English
资源说明：How should we use data to help us analyse our beliefs? This book is concerned with the subjectivist analysis of uncertainty, and develops methods that combine prior judgements with information derived from relevant data. Whenever we move from broadly data-focused questions, such as ‘Does this data set suggest that a certain medical treatment is likely to be effective?’, to broadly decision-motivated questions, such as ‘Are we sufficiently confident, given all that we know about this treatment, to recommend its widespread use?’, then we must make such a synthesis of data with more generalized forms of information. Because we may find this hard to achieve, we need some methodology to help us. This methodology should be clear, helpful, logically well founded and tractable.
The Bayesian approach to statistics is the natural methodology for this purpose. This approach treats all uncertainties within a common probabilistic framework, combining the different sources of information using the rules of probability. This approach has a sound logical foundation and a well-developed methodology and is popular and successful in many areas of application.
However, in large-scale applications, the Bayesian approach can easily become the victim of its own ambition. Representing all uncertainties in probabilistic form is a daunting task for complicated problems. This is partly because of the intrinsic difficulties in judging the value of each relevant source of knowledge. However, in large part, the task is difficult because the Bayesian approach requires us to specify our uncertainties to an extreme level of detail. In practice, it is usually beyond our ability to make meaningful specifications for our joint probability distributions for multiple outcomes.
If we do wish to follow a broadly Bayesian path, then we must either choose to make specifications that do not correspond to our actual uncertainties or be more modest about our ability to render our beliefs in probabilistic form. If the data are plentiful and unambiguous in their message or if the problem is not sufficiently important to merit careful analysis, then little harm is done by somewhat misrepresenting our beliefs. However, when the issue is important and data are less plentiful, then we must be more careful and honest. When we cannot make full belief specifications, we require alternative methods that respect the limitations on our abilities to specify meaningful beliefs and allow us to conduct partial analyses strictly in terms of the actual limited aspects of our beliefs that we are able to specify.
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