tailieunhanh - Operational Risk Modeling Analytics phần 8

Như trước đây, tham số 6 có thể là vô hướng hoặc vector có giá trị. Xác định phân phối trước đã luôn là một trong những rào cản cho việc chấp nhận rộng rãi của các phương pháp Bayesian. Nó gần như chắc chắn các trường hợp kinh nghiệm của bạn đã cung cấp một số hiểu biết về các giá trị tham số có thể xảy ra trước khi các điểm dữ liệu đầu tiên đã được quan sát. | BAYESIAN ESTIMATION 305 As before the parameter 9 may be scalar or vector valued. Determination of the prior distribution has always been one of the barriers to the widespread acceptance of Bayesian methods. It is almost certainly the case that your experience has provided some insights about possible parameter values before the first data point has been observed. If you have no such opinions perhaps the wisdom of the person who assigned this task to you should be questioned. The difficulty is translating this knowledge into a probability distribution. An excellent discussion about prior distributions and the foundations of Bayesian analysis can be found in Lindley 76 and for a discussion about issues surrounding the choice of Bayesian versus frequentist methods see Efron 26 . A good source for a thorough mathematical treatment of Bayesian methods is the text by Berger 15 . In recent years many advancements in Bayesian calculations have occurred. A good resource is 21 . The paper by Scollnik addresses loss distribution modeling using Bayesian software tools. Because of the difficulty of finding a prior distribution that is convincing you will have to convince others that your prior opinions are valid and the possibility that you may really have no prior opinion the definition of prior distribution can be loosened. Definition An improper prior distribution is one for which the probabilities or pdf are nonnegative but their sum or integral is infinite. A great deal of research has gone into the determination of a so-called noninformative or vague prior. Its purpose is to reflect minimal knowledge. Universal agreement on the best way to construct a vague prior does not exist. However there is agreement that the appropriate noninformative prior for a scale parameter is 7r ớ l ớ ớ 0. Note that this is an improper prior. For a Bayesian analysis the model is no different than before. Definition The model distribution is the probability distribution for the .