日期精度：到日 10 篇 · 到月 12 篇 · 到年 5 篇
贝叶斯与非贝叶斯方法的折中：简要综述
Various compromises that have occurred between Bayesian and non-Bayesian methods are reviewed. (A citation is provided that discusses the inevitability of compromises within the Bayesian approach.) One example deals with the masses of elementary particles, but no knowledge of physics will be assumed.
列联表独立性的混合 Dirichlet 贝叶斯检验：稳健性与敏感性
A mixed-Dirichlet prior was previously used to model the hypotheses of "independence" and "dependence" in contingency tables, thus leading to a Bayesian test for independence. Each Dirichlet has a main hyperparameter $\kappa$ and the mixing is attained by assuming a hyperprior for $\kappa$. This hyperparameter can be regarded as a flattening or shrinking constant. We here review the method, generalize it and check the robustness and sensitivity with respect to variations in…
二乘二列联表的合并及其几何性质
If a pair of two-by-two contingency tables are amalgamated by addition it can happen that a measure of association for the amalgamated table lies outside the interval between the association measures of the individual tables. We call this the amalgamation paradox and we show how it can be avoided by suitable designs of the sampling experiments. We also study the conditions for the "homogeneity" of two subpopulations with respect to various measures of association. Some of…
结构对称性下矩阵分布所诱导的不变分布
Summary Let Y(n x m) be a random matrix in the space F n x m of real matrices having location-scale parameters (θ, Ω) such that (i) θ belongs to a linear subspace M of F n x m; (ii) the distribution L(Y) exhibits a type of structural symmetry; and (iii) a certain transformation T(Y) is translation-invariant with respect to M and is invariant under changes of scale. Then the distribution L{T(Y)} is invariant for all underlying symmetric distributions L(Y). The types of…
对称 Dirichlet 分布及其混合在列联表中的应用：第二部分
This paper is a continuation of a paper in the Annals of Statistics (1976), 4 1159-1189 where, among other things, a Bayesian approach to testing independence in contingency tables was developed. Our first purpose now, after allowing for an improvement in the previous theory (which also has repercussions on earlier work on the multinomial), is to give extensive numerical results for two-dimensional tables, both sparse and nonsparse. We deal with the statistics $X^2, \Lambda$…
惩罚似然密度估计与峰值识别：散射及陨石数据示例
The (maximum) penalized-likelihood method of probability density estimation and bump-hunting is improved and exemplified by applications to scattering and chondrite data. We show how the hyperparameter in the method can be satisfactorily estimated by using statistics of goodness of fit. A Fourier expansion is found to be usually more expeditious than a Hermite expansion but a compromise is useful. The best fit to the scattering data has 13 bumps, all of which are evaluated…
非正态变量二次型的分布及其在方差比中的应用
Summary Good (1968a, b) using non-rigorous arguments, gave an expression for the characteristic function C.F. (x‘A x, t) of a quadratic form in a non-normal random column vector x whose characteristic function is known, where A is positive semi-definite. A general formula for C.F. (x‘A x, t) is proved here, which coincides with Good's expression when x has a real stable characteristic function. In the general formula, A need not be positive semi-definite and this greater…
对称狄利克雷先验下反对多项总体等概率的贝叶斯因子
A sample $(n_1, n_2,\cdots, n_t)$ is taken from a $t$-category multinomial population. The hypothesis of equiprobability, that the $t$ physical probabilities associated with the cells are all equal to $1/t$, is called the null hypothesis. Conditional on the non-null hypothesis, a symmetric Dirichlet prior of parameter $k$ is assumed $(k \geqq 0)$ and the Bayes factor against the null hypothesis, with this assumption, is denoted by $F(k)$. A conjecture made in 1965 is almost…
再生二元马尔可夫链中游程长度的联合概率生成函数及应用
Gontcharov obtained the joint probability generating function for the numbers of runs of all lengths, both of successes and failures, in a Bernoulli sequence. This is here generalized to a class of regenerative binary Markov processes. For an allied class of Markov processes, the probability generating function is obtained for a "total score" defined in terms of runs of successes only, and asymptotic formulas are derived for the expectation and variance of the score.
等概率多项分布下卡方与似然比统计量的精确分布
A sample of size N is taken from an equiprobable t-category multinomial distribution. The precise values of Pearson's X 2 and the likelihood ratio statistic A were computed for t = 3(1)6, N = 3(1)12; t = 6(1)14, N = 6(1)2t; t=15(1)18, N = 6(1)28. The logarithms of the tail areas were smoothed and fitted by means of quadratic expressions. Much information is given concerning the accuracy of the chi-squared fits to the distributions of X 2 and A. A table of −log10 P(χ2 > a) is…
二次型服从卡方分布的条件
Suppose that x has a multinormal distribution and A is a symmetrio matrix. Necessary and sufficient conditions are proved for x′Ax to have a chi-squared distribution with r degrees of freedom. Let x be a column vector of n components having a multinormal distribution of mean 0 and covariance matrix C, possibly singular. Let A be an n × n symmetric matrix.
二次型服从卡方分布的条件
Suppose that x has a multinormal distribution and A is a symmetrio matrix. Necessary and sufficient conditions are proved for x′Ax to have a chi-squared distribution with r degrees of freedom. Let x be a column vector of n components having a multinormal distribution of mean 0 and covariance matrix C, possibly singular. Let A be an n × n symmetric matrix.
多项分布的贝叶斯显著性检验
Summary A Bayesian significance test for multinomial distributions is discussed, together with the results of 18 numerical experiments in which the test is compared with non-Bayesian methods. Several different non-Bayesian criteria are considered because the circumstances under which their tail-area probabilities can be conveniently approximated differ from one to the other. A provisional empirical formula, connecting the Bayes factors with the tail-area probabilities, is…
马尔可夫链状态频数的二次式与二阶二元链
SUMMARY Let nr be the frequency of the state r in a segment of a regular ergodic Markov chain. It is shown how to obtain the asymptotic distribution of any quadratic expression in the nr’s. The method is especially convenient where the Markov chain is produced by a random motion on a circle. An explicit formula is given for the asymptotic variance of the number of 0’s in a binary Markov chain of order 2.
对1955年《马尔可夫链的似然比检验》一文的更正
‘The likelihood ratio test for Markoff ohains.’ Mr Leo A. Goodman has been kind enough to allow me to see some work that he has not yet published in which, among other things, he points out that my paper in Biometrika, 42 (1955), 531–3 contains a number of inaccuracies concerning the non-cyclic (noncircularized) case. In addition he mentions the following errata. Equation (7) should read In the last line § 5, should be replaced by . For further details the reader is referred…
列联表中小频数的估计
Summary Suppose that we require estimates of the population frequencies corresponding to small entries in a large pure contingency table containing heterogeneity. It would be natural to lump rows or columns together with weights depending on the correlation coefficients. But if the rows, say, are nearly orthogonal, no lumping method will be reasonable. Moreover, if many of the entries in the table are missing, a lumping method may fail. A method is given here (which it may…