byte_search_math.py

    @staticmethod
    def bayes(h, e_given_h, e_given_not_h):
        """Update the posterior probability of h given e.
        
        e: evidence
        h: hypothesis
        e_given_h: probability of e given h
        e_given_not_h: probability of e given not h
        """
        return e_given_h * h / (e_given_h * h + e_given_not_h * (1 - h))

    @staticmethod
    def get_updated_confidences(confidences, index, result):
        new_confidences = confidences[:]  # shallow copy
        for j in range(256):
            p_h = confidences[j]
            if index == j:
                p_e_given_h = 1 - FN_RATE if result else FN_RATE
                p_e_given_not_h = FP_RATE if result else 1 - FP_RATE
            else:
                p_e_given_h = FP_RATE if result else 1 - FP_RATE
                p_hi_given_not_hj = confidences[index] / (1 - confidences[j])
                p_not_hi_given_not_hj = 1 - p_hi_given_not_hj
                if result:
                    p_e_given_not_h = p_hi_given_not_hj * (1 - FN_RATE) + p_not_hi_given_not_hj * FP_RATE
                else:
                    p_e_given_not_h = p_hi_given_not_hj * FN_RATE + p_not_hi_given_not_hj * (1 - FP_RATE)
            new_confidences[j] = ByteSearch.bayes(p_h, p_e_given_h, p_e_given_not_h)
        return new_confidences

    @staticmethod
    def get_entropy(dist):
        return -sum(p * log2(p) for p in dist if p)