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Bayes' Rule
Joeven
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p_down = 0.10 p_up = 1.0 - p_down p_timeout_if_down = 0.90 p_timeout_if_up = 0.05 p_timeout = p_timeout_if_down * p_down + p_timeout_if_up * p_up p_down_if_timeout = (p_timeout_if_down * p_down) / p_timeout print("P(timeout)", round(p_timeout, 4)) print("P(down | timeout)", round(p_down_if_timeout, 4)) mass_down = p_timeout_if_down * p_down mass_up = p_timeout_if_up * p_up z = mass_down + mass_up print("posterior down, up", round(mass_down / z, 4), round(mass_up / z, 4)) mass_down2 = mass_down * p_timeout_if_down mass_up2 = mass_up * p_timeout_if_up z2 = mass_down2 + mass_up2 print("after 2 timeouts, P(down)", round(mass_down2 / z2, 4))
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