B ∣ Aj ) P(Aj )

108. ### P(Hea d s) = P(Hea d s ∣ \$\$\$)P(\$\$\$) +

P(Hea d s ∣ \$0)P(\$0) \$3.7 mil \$0 Heads Tails
109. ### \$3.7 mil \$0 P(Hea d s) = P(Hea d s

∣ \$\$\$)P(\$\$\$) + P(Hea d s ∣ \$0)P(\$0) Heads Tails
110. ### P(B) = ∑ j P(B ∣ Aj ) P(Aj )

Total Probability
111. ### P(B) = H H H T probability of heads P(B)

= 0.5 * 0.5 + 0.5 * 1 0.75 P(B) =
112. ### P(B) = ∑ j P(B ∣ Aj ) P(Aj )

P(Hea d s) = P(Hea d s ∣ \$\$\$)P(\$\$\$) + P(Hea d s ∣ \$0)P(\$0) Total Probability

114. ### P(Ai ∣ B) = P(B ∣ Ai ) P(Ai )

∑ j P(B ∣ Aj ) P(Aj )
115. ### P(Coini ∣ HH ) = P(HH ∣ Coini ) P(Coini

) ∑ j P(HH ∣ Coinj ) P(Coinj )
116. ### P(Coini ∣ HH ) = P(HH ∣ Coini ) P(Coini

) ∑ j P(HH ∣ Coinj ) P(Coinj ) P(HH ∣ Coini ) = 0.5 * 0.5
117. ### P(Coini ∣ HH ) = P(HH ∣ Coini ) P(Coini

) ∑ j P(HH ∣ Coinj ) P(Coinj ) 0.5 P(Coini ) =
118. ### P(Coini ∣ HH ) = P(HH ∣ Coini ) P(Coini

) ∑ j P(HH ∣ Coinj ) P(Coinj ) ∑ j P(B ∣ Aj ) P(Aj ) = P(HH ∣ \$\$\$)P(\$\$\$) + P(HH ∣ \$0)P(\$0) ∑ j P(B ∣ Aj ) P(Aj ) = 0.25(0.5) + 1.0(0.5)
119. ### P(Coini ∣ HH ) = P(HH ∣ Coini ) P(Coini

) ∑ j P(HH ∣ Coinj ) P(Coinj ) ∑ j P(B ∣ Aj ) P(Aj ) = P(HH ∣ \$\$\$)P(\$\$\$) + P(HH ∣ \$0)P(\$0) ∑ j P(B ∣ Aj ) P(Aj ) = 0.25(0.5) + 1.0(0.5)
120. ### P(Coin\$\$\$ ∣ HH ) = 0.25(0.5) 0.625 = 1 5

= 0.2 P(Coini ∣ HH ) = P(HH ∣ Coini ) P(Coini ) ∑ j P(HH ∣ Coinj ) P(Coinj )
121. ### P(Coin\$\$\$ ∣ HH ) = 0.25(0.5) 0.625 = 1 5

= 0.2 P(Coini ∣ HH ) = P(HH ∣ Coini ) P(Coini ) ∑ j P(HH ∣ Coinj ) P(Coinj )
122. ### P(Coini ∣ HH ) = 0.25(0.5) 0.625 = 1 5

= 0.2 P(Coini ∣ HH ) = P(HH ∣ Coini ) P(Coini ) ∑ j P(HH ∣ Coinj ) P(Coinj )

127. ### P(A ∣ B) = P(B ∣ A) P(A) P(B) P(Ai

∣ B) = P(B ∣ Ai ) P(B) P(Ai )

) Prior

) Posterior

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135. ### alt it u decurrent time = 0.75 alt it u

deprevious time
136. ### alt it u decurrent time = 0.75 alt it u

deprevious time
137. ### a = rate_of_decent = 0.75 x = initial_position = 1000

r = measure_error = x * 0.20

[]

140. ### for k in range(10): measure = measure_array[k] # Predict x_guess

= a * x_guess
141. ### for k in range(10): measure = measure_array[k] # Predict x_guess

= a * x_guess p = a * p * a
142. ### for k in range(10): measure = measure_array[k] # Predict x_guess

= a * x_guess p = a * p * a # Update gain = p / (p + r) x_guess = x_guess + gain * (measure - x_guess)
143. ### for k in range(10): measure = measure_array[k] # Predict x_guess

= a * x_guess p = a * p * a # Update gain = p / (p + r) x_guess = x_guess + gain * (measure - x_guess) Low Predict Error, low gain
144. ### for k in range(10): measure = measure_array[k] # Predict x_guess

= a * x_guess p = a * p * a # Update gain = p / (p + r) x_guess = x_guess + 0 * (measure - x_guess) Low Predict Error, low gain
145. ### for k in range(10): measure = measure_array[k] # Predict x_guess

= a * x_guess p = a * p * a # Update gain = p / (p + r) x_guess = x_guess + 0 * (measure - x_guess) Low Predict Error, low gain
146. ### for k in range(10): measure = measure_array[k] # Predict x_guess

= a * x_guess p = a * p * a # Update gain = p / (p + r) x_guess = x_guess + 1 * (measure - x_guess) High Predict Error, High gain
147. ### for k in range(10): measure = measure_array[k] # Predict x_guess

= a * x_guess p = a * p * a # Update gain = p / (p + r) x_guess = x_guess + 1 * (measure - x_guess) High Predict Error, High gain

150. ### for k in range(10): measure = measure_array[k] # Predict x_guess

= a * x_guess p = a * p * a # Update gain = p / (p + r) x_guess = x_guess + gain * (measure - x_guess) p = (1 - g) * p
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