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综合可靠性的概念及其层级贝叶斯估计AI 解读

In this article we introduce the notion of “composite reliability” as a measure of the overall reliability of a collection of heterogeneous but similar items. We then propose a hierarchical Bayes model for estimating the composite reliability of systems whose lifelengths are expressed as binary random variables. Subsequently, we develop an alternative approach for the simultaneous inference about many small but related binomial parameters. We propose a two-stage prior for…

四人家庭收入中位数估计：贝叶斯时间序列方法AI 解读

This article develops a general methodology for small domain estimation based on data from repeated surveys. The results are directly applied to the estimation of median income of four-person families for the 50 states and the District of Columbia. These estimates are needed by the U.S. Department of Health and Human Services (HHS) to formulate its energy assistance program for low income families. The U.S. Bureau of the Census, by an informal agreement, has provided such…

离散持续期与竞争风险模型中风险函数和时变效应的平滑AI 解读

State-space or dynamic approaches to discrete or grouped duration data with competing risks or multiple terminating events allow simultaneous modeling and smooth estimation of hazard functions and time-varying effects in a flexible way. Full Bayesian or posterior mean estimation, using numerical integration techniques or Monte Carlo methods, can become computationally rather demanding or even infeasible for higher dimensions and larger datasets. Therefore, based on previous…

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SUMMARY This paper describes an approach to Bayesian sensitivity analysis that uses an influence statistic and an outlier statistic to assess the sensitivity of a model to perturbations. The basic outlier statistic is a Bayes factor, whereas the influence statistic depends strongly on the purpose of the analysis. The task of influence analysis is aided by having an interpretable influence statistic. Two alternative divergences, an L 1-distance and a χ2-divergence, are…

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干中学与技术选择AI 解读

In a Bayesian model of learning, the more an agent uses a technology, the better he learns its parameters. This expertise is a form of human capital. Switching to a new technology temporarily reduces expertise: the bigger the leap, the bigger the loss. This may prevent the agent from climbing the technological ladder too fast. Someone skilled may want to stick to his technology and experience no growth in the long run. But someone less skilled may want to switch technologies…

贝叶斯风险的信息不等式AI 解读

This paper presents a lower bound, derived from the information inequality for the Bayes risk with respect to truncated priors under quadratic loss. It is discussed in cases where the regularity condition of Brown and Gajek is not always satisfied. A related result for the minimax risk is also given.

稀疏概率表的贝叶斯模型AI 解读

We wish to make inferences about the conditional probabilities $p(y|x)$, many of which are zero, when the distribution of X is unknown and one observes only a multinomial sample of the Y variates. To do this, fixed likelihood ratio models and quasi-incremental distributions are defined. It is shown that quasi-incremental distributions are intimately linked to decomposable graphs and that these graphs can guide us to transformations of X and Y which admit a conjugate Bayesian…

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…

部分指定异方差结构模型的最优贝叶斯设计AI 解读

We consider the problem of finding a nonsequential optimal design for estimating parameters in a generalized exponential growth model. This problem is solved by first considering polynomial regression models with error variances that depend on the covariate value and unknown parameters. A Bayesian approach is adopted, and optimal Bayesian designs supported on a minimal number of support points for estimating the coefficients in the polynomial model are found analytically.…

处理—对照设计的可容许性与最优性AI 解读

The relationship between admissible incomplete block designs for confidence intervals with maximal coverage probability for treatment-control contrasts and optimal designs for estimation is investigated. For certain types of designs, admissible designs are shown to be precisely those with the number of replications of the control less than or equal to that of an optimal design. Moreover, admissible designs are the Bayes optimal designs for a class of priors.

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随机贴现因子的贝叶斯估计AI 解读

This article provides a Bayesian method of estimating the marginal posterior distributions for stochastic discount factors associated with observed asset returns. These estimates can be used to provide measures of fit for asset pricing models and to identify broad features of the characteristics that should be explained. These measures of fit can be used to supplement model evaluation exercises based on L. P. Hansen-R. Jagannathan bounds.

通过整合多个模型预测转折点AI 解读

A new method for forming composite turning point (or other qualitative) forecasts is proposed. Rather than forming composite forecasts by the standard Bayesian approach with weights proportional to each model's posterior odds, weights are assigned to the individual models in proportion to the probability of each model's having the correct turning point prediction. These probabilities are generated by logit models estimated with data on the models' past turning point…

无需预先确定平稳化方式的股票价格建模：计算更正AI 解读

In “Modeling Stock Prices without Knowing How to Induce Stationarity” (1994, Econometric Theory 10, 701–719), we used posterior-odds calculations to evaluate restrictions imposed by a present-value model of stock prices across the equations of a VAR representation of stock prices and dividends. The results we reported are tainted by the omission of two factors: the Jacobians induced by the mapping of our priors over VAR parameters β into the restricted sample spaces relevant…

涵盖性与特异性AI 解读

A model M is said to encompass another model N if the former can explain the results obtained by the latter. In this paper, we propose a general notion of encompassing that covers both classical and Bayesian viewpoints and essentially represents a concept of sufficiency among models. We introduce the parent notion of specificity that aims at measuring lack of encompassing. Tests for encompassing are discussed and the test statistics are compared to Bayesian posterior odds.…