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动态计算机程序的高斯过程仿真代理AI 解读

Computer codes are used in scientific research to study and predict the behaviour of complex systems. Their run times often make uncertainty and sensitivity analyses impractical because of the thousands of runs that are conventionally required, so efficient techniques have been developed based on a statistical representation of the code. The approach is less straightforward for dynamic codes, which represent time-evolving systems. We develop a novel iterative system to build…

先验征询中的不确定性：非参数方法AI 解读

A key task in the elicitation of expert knowledge is to construct a distribution from the finite, and usually small, number of statements that have been elicited from the expert. These statements typically specify some quantiles or moments of the distribution. Such statements are not enough to identify the expert's probability distribution uniquely, and the usual approach is to fit some member of a convenient parametric family. There are two clear deficiencies in this…

贝叶斯线性充分性与专家后验评估系统AI 解读

SUMMARY Data arising in the form of expert assessments are received by a decision maker. The decision maker is required to estimate a set of unknown quantities, and receives expert assessments at varying levels of accuracy, on samples of the quantities of interest. We present a Bayes linear analysis of this problem. In the absence of other assessments, the decision maker will accept as his or her current estimate of any single quantity the most accurate received assessment…

位置参数推断中的异常值与尾部可信度AI 解读

Heavy-tailed distributions are important for modeling problems in which there may be outlying observations or parameters. Examples of their use are given in O'Hagan (1988). This article develops some general theory, based on the notion of credence, for inference about unknown location parameters in the case of known variances. A density on the real line is defined to have credence c if it is bounded above and below by positive multiples of (1 + x 2)-c/2. For instance, a t…

随机化回答模型的贝叶斯线性估计量AI 解读

Bayes linear estimators provide simple Bayesian methods and require a minimum of prior specification. In this article, Bayes linear estimators are derived for a variety of randomized response models. Randomized response aims to reduce false responses on sensitive questions, at the expense of some loss of information in each observation. In this context, Bayesian methods are attractive because they permit the incorporation of potentially useful prior information. The basic…

犹疑之矩：先验与样本冲突下的后验方差AI 解读

For a suitably thick-tailed prior density and a sufficiently large observation, the sample information dominates the prior information. Similarly, a thick-tailed sampling distribution can be dominated by the prior if the observation is sufficiently large. We show, in the case where the dominating density is normal, that less extreme observations produce very large posterior variances.

犹疑的一刻：先验与数据冲突中的后验方差AI 解读

We consider inference from a single observation X about a location parameter 0. That is, given 0 = 0, the density function of X has the form f (x -0) for some known function f. The prior distribution for 0 has density g(6). It is well known that if f and g are both normal densities then the posterior density is normal with a variance independent of x and less than the variance of either f or g. Very different behaviour can occur if either component is not normal. Dawid…

贝叶斯推断中的离群值排斥现象AI 解读

Summary Inference is considered for a location parameter given a random sample. Outliers are not explicitly modelled, but rejection of extreme observations occurs naturally in any Bayesian analysis of data from distributions with suitably thick tails. For other distributions outlier rejection behaviour can never occur. These phenomena motivate new definitions of outlier-proneness and outlier-resistance. The definitions and methodology are Bayesian but the conclusions also…

后验联合众数与边际众数AI 解读

Posterior joint modes have often been used as point estimators in Bayesian applications to avoid laborious numerical integration of complicated posterior densities. We present methods facilitating the straightforward computation of posterior marginal modes in a wide variety of models, and discuss whether marginal modes provide better approximations than joint modes to the posterior means.

参数约束不确定性下的贝叶斯估计AI 解读

When estimating a normal location parameter, an inequality constraint is sometimes indicated by theoretical considerations. If, however, this constraint is assumed a priori definitely to hold, then the data will never be permitted to formally contradict the theory. We propose a family of skew prior distributions which reflect uncertainty about the constraint.

后验联合众数与边际众数AI 解读

Posterior joint modes have often been used as point estimators in Bayesian applications to avoid laborious numerical integration of complicated posterior densities. We present methods facilitating the straightforward computation of posterior marginal modes in a wide variety of models, and discuss whether marginal modes provide better approximations than joint modes to the posterior means.

参数约束存在不确定性时的贝叶斯估计AI 解读

When estimating a normal location parameter, an inequality constraint is sometimes indicated by theoretical considerations. If, however, this constraint is assumed a priori definitely to hold, then the data will never be permitted to formally contradict the theory. We propose a family of skew prior distributions which reflect uncertainty about the constraint.

凸二次回归曲线的贝叶斯估计AI 解读

The estimation of a quadratic regression curve when the quadratic coefficient is known to be positive is treated by a Bayesian method. The method extends easily to deal with a general linear model under parameter constraints.

凸二次回归曲线的贝叶斯估计AI 解读

The estimation of a quadratic regression curve when the quadratic coefficient is known to be positive is treated by a Bayesian method. The method extends easily to deal with a general linear model under parameter constraints.