Improving Convergence of the HastingsMetropolis Algorithm with an Adaptive Proposal

The HastingsMetropolis algorithm is a general MCMC method for sampling from a density known up to a constant. Geometric convergence of this algorithm has been proved under conditions relative to the instrumental (or proposal) distribution. We present an inhomogeneous HastingsMetropolis algorithm for which the proposal density approximates the target density, as the number of iterations increases. The proposal density at the n th step is a non-parametric estimate of the density of the algorithm, and uses an increasing number of i.i.d. copies of the Markov chain. The resulting algorithm converges (in n ) geometrically faster than a HastingsMetropolis algorithm with any fixed proposal distribution. The case of a strictly positive density with compact support is presented first, then an extension to more general densities is given. We conclude by proposing a practical way of implementation for the algorithm, and illustrate it over simulated examples.     

Design and implementation methodology based on Petri net formalism of flexible manufacturing systems control

This paper presents an aided design methodology of flexible manufacturing system control with a view to industrial implementation. The approach considered through a modelling phase, the a validation phase by simulation and finally a distributed implementation phase. In the modelling phase, based on the Petri net formalism, we demonstrate the hierarchical aspect which separates the part flow control and the product resource control. In addition, we emphasize generic aspects which allow us to use an object-oriented approach. These aspects and the set of modelled objects are directly used in the simulation and production phases after an automatic translation in an implementation language (ADA in our case). In consequence, the distributed location for those two phases is well facilitated from the viewpoint of the approach used.     

Taking into account the rescheduling problem during the scheduling phase

The scheduling problem in production management has been studied for a considerable time, and several types of software are used. A problem arises in updating the production planning, or ‘rescheduling’, when an unexpected event occurs in the shop control. Solving this problem is difficult because the implications of such events are usually impossible to forecast. To prevent this problem, we propose to manipulate a set of equivalent schedules during the short time schedule. Then, if an unexpected event prevents realization of a given schedule, it will be possible to find an equivalent one, without full rescheduling. The primary requirement is to find a formal representation of a set of schedules. This has already been explored using CPM graphs with nodes associated to a set of tasks. We propose in this paper to use an extension of such graphs, PQR trees, that represent both precedence and group constraints. We first reiterate the notion of PQR trees. We present methods to take into account date constraints in such a structure, and we give a model for the general job-shop problem.     

Anthropologie économique des communautés indigenes de la Sierra Norte de Puebla (Mexique) 2: Les villages de haute montagne

In a preceding article, the author has shown how Indian communities of the tierra templada have been transformed by a century of coffee-growing. Those of the adjacent highlands, although linked to the latter by language and a long cultural tradition, have known a different evolution. Until a generation ago the absence of any important cash crop has meant little inner social differentiation: the subsistence growing of maize alternating, for most Indians, with migrant wage labour. The typical class structure is here much more complex than in the lower zone, since it opposes the peasant both to the bourgeoisie of the Lowlands, as a migrant farm labourer, and to the petty bourgeoisie of merchants and landowners in the Sierra, as a customer and a share-cropper. The latter opposition reveals itself both in the classical “ethnic” form (mestizo vs. Indians) and as a political opposition between the county town (mestizo) and the Indian villages. For a few decades, diversification of production activities and relations of production linked with these have lead to a far greater structural variation in the villages than is the case in the coffee-growing area. Dans un article précédent l'auteur a montré comment les communautés indigènes de tierra templada s'étaient transformées sous 1'impact de la culture du café. Celles de la haute montagne adjacente, très apparentées aux premières, linguistiquement et culturellement, ont connu une évolution fort différente. Jusqu’à une époque toute récente, l'absence de production commerciale importante s'est traduite par une faible différenciation interne des classes: la culture vivrière du maïs se combinant, pour la majorité des Indiens, avec le travail salarié migratoire à la côte. La structure de classes caractéristique est ici plus complexe qu'en basse montagne puisqu'elle oppose le paysan indien, comme ouvrier agricole saison-nier, à la grande bourgeoisie de la côte et comme metayer/client à la petite bourgeoisie marchande et terrienne de la Sierra. Cette dernière opposition se manifeste, à la fois sous la forme « ethnique » classique (Metis/Indiens) et comme opposition politique entre le chef-lieu métis et les villages indiens. Depuis quelques décennies, la diversification des activités productives et des rapports de production qui s'y rattachent, entraine une variation beaucoup plus grande dans les structures sociales villageoises qu'en basse montagne.     

A Non‐Parametric Estimator of the Spectral Density of a Continuous‐Time Gaussian Process Observed at Random Times

Abstract. In numerous applications data are observed at random times and an estimated graph of the spectral density may be relevant for characterizing and explaining phenomena. By using a wavelet analysis, one derives a non‐parametric estimator of the spectral density of a Gaussian process with stationary increments (or a stationary Gaussian process) from the observation of one path at random discrete times. For every positive frequency, this estimator is proved to satisfy a central limit theorem with a convergence rate depending on the roughness of the process and the moment of random durations between successive observations. In the case of stationary Gaussian processes, one can compare this estimator with estimators based on the empirical periodogram. Both estimators reach the same optimal rate of convergence, but the estimator based on wavelet analysis converges for a different class of random times. Simulation examples and an application to biological data are also provided.     

Regularized Posteriors in Linear Ill‐Posed Inverse Problems

Abstract. We study the Bayesian solution of a linear inverse problem in a separable Hilbert space setting with Gaussian prior and noise distribution. Our contribution is to propose a new Bayes estimator which is a linear and continuous estimator on the whole space and is stronger than the mean of the exact Gaussian posterior distribution which is only defined as a measurable linear transformation. Our estimator is the mean of a slightly modified posterior distribution called regularized posterior distribution. Frequentist consistency of our estimator and of the regularized posterior distribution is proved. A Monte Carlo study and an application to real data confirm good small‐sample properties of our procedure.     

Choice between Semi-parametric Estimators of Markov and Non-Markov Multi-state Models from Coarsened Observations

Abstract.  We consider models based on multivariate counting processes, including multi-state models. These models are specified semi-parametrically by a set of functions and real parameters. We consider inference for these models based on coarsened observations, focusing on families of smooth estimators such as produced by penalized likelihood. An important issue is the choice of model structure, for instance, the choice between a Markov and some non-Markov models. We define in a general context the expected Kullback–Leibler criterion and we show that the likelihood-based cross-validation (LCV) is a nearly unbiased estimator of it. We give a general form of an approximate of the leave-one-out LCV. The approach is studied by simulations, and it is illustrated by estimating a Markov and two semi-Markov illness–death models with application on dementia using data of a large cohort study.     

Semiparametric Estimation of a Two-component Mixture Model where One Component is known

Abstract.  We consider a two-component mixture model where one component distribution is known while the mixing proportion and the other component distribution are unknown. These kinds of models were first introduced in biology to study the differences in expression between genes. The various estimation methods proposed till now have all assumed that the unknown distribution belongs to a parametric family. In this paper, we show how this assumption can be relaxed. First, we note that generally the above model is not identifiable, but we show that under moment and symmetry conditions some 'almost everywhere' identifiability results can be obtained. Where such identifiability conditions are fulfilled we propose an estimation method for the unknown parameters which is shown to be strongly consistent under mild conditions. We discuss applications of our method to microarray data analysis and to the training data problem. We compare our method to the parametric approach using simulated data and, finally, we apply our method to real data from microarray experiments.     

INSTITUTIONAL CHANGE AND THE VELOCITY OF MONEY: A CENTURY OF EVIDENCE

We study common features in the income velocity of money, income, and interest rates for Canada, the U.S., the U.K., Sweden and Norway using annual data from 1870. The recently developed and refined techniques of testing for cointegration are employed.
The evidence suggests there is a unique long-run relationship in velocity but not in income and interest rates. Moreover, we find that only a model which includes institutional change proxies is properly specified. We argue that the evidence is best interpreted in the context of common historical developments in the respective countries' financial systems.