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采用新先验族的多元正态协方差矩阵贝叶斯分析AI 解读

Bayesian analysis for the covariance matrix of a multivariate normal distribution has received a lot of attention in the last two decades. In this paper, we propose a new class of priors for the covariance matrix, including both inverse Wishart and reference priors as special cases. The main motivation for the new class is to have available priors—both subjective and objective—that do not “force eigenvalues apart,” which is a criticism of inverse Wishart and Jeffreys priors.…

通过贝叶斯随机搜索选择多元随机波动率模型AI 解读

We propose a Bayesian stochastic search approach to selecting restrictions on multivariate regression models where the errors exhibit deterministic or stochastic conditional volatilities. We develop a Markov chain Monte Carlo (MCMC) algorithm that generates posterior restrictions on the regression coefficients and Cholesky decompositions of the covariance matrix of the errors. Numerical simulations with artificially generated data show that the proposed method is effective…

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向量自回归脉冲响应的内在贝叶斯估计AI 解读

We propose an information-theoretic alternative to the conventional Bayesian posterior mean estimator of impulse responses in vector autoregression (VAR) models. The proposed estimator is based on the intrinsic entropy loss function, which is invariant to nonlinear transformations of parameters. Consequently, intrinsic estimation of impulse responses is equivalent to that of VAR parameters. The Bayesian estimator under the entropy loss involves a frequentist expectation of…

向量自回归模型的贝叶斯估计AI 解读

This article examines frequentist risks of Bayesian estimates of vector autoregressive (VAR) regression coefficient and error covariance matrices under competing loss functions, under various noninformative priors, and in the normal and Student-t models. Simulation results show that for the regression coefficient matrix, an asymmetric LINEX estimator does better overall than the posterior mean. No dominating estimator emerges for the error covariance matrix. We find that the…

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利用二重条件自回归模型改进死亡率估计的双变量贝叶斯方法AI 解读

A bivariate Bayes method is proposed for estimating the mortality rates of a single disease for a given population, using additional information from a second disease. The information on the two diseases is assumed to be from the same population groups or areas. The joint frequencies of deaths for the two diseases for given populations are assumed to have a bivariate Poisson distribution with joint means proportional to the population sizes. The relationship between the…

有理函数模型的最优实验设计AI 解读

In this paper, experimental designs for a rational model, $Y = P(x)/Q(x) + \varepsilon$, are investigated, where $P(x) = \theta_0 + \theta_1 x + \dots + \theta_p x^p$ and $Q(x) = 1 + \theta_{p + 1} x + \dots + \theta_{p+q} x^q$ are polynomials and $\varepsilon$ is a random error. Two approaches, Bayesian D-optimal and Bayesian optimal design for extrapolation, are examined. The first criterion maximizes the expected increase in Shannon information provided by the experiment…

正态均值乘积的参考先验贝叶斯分析AI 解读

Two reference priors for the product of means of n normal distributions with common known variance are developed. One of them induces an improper posterior distribution and therefore is not of much interest. The other is a generalized form of the n = 2 case derived by Berger and Bernardo. The latter is compared with the uniform prior (the Jeffreys prior) in posterior inference and the optimal frequentist coverage criterion. The reference prior is shown to be better than the…

双参数指数族后验分布的可积展开AI 解读

Asymptotic expansions of posterior distributions are derived for a two-dimensional exponential family, which includes normal, gamma, inverse gamma and inverse Gaussian distributions. Reparameterization allows us to use a data-dependent transformation, convert the likelihood function to the two-dimensional standard normal density and apply a version of Stein's identity to assess the posterior distributions. Applications are given to characterize optimal noninformative priors…

Poly-Weibull 分布的贝叶斯分析AI 解读

In this article Bayesian analysis for a Poly-Weibull distribution using informative priors is discussed. This distribution typically arises when the data is the minimum of several Weibull failure times from competing risks. To perform the Bayesian computations, simulation using the Gibbs sampler is suggested. This can be used to find posterior moments, the marginal posterior probability density function, and the predictive risk or reliability.