Henri Caussinus

Choosing a linear model with a random number of change-points and outliers

The problem of determining a normal linear model with possible perturbations, viz. change-points and outliers, is formulated as a problem of testing multiple hypotheses, and a Bayes invariant optimal multi-decision procedure is provided for detecting at most k (k > 1) such perturbations. The asymptotic form of the procedure is a penalized log-likelihood procedure which does not depend on the loss function nor on the prior distribution of the shifts under fairly mild assumptions. The term which penalizes too large a number of changes (or outliers) arises mainly from realistic assumptions about their occurrence. It is different from the term which appears in Akaike‘s or Schwarz‘ criteria, although it is of the same order as the latter. Some concrete numerical examples are analyzed.

SPLIDHOM: A Method for Homogenization of Daily Temperature Observations

One major concern of climate change is the possible rise of temperature extreme events, in terms of occurrence and intensity. To study this phenomenon, reliable daily series are required, for instance to compute daily-based indices: high-order quantiles, annual extrema, number of days exceeding thresholds, and so on. Because observed series are likely to be affected by changes in the measurement conditions, adapted homogenization procedures are required. Although a very large number of procedures have been proposed for adjustment of observed series at a monthly time scale, few have been proposed for adjustment of daily temperature series. This article proposes a new adjustment method for temperature series at a daily time scale. This method, called spline daily homogenization (SPLIDHOM), relies on an indirect nonlinear regression method. Estimation of the regression functions is performed by cubic smoothing splines. This method is able to adjust the mean of the series as well as high-order quantiles and moments of the series. When using well-correlated series, SPLIDHOM improves the results of two widely used methods, as a result of an optimal selection of the smoothing parameter. Applications to the Toulouse, France, temperature series are shown as a real example.

A monitoring display of multivariate outliers

A projection pursuit approach is considered for the detection and visualization of multivariate outliers, the term outlier being used in a broad sense. Such a framework leads to assess the significance of the displays themselves rather than the significance of suspected observations. The necessary mathematical results to implement this strategy are provided in the case of a generalized principal component analysis aimed to the display of discordant observations. Three examples illustrate the various aspects of the proposed technique.

Estimating the age structure of a buried adult population: A new statistical approach applied to archaeological digs in France

Paleodemographers have developed several methods for estimating the age structure of historical populations in absence of civil registration data. Starting from biological indicators alone, they use a reference population of known sex and age to assess the conditional distribution of the biological indicator given age. However, the small amount of data available and the unstable nature of the related statistical problem mean that most methods are disappointing. Using the most reliable reference data possible, we propose a simple statistical method, integrating the maximum amount of information included in the actual data, which quite significantly improves age estimates for a buried population. Here the method is applied to a French cemetery used from Late Antiquity to the end of the Early Middle Ages.

Analysing dependence in large contingency tables: Dimensionality and patterns in scatter-plots

Abstract We consider the association and the correlation models of order M for the analysis of contingency tables. We investigate some theoretical and practical implications resulting from the assumption of a latent 2 x M-dimensional normal distribution generating a two-way contingency table through discretization. We present also a class of “power models” which generalizes both models. Their common feature is to specify the interaction terms as elements of a rank M matrix. Accordingly the interactions can be visualized by means of a M-dimensional biplot.

Comparing the parameters of a model for several units by means of principal component analysis

We discuss an appropriate way of performing Principal Component Analysis when the variates are estimates of the p parameters of a given model. We give several examples of application with simulated or real life data. These include the comparison of a set of dispersion matrices and the comparison of a set of parametric growth curves.

Classification and Generalized Principal Component Analysis

In previous papers, we propose a generalized principal component analysis (GPCA) aimed to display salient features of a multidimensional data set, in particular the existence of clusters. In the light of an example, this article evidences how GPCA and clustering methods are complementary. The projections provided by GPCA and the sequence of eigenvalues give useful indications on the number and the type of clusters to be expected; submitting GPCA principal components to a clustering algorithm instead of the raw data can improve the classification. The use of a convenient robustification of GPCA is also evoked.

Estimer l'âge sans le mesurer en paléodémographie

To estimate the structure of past populations by age at death, with only biological indicators available, paleodemographers have developed several methods that rely on a reference population whose biological indicators and ages at death are known. First, we examine these approaches with their underlying assumptions, and show their weaknesses. To offset these drawbacks, we propose a new statistical method that provides a more reliable estimate of the age distribution of deaths. It is a Bayesian method, whose principle and whose practical use involve choosing a prior distribution, determining a posterior distribution, and applying credibility intervals. A simulation-based comparison with earlier methods shows the clear superiority of our approach, which we then apply to actual archaeological data. The article concludes with an overview of the main advantages of the proposed method: its flexibility and efficiency.

A note on the analysis of covariance: efficiency of concomitant variables

Abstract The paper gives an explicit formula for expressing the efficiency of the analysis of covariance, that is for measuring the improvement of a least squares estimator when concomitant variables are taken into account. In the derivation of it, a general Gauss-Markov multivariate linear model with the normality assumption for all variables is considered.Suggestions on application in the analysis of a designed experiment and of a growth curves model are given.

Atouts d'une procédure récente d'inférence bayésienne pour l'étude de l'impact des crises démographiques. Application à trois sites médiévaux bas-normands

RésuméPour mettre en lumière les caractéristiques démographiques de populations issues de contextes archéologiques, le paléodémographe doit pouvoir restituer sans biais la composition par sexe et par âge de ces populations. Nous proposons pour cela une nouvelle procédure d’inférence bayésienne qui permet d’estimer des probabilités de décès, aux âges adultes, assorties de marges d’erreur fiables. Une telle analyse appelle quelques réflexions préalables. Tout d’abord, il convient de vérifier que les différences mises en évidence entre les sites ne peuvent pas être attribuées à des artefacts méthodologiques, notamment lors de l’observation de l’indicateur biologique. Elle suppose aussi l’acceptation du principe d’uniformité biologique entre les populations historiques et les populations de référence préindustrielles. Pour illustrer l’intérêt de cette démarche, nous l’avons appliquée à trois sites bas-normands d’époque mérovingienne susceptibles d’avoir été touchés par la crise démographique des premiers siècles du Moyen Âge décrite par les chroniqueurs et les historiens. Les résultats obtenus montrent clairement que le nombre de décédés est particulièrement élevé dans la première classe d’âge. Si l’explication peut être envisagée en termes de mortalité, on peut y voir aussi l’incidence de mouvements migratoires, cette hypothèse trouvant un écho dans les sources archéologiques qui voient le haut Moyen Âge comme une période d’immigration dans la plaine de Caen.AbstractTo bring out the demographic characteristics of populations from archaeological contexts, palaeodemographers have to determine their composition by sex and age without introducing any bias. The new Bayesian inference procedure proposed here for this purpose estimates the probabilities of death, for adult age groups, coupled with reliable margins of error. Some preliminaries have to be observed before undertaking this kind of analysis. First, it should be checked that differences identified between sites cannot be attributed to methodological artefacts, especially when observing the biological indicator. Second, the procedure rests on the assumption that the principle of uniformity among biological populations and historical preindustrial reference populations is accepted. To illustrate the usefulness of this approach, we applied it to three Merovingian sites in Lower Normandy that are likely to have been affected by the demographic crisis of the early Middle Ages described by chroniclers and historians. The results clearly show that the number of deaths is particularly high in the first age class, especially among males. While this could be explained in terms of mortality, the impact of migration could also be a factor, a hypothesis that is echoed in archaeological sources that consider the early Middle Ages to be a period of immigration into the Caen lowlands.