论文检索

贝叶斯渐近计算中的指数倾斜AI 解读

We use exponential tilting to obtain versions of asymptotic formulae for Bayesian computation that do not involve conditional maxima of the likelihood function, yielding a more stable computational procedure and significantly reducing computational time. In particular we present an alternative version of the Laplace approximation for a marginal posterior density. Implementation of the asymptotic formulae and a modified signed root based importance sampler are illustrated…

覆盖概率偏差、客观贝叶斯与似然原则AI 解读

We review objective Bayes procedures based on both parametric and predictive coverage probability bias and explore the extent to which such procedures contravene the likelihood principle in the case of a scalar parameter. The discussion encompasses choice of objective priors, objective posterior probability statements and objective predictive probability statements. We conclude with some remarks concerning the future development and implementation of objective priors based…

删失时间存在误差时指数分布删失数据的估计AI 解读

SUMMARY The problem of estimating the parameter of the negative exponential distribution with censored data may be complicated by a lack of complete knowledge of the censoring times. The effect of ignoring these errors in the censoring times rather than using a complete maximum likelihood estimation approach is investigated and it is shown that the loss in efficiency is generally small for the inverted gamma model considered in this paper. The theory is supplemented by some…

摘要暂缺

近似条件推断的贝叶斯方法AI 解读

Sweeting (1995) studies regular Bayesian and frequentist approximations within a unified framework in the case of a single parameter, and shows that higher-order approximations to sampling distributions arise from their Bayesian counterparts via an unsmoothing argument. In the present paper we extend this programme to include formulae in approximate conditional inference. In particular it is shown how Bayesian arguments may be used to derive some formulae developed by…

统计中的贝叶斯与似然近似统一框架AI 解读

Regular Bayesian and frequentist approximations in statistics are studied within a unified framework. In particular it is shown how some higher-order likelihood-based approximations arise from their Bayesian counterparts via an unsmoothing argument. This approach serves to shed new light on these formulae and to clarify relationships between Bayesian and frequentist inferences. For example, Bayesian interpretations of higher-order approximations can give insights into the…

摘要暂缺

再论随机过程的后验渐近正态性AI 解读

SUMMARY The problem of demonstrating the limiting normality of a posterior distribution arising from some stochastic process is revisited. It is shown that certain processes of practical interest are not covered by conditions currently available in the literature. In this paper we present a fairly general set of conditions for asymptotic posterior normality which cover a wide class of problems. The theory is applied to a nonhomogeneous Poisson process and birth process.

渐近独立的尺度无关间距及其异常值检验应用AI 解读

Motivated by the construction of independent scale-free spacings for the exponential distribution, analogous quantities are defined for an arbitrary distribution, and their joint asymptotic behaviour studied under suitable tail conditions. These scale-free spacings provide a unified approach to the problem of consecutive discordancy testing when location and scale parameters are unknown. A normal example is discussed and the accuracy of the approximations assessed via some…

超临界 Galton–Watson 过程子代均值的渐近条件推断AI 解读

Consider a supercritical Galton-Watson process $(Z_n)$ with offspring distribution a member of the power series family, and having unknown mean $\theta$. The conditional asymptotic normality of the suitably normalized maximum likelihood estimator of $\theta$ given the conditional information is established. The conditional information here is proportional to the total number of ancestors $V_n$, and it is also seen that this statistic is asymptotically ancillary for $\theta$ i…

极大似然估计量的一致渐近正态性AI 解读

A very general result concerning the weak consistency and uniform asymptotic normality of the maximum likelihood estimator is presented. The result proves to be of particular value in establishing uniform asymptotic normality of randomly normalized maximum likelihood estimators of parameters in stochastic processes. The only conditions imposed are certain regularity conditions on the (random) information function, easily verified in practice. Application of the result is…