Jean-Marc Bernard

An introduction to the imprecise Dirichlet model for multinomial data

The imprecise Dirichlet model (IDM) was recently proposed by Walley as a model for objective statistical inference from multinomial data with chances @q. In the IDM, prior or posterior uncertainty about @q is described by a set of Dirichlet distributions, and inferences about events are summarized by lower and upper probabilities. The IDM avoids shortcomings of alternative objective models, either frequentist or Bayesian. We review the properties of the model, for both parametric and predictive inferences, and some of its recent applications to various statistical problems.

Length Representation in Normal and Neglect Subjects with Opposite Reading Habits Studied Through a Line Extension Task

In the first part of this paper, 45 French (left-to-right readers) and 30 Israeli (right-to-left readers) normal dextrals were given half a line and requested to construct the missing other with the same length (either the left one or the right one). Using this line extension task, a significant effect of reading habits on the performance was found, with no significant bias for Israeli subjects, and a significant underconstruction when building the left half from the right one for French subjects. In the second part, two patients with opposite reading habits (one French, one Israeli) suffering from left unilateral neglect were submitted to the same protocol. Both patients were found to under-construct the right half of the line from the left given half, and to over-construct the left half from the right given one, hence reproducing the well-known line bisection bias. Results are discussed with regard to enhancement and activation hypotheses, and current theories of the neglect syndrome.

Shared picture-book reading: A sequential analysis of adult-child verbal interactions

The purpose of this study was to determine whether adults and children influence each others representations of objects or events during joint picture-book reading. It was hypothesized that each partner adjusts his or her point of view on objects in order to share knowledge about pictures in the book. Seventeen adult/3-year-old child dyads were filmed during a reading session in a day-care centre. Sequences of child-adult and adult-child utterances were considered within exchanges on a common topic and were classified according to the level of abstraction conveyed. A novel Bayesian method for the analysis of directional dependencies revealed that the level of abstraction a partner adopts depends on the level that the other partner has just expressed. A constant reciprocal adaptation is attested by the overrepresentation of sequences of partners’ utterances belonging to the same level. Moreover, adults raise the level of abstraction more often than children, creating a ‘zone of proximal development’. Adults thus appear to stimulate the childs representational abilities since the child is found to follow the adult when the latter changes the level of abstraction.

Implicative analysis for multivariate binary data using an imprecise Dirichlet model

Abstract Bayesian implicative analysis was proposed for summarizing the association in a 2×2 contingency table in possibly asymmetrical terms such as “presence of feature a implies, usually, presence of feature b ” (“ a quasi-implies b ” in short). Here, we consider the multivariate version of this problem: having n units which are classified according to q binary questions, we want to summarize the association between questions in terms of quasi-implications between features. We will first show how, at a descriptive level, the notion of implication can be weakened into that of quasi-implication. The inductive step assumes that the n units are a sample from a 2 q -multinomial population. Uncertainty about the patterns’ true frequencies is expressed by an imprecise Dirichlet model which yields upper and lower posterior probabilities for any quasi-implicative statement. This model is shown to have several advantages over the Bayesian models based on a single Dirichlet prior, especially when 2 q is large and many patterns are thus unobserved by design.

Nonprobabilistic Statistical Inference: A Set-Theoretic Approach

Abstract The familiar sampling procedures of statistical inference can be recast within a purely set-theoretic (ST) framework, without resorting to probabilistic prerequisites. This article is an introduction to the ST approach of statistical inference, with emphasis on its attractiveness for teaching. The main points treated are unsophisticated ST significance testing and ST inference for a relative frequency (proportion).