MML clustering of multi-state,Poisson, von Mises circular and Gaussian distributions

Minimum Message Length (MML) is an invariant Bayesian point estimation technique which is also statistically consistent and efficient. We provide a brief overview of MML inductive inference (Wallace C.S. and Boulton D.M. 1968. Computer Journal, 11: 185–194; Wallace C.S. and Freeman P.R. 1987. J. Royal Statistical Society (Series B), 49: 240–252; Wallace C.S. and Dowe D.L. (1999). Computer Journal), and how it has both an information-theoretic and a Bayesian interpretation. We then outline how MML is used for statistical parameter estimation, and how the MML mixture modelling program, Snob (Wallace C.S. and Boulton D.M. 1968. Computer Journal, 11: 185–194; Wallace C.S. 1986. In: Proceedings of the Nineteenth Australian Computer Science Conference (ACSC-9), Vol. 8, Monash University, Australia, pp. 357–366; Wallace C.S. and Dowe D.L. 1994b. In: Zhang C. et al. (Eds.), Proc. 7th Australian Joint Conf. on Artif. Intelligence. World Scientific, Singapore, pp. 37–44. See http://www.csse.monash.edu.au/-dld/Snob.html) uses the message lengths from various parameter estimates to enable it to combine parameter estimation with selection of the number of components and estimation of the relative abundances of the components. The message length is (to within a constant) the logarithm of the posterior probability (not a posterior density) of the theory. So, the MML theory can also be regarded as the theory with the highest posterior probability. Snob currently assumes that variables are uncorrelated within each component, and permits multi-variate data from Gaussian, discrete multi-category (or multi-state or multinomial), Poisson and von Mises circular distributions, as well as missing data. Additionally, Snob can do fully-parameterised mixture modelling, estimating the latent class assignments in addition to estimating the number of components, the relative abundances of the parameters and the component parameters. We also report on extensions of Snob for data which has sequential or spatial correlations between observations, or correlations between attributes.     

航空动力装置两类典型起动故障分析

航空动力装置的起动是维护人员的一项经常性工作,能否开得动,对飞行器能否完成任务是至关重要的。本文对某航空动力装置在起动过程中常遇的故障进行分析,为排故人员判断该型发动机起动故障提供了理论依据,为机务人员实际排故提供了有价值的参考。     

脚本理论对话语理解的解释力——兼论ST与AT的互补性

话语理解是一个认知推理的过程。文章试以ST和AT为视点来解读话语理解过程，并提出话语理解的成功解读不仅依赖于以“预料”为基础的概念和脚本，同时，依赖于语境的顺应。文章同时指出，ST与AT在话语理解中具有互补性。只有把两者结合起来，才能对话语的理解有更强的解释力。为此，文章提出了一个认知示意图。     

Exponential progressive step-stress life-testing with link function based on Box–Cox transformation

In order to quickly extract information on the life of a product, accelerated life-tests are usually employed. In this article, we discuss a k-stage step-stress accelerated life-test with M-stress variables when the underlying data are progressively Type-I group censored. The life-testing model assumed is an exponential distribution with a link function that relates the failure rate and the stress variables in a linear way under the Box–Cox transformation, and a cumulative exposure model for modelling the effect of stress changes. The classical maximum likelihood method as well as a fully Bayesian method based on the Markov chain Monte Carlo (MCMC) technique is developed for inference on all the parameters of this model. Numerical examples are presented to illustrate all the methods of inference developed here, and a comparison of the ML and Bayesian methods is also carried out.     

Simple and Globally Convergent Methods for Accelerating the Convergence of Any EM Algorithm

Abstract.  The expectation-maximization (EM) algorithm is a popular approach for obtaining maximum likelihood estimates in incomplete data problems because of its simplicity and stability (e.g. monotonic increase of likelihood). However, in many applications the stability of EM is attained at the expense of slow, linear convergence. We have developed a new class of iterative schemes, called squared iterative methods (SQUAREM), to accelerate EM, without compromising on simplicity and stability. SQUAREM generally achieves superlinear convergence in problems with a large fraction of missing information. Globally convergent schemes are easily obtained by viewing SQUAREM as a continuation of EM. SQUAREM is especially attractive in high-dimensional problems, and in problems where model-specific analytic insights are not available. SQUAREM can be readily implemented as an 'off-the-shelf' accelerator of any EM-type algorithm, as it only requires the EM parameter updating. We present four examples to demonstrate the effectiveness of SQUAREM. A general-purpose implementation (written in R) is available.     

A Bayesian model for multinomial sampling with misclassified data

In this paper the issue of making inferences with misclassified data from a noisy multinomial process is addressed. A Bayesian model for making inferences about the proportions and the noise parameters is developed. The problem is reformulated in a more tractable form by introducing auxiliary or latent random vectors. This allows for an easy-to-implement Gibbs sampling-based algorithm to generate samples from the distributions of interest. An illustrative example related to elections is also presented.     

On the Order of Data Reductions by Ancillarity and by Sufficiency

In the context of frequentist inference there are strong arguments in favour of data reduction by both (a) conditioning on the most appropriate ancillary statistic and (b) restricting attention to a minimal sufficient statistic. However, significantly for the study of the foundations of frequentist inference, there are some examples in which the order of application of these data reductions has an important bearing on the statistical inference of interest. This paper presents a new simple example of this kind.     

Nonparametric adaptive likelihood weights

The weighted likelihood can be used to make inference about one population when data from similar populations are available. The author shows heuristically that the weighted likelihood can be seen as a special case of the entropy maximization principle. This leads him to propose the minimum averaged mean squared error (MAMSE) weights. He describes an algorithm for calculating these weights and shows its convergence using the Kuhn‐Tucker conditions. He explores the performance and properties of the weighted likelihood based on MAMSE weights through simulations.     

In-Sample or Out-of-Sample Tests of Predictability: Which One Should We Use?

Abstract

It is widely known that significant in-sample evidence of predictability does not guarantee significant out-of-sample predictability. This is often interpreted as an indication that in-sample evidence is likely to be spurious and should be discounted. In this paper, we question this interpretation. Our analysis shows that neither data mining nor dynamic misspecification of the model under the null nor unmodelled structural change under the null are plausible explanations of the observed tendency of in-sample tests to reject the no-predictability null more often than out-of-sample tests. We provide an alternative explanation based on the higher power of in-sample tests of predictability in many situations. We conclude that results of in-sample tests of predictability will typically be more credible than results of out-of-sample tests.     

The posterior distribution of the fixed and random effects in a mixed-effects linear model

The subject of this paper is Bayesian inference about the fixed and random effects of a mixed-effects linear statistical model with two variance components. It is assumed that a priori the fixed effects have a noninformative distribution and that the reciprocals of the variance components are distributed independently (of each other and of the fixed effects) as gamma random variables. It is shown that techniques similar to those employed in a ridge analysis of a response surface can be used to construct a one-dimensional curve that contains all of the stationary points of the posterior density of the random effects. The “ridge analysis” (of the posterior density) can be useful (from a computational standpoint) in finding the number and the locations of the stationary points and can be very informative about various features of the posterior density. Depending on what is revealed by the ridge analysis, a multivariate normal or multivariate-t distribution that is centered at a posterior mode may provide a satisfactory approximation to the posterior distribution of the random effects (which is of the poly-t form).