Các đồng tiền uốn cong và mẫu so sánh mô hình so sánh như suy luận để thực hiện so sánh mô hình, chúng tôi viết ra định lý Bayes 'một lần nữa, nhưng lần này với một đối số khác nhau ở phía bên tay trái. Chúng tôi muốn biết làm thế nào H1 có thể là các dữ liệu. | Copyright Cambridge University Press 2003. On-screen viewing permitted. Printing not permitted. http 0521642981 You can buy this book for 30 pounds or 50. See http mackay itila for links. Arithmetic codes 117 probabilistic model used in the preceding example we first encountered this model in exercise p. 30 . Assumptions The model will be described using parameters p2 pa and Pb defined below which should not be confused with the predictive probabilities in a particular context for example P a I s baa . A bent coin labelled a and b is tossed some number of times l which we don t know beforehand. The coin s probability of coming up a when tossed is pa and pb 1 pa the parameters pa pb are not known beforehand. The source string s baaba2 indicates that l was 5 and the sequence of outcomes was baaba. 1. It is assumed that the length of the string l has an exponential probability distribution P l 1 - pn W This distribution corresponds to assuming a constant probability p2 for the termination symbol 2 at each character. 2. It is assumed that the non-terminal characters in the string are selected independently at random from an ensemble with probabilities P pa pbg the probability pa is fixed throughout the string to some unknown value that could be anywhere between 0 and 1. The probability of an a occurring as the next symbol given pa if only we knew it is 1 p2 pa. The probability given pa that an unterminated string of length F is a given string s that contains Fa Fbg counts of the two outcomes is the Bernoulli distribution P s I pa F pf 1 - pa Fb . 3. We assume a uniform prior distribution for pa P pa 1 pa 2 0 1 and define pb 1 pa. It would be easy to assume other priors on pa with beta distributions being the most convenient to handle. This model was studied in section . The key result we require is the predictive distribution for the next symbol given the string so far s. This probability that the .
