The penalized biclustering model and related algorithms

Biclustering is the simultaneous clustering of two related dimensions, for example, of individuals and features, or genes and experimental conditions. Very few statistical models for biclustering have been proposed in the literature. Instead, most of the research has focused on algorithms to find biclusters. The models underlying them have not received much attention. Hence, very little is known about the adequacy and limitations of the models and the efficiency of the algorithms. In this work, we shed light on associated statistical models behind the algorithms. This allows us to generalize most of the known popular biclustering techniques, and to justify, and many times improve on, the algorithms used to find the biclusters. It turns out that most of the known techniques have a hidden Bayesian flavor. Therefore, we adopt a Bayesian framework to model biclustering. We propose a measure of biclustering complexity (number of biclusters and overlapping) through a penalized plaid model, and present a suitable version of the deviance information criterion to choose the number of biclusters, a problem that has not been adequately addressed yet. Our ideas are motivated by the analysis of gene expression data.     

Scale invariance and similar invariance conditions for bankruptcy problems

A frequent motivation for the use of scale invariance in the bankruptcy literature is that it imposes that the outcome of a bankruptcy problem does not depend on the units of measurement. We show that this interpretation is not correct. Scale invariance is an invariance condition that applies when all amounts are multiplied by a constant (without change of units). With this interpretation in mind, it is natural to consider other invariance conditions, for example one that applies when all amounts are increased by the same constant. In this paper, we analyze the consequences of several invariance conditions. An erratum to this article can be found at     

Segregation, entrepreneurship and work values: the case of France

This paper studies the interaction between labour market integration, “work values” and entrepreneurial capital inside minority communities. A simple model of labour market segmentation with ethnic capítal and endogenous transmission of cultural values inside a minority group is presented. It emphasizes the role of entrepreneurial capital as an important driver of labour market integration and as a promoter of meritocratic work values inside the community. The case immigrants in France is then empirically studied as an example. We show that the contrasted labour market outcomes and work values of immigrants from Maghreb versus Southern Europe are, statistically, totally explained away by their different levels of entrepreneurial capital.     

A History of Threat in Europe and Belgium (1920–1993)

A general index of social, economic, and political threat in Europe and Belgium was developed for the years 1920 to 1993. We asked 91 Belgian historians, experts in contemporary history, to rate, on 7-point intensity scales, the extent to which each year, between 1920 to 1993, the security and existence of either Europe or Belgium was threatened. In making their judgments, the historians must integrate most of the information contained in objective data known to them as causes of fear (crime, unemployment, apprehension at starting a family, buying a car, or starting a new business, etc.). The present threat index rests on a synthetic judgment because many official objective data available to historians either are incomplete or lack conceptual coherence. The index obtained has then been compared to known objective indicators of social, economic, or political threat. We obtained Cronbach's coefficients of 0.99 for Belgian historians. Corrected for serial dependency, the threat index for Belgium is found to depend on a 5-variable subset composed of: suicide, unemployment, and balance of trade, for the positive associations; and GNP and car registrations, for the negative associations. The Pearson correlation between the threat index for Europe and Belgium is 0.95 (N = 74, p < 0.001). Just as McCann and Stewin (1990) had developed a similar tool for North America, the aim of this multi-purpose tool was to monitor the mood of Europe and Belgium over time based on evaluations made by professional historians. McCann and Stewin's (1990) threat index for the US has a Pearson correlation of 0.65 (N = 67, p < 0.001) with the European threat index. The article concludes with a discussion first on the question of the role of threat producing discourses in the perception of threat, and second, on the question of Europe as a concept.     

Capturing the re-admission process: focus on time window

In the majority of studies on patient re-admissions, a re-admission is deemed to have occurred if a patient is admitted within a time window of the previous discharge date. However, these time windows have rarely been objectively justified. We capture the re-admission process from the community using a special case of a Coxian phase-type distribution, expressed as a mixture of two generalized Erlang distributions. Using the Bayes theorem, we compute the optimal time windows in defining re-admission. From the national data set in England, we defined re-admission for chronic obstructive pulmonary disease (COPD), stroke, congestive heart failure, and hip- and thigh-fractured patients as 41, 9, 37, and 8 days, respectively. These time windows could be used to classify patients into two groups (binary response), namely those patients who are at high risk (e.g. within 41 days for COPD) and low risk of re-admission group (respectively, greater than 41 days). The generality of the modelling framework and the capability of supporting a broad class of distributions enables the applicability into other domains, to capture the process within the field of interest and to determine an appropriate time window (a cut-off value) based on evidence objectively derived from operational data.     

Panel Binary Variables and Sufficiency: Generalizing Conditional Logit

This paper extends the conditional logit approach (Rasch, Andersen, Chamberlain) used in panel data models of binary variables with correlated fixed effects and strictly exogenous regressors. In a two‐period two‐state model, necessary and sufficient conditions on the joint distribution function of the individual‐and‐period specific shocks are given such that the sum of individual binary variables across time is a sufficient statistic for the individual effect. By extending a result of Chamberlain, it is shown that root‐n consistent regular estimators can be constructed in panel binary models if and only if the property of sufficiency holds. In applied work, the estimation method amounts to quasi‐differencing the binary variables as if they were continuous variables and transforming a panel data model into a cross‐section model. Semiparametric approaches can then be readily applied.     

Formal and Informal Risk Sharing in LDCs: Theory and Empirical Evidence

We develop and estimate a model of dynamic interactions in which commitment is limited and contracts are incomplete to explain the patterns of income and consumption growth in village economies of less developed countries. Households can insure each other through both formal contracts and informal agreements, that is, self‐enforcing agreements specifying voluntary transfers. This theoretical setting nests the case of complete markets and the case where only informal agreements are available. We derive a system of nonlinear equations for income and consumption growth. A key prediction of our model is that both variables are affected by lagged consumption as a consequence of the interplay of formal and informal contracting possibilities. In a semiparametric setting, we prove identification, derive testable restrictions, and estimate the model with the use of data from Pakistani villages. Empirical results are consistent with the economic arguments. Incentive constraints due to self‐enforcement bind with positive probability and formal contracts are used to reduce this probability.     

Random walk Green kernels in the neutral Moran model conditioned on survivors at a random time to origin

In the theory of finite discrete-time birth and death chains with absorbing endpoint boundaries, the evaluation of both additive and multiplicative path functionals is made possible by their Green and λ–potential kernels. These computations are addressed in the context of such Markov chains. The application to the neutral Moran model of population genetics yields first hitting and return times. A neutral Moran bridge model, forward and backward in time, for a given total number x of survivors of a single common ancestor at some random time T to the origin of times, yields the age of a mutant allele currently observed to have x copies of itself. This forward theory of age, made possible by Green kernels, is comparable to Watterson’s backward theory of age, which makes use of the reversibility of the Moran chain.