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| Author | : TaChen Liang |
| Publisher | : |
| Total Pages | : 12 |
| Release | : 1991 |
| Genre | : |
| ISBN | : |
| Author | : STANFORD UNIV CALIF DEPT OF STATISTICS. |
| Publisher | : |
| Total Pages | : 41 |
| Release | : 1967 |
| Genre | : |
| ISBN | : |
A sequence of decision problems is considered where for each problem the observation has discrete probability function of the form p(x) = h(x) beta (lambda) lambda to the power x, x = 0,1,2, ..., and where lambda is selected independently for each problem according to an unknown prior distribution G(lambda). It is supposed that for each problem one of two possible actions (e.g., 'accept' or 'reject') must be selected. Under various assumptions about h(x) and G(lambda) the rate at which the risk of the nth problem approaches the smallest possible risk is determined for standard empirical Bayes procedures. It is shown that for most practical situations, the rate of convergence to 'optimality' will be at least as fast as L(n)/n where L(n) is a slowly varying function (e.g., log n). The rate cannot be faster than 1/n and this exact rate is achieved in some cases. Arbitrarily slow rates will occur in certain pathological situations. (Author).
| Author | : Ta Chen Liang |
| Publisher | : |
| Total Pages | : 16 |
| Release | : 1987 |
| Genre | : |
| ISBN | : |
The purpose of this paper is to investigate the convergence rates of a sequence of empirical Bayes decision rules for the two-action decision problems where the distributions of the observations belong to a discrete exponential family. It is found that the sequence of the empirical Bayes decision rules under study is asymptotically optimal, and the order of associated convergence rates is O(exp( -cn)), for some positive constant c, where n is the number of accumulated past experience (observations) at hand. Two examples are provided to illustrate the performance of the proposed empirical Bayes decision rules. A comparison is also made between the proposed empirical Bayes rules and some earlier existng empirical Bayes rules.
| Author | : M. V. Johns (Jr.) |
| Publisher | : |
| Total Pages | : 28 |
| Release | : 1967 |
| Genre | : |
| ISBN | : |
| Author | : STANFORD UNIV CALIF DEPT OF STATISTICS. |
| Publisher | : |
| Total Pages | : 28 |
| Release | : 1967 |
| Genre | : |
| ISBN | : |
A sequence of decision problems is considered where for each problem the observation has a probability density function of exponential type with parameter lambda where lambda is selected independently for each problem according to an unknown prior distribution G(lambda). It is supposed that in each of the problems, one of two possible actions (e.g., 'accept' or 'reject') must be taken. Under various assumptions, reasonably sharp upper bounds are found for the rate at which the risk of the nth problem approaches the smallest possible risk for certain refinements of the standard empirical Bayes procedures. For suitably chosen procedures, under situations likely to occur in practice, rates faster than n to the power ( -1 + epsilon) may be obtained for arbitrarily small epsilon> 0. Arbitrarily slow rates can occur in pathological situations. (Author).
| Author | : Benito Ong Yu |
| Publisher | : |
| Total Pages | : 160 |
| Release | : 1970 |
| Genre | : Bayesian statistical decision theory |
| ISBN | : |
| Author | : Pekka Laippala |
| Publisher | : |
| Total Pages | : 92 |
| Release | : 1980 |
| Genre | : Bayesian statistical decision theory |
| ISBN | : |
| Author | : Omkar Muralidharan |
| Publisher | : Stanford University |
| Total Pages | : 89 |
| Release | : 2011 |
| Genre | : |
| ISBN | : |
Many modern statistical problems require making similar decisions or estimates for many different entities. For example, we may ask whether each of 10,000 genes is associated with some disease, or try to measure the degree to which each is associated with the disease. As in this example, the entities can often be divided into a vast majority of "null" objects and a small minority of interesting ones. Empirical Bayes is a useful technique for such situations, but finding the right empirical Bayes method for each problem can be difficult. Mixture models, however, provide an easy and effective way to apply empirical Bayes. This thesis motivates mixture models by analyzing a simple high-dimensional problem, and shows their practical use by applying them to detecting single nucleotide polymorphisms.
| Author | : N. Balakrishnan |
| Publisher | : CRC Press |
| Total Pages | : 562 |
| Release | : 2003-04-24 |
| Genre | : Mathematics |
| ISBN | : 9780203493205 |
At the International Indian Statistical Association Conference, held at McMaster University in Ontario, Canada, participants focused on advancements in theory and methodology of probability and statistics. This is one of two volumes containing invited papers from the meeting. The 32 chapters deal with different topics of interest, including stochastic processes and inference, distributions and characterizations, inference, Bayesian inference, selection methods, regression methods, and methods in health research. The text is ideal for applied mathematicians, statisticians, and researchers in the field.
| Author | : S.E. Ahmed |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 242 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461301416 |
Bayesian and such approaches to inference have a number of points of close contact, especially from an asymptotic point of view. Both emphasize the construction of interval estimates of unknown parameters. In this volume, researchers present recent work on several aspects of Bayesian, likelihood and empirical Bayes methods, presented at a workshop held in Montreal, Canada. The goal of the workshop was to explore the linkages among the methods, and to suggest new directions for research in the theory of inference.
