Comparative experiences of two teacher educators: a self-study

This paper focuses on the reflections of a less experienced and a veteran teacher educator at a new university and compares and contrasts their experiences of primary teacher education. The paper draws on the power of the narrative to share these experiences through aspects of self-study. Autobiographical research methods were used to elicit reflection on significant events in the teacher educators’ different and individual pasts in order to understand more about effective learning and teaching in their present roles. This process led to an examination of the values that underpinned and continue to underpin practice. The collaborative examination of significant aspects of personal practice has led to renewed confidence and implications for primary teacher education within the University. Key Words Self-study; narrative; teacher-educator; stories; values; reflection

A Comparative Study of Sparse Associative Memories

We study various models of associative memories with sparse information, i.e. a pattern to be stored is a random string of $0$s and $1$s with about $\log N$ $1$s, only. We compare different synaptic weights, architectures and retrieval mechanisms to shed light on the influence of the various parameters on the storage capacity.Comment: 28 pages, 2 figure

Posterior concentration rates for empirical Bayes procedures, with applications to Dirichlet Process mixtures

In this paper we provide general conditions to check on the model and the prior to derive posterior concentration rates for data-dependent priors (or empirical Bayes approaches). We aim at providing conditions that are close to the conditions provided in the seminal paper by Ghosal and van der Vaart (2007a). We then apply the general theorem to two different settings: the estimation of a density using Dirichlet process mixtures of Gaussian random variables with base measure depending on some empirical quantities and the estimation of the intensity of a counting process under the Aalen model. A simulation study for inhomogeneous Poisson processes also illustrates our results. In the former case we also derive some results on the estimation of the mixing density and on the deconvolution problem. In the latter, we provide a general theorem on posterior concentration rates for counting processes with Aalen multiplicative intensity with priors not depending on the data.Comment: With supplementary materia

L’écologie sociale du suicide au Québec

La fréquence exceptionnelle du suicide au Québec, depuis une trentaine d’années, est-elle généralisée, où se concentre-t-elle surtout dans sa majorité ethnoculturelle, de tradition canadienne-française ? Tandis qu’elle se stabilisait dans la région montréalaise, elle augmentait en périphérie. Est-ce dû au fait que les immigrants et les anglophones se concentrent en métropole ? Une comparaison entre les districts de CLSC de l’Île de Montréal selon leur rang sur l’échelle du suicide et sur celle d’autres indicateurs comme la langue maternelle, le statut d’immigrant, la religion, la solitude et la pauvreté, puis, plus succinctement, entre les régions du Québec, confirme que le suicide semble plus courant dans les milieux de vieille souche francophone. Mais pour en explorer davantage les raisons, il faudrait mieux comprendre comment le logement solitaire ou le faible revenu infléchissent les probabilités de se donner la mort.Is the exceptionally high frequency of suicide in Québec over the past thirty years a generalized phenomenon, or is it mainly concentrated in the ethnocultural majority, of the French-Canadian tradition? While the rate was levelling off in the Montréal region, it was increasing in the outlying areas. Is this due to the concentration of immigrants and of the English-speaking population in Québec’s largest city? A comparison between the districts of the CLSCs (local health service centres) on Montréal Island, ranked according to suicide rate, and based on other indicators such as first language, immigrant status, religion, living alone, and poverty, and then more succinctly, between the regions of Québec, seems to confirm that suicide is more common among the long-established French-speaking population. But for a further exploration of the reasons, a better understanding would be needed of how living alone or having a low income affect the probability of taking ones own lif

Scalable and adaptive variational Bayes methods for Hawkes processes

Hawkes processes are often applied to model dependence and interaction phenomena in multivariate event data sets, such as neuronal spike trains, social interactions, and financial transactions. In the nonparametric setting, learning the temporal dependence structure of Hawkes processes is generally a computationally expensive task, all the more with Bayesian estimation methods. In particular, for generalised nonlinear Hawkes processes, Monte-Carlo Markov Chain methods applied to compute the doubly intractable posterior distribution are not scalable to high-dimensional processes in practice. Recently, efficient algorithms targeting a mean-field variational approximation of the posterior distribution have been proposed. In this work, we first unify existing variational Bayes approaches under a general nonparametric inference framework, and analyse the asymptotic properties of these methods under easily verifiable conditions on the prior, the variational class, and the nonlinear model. Secondly, we propose a novel sparsity-inducing procedure, and derive an adaptive mean-field variational algorithm for the popular sigmoid Hawkes processes. Our algorithm is parallelisable and therefore computationally efficient in high-dimensional setting. Through an extensive set of numerical simulations, we also demonstrate that our procedure is able to adapt to the dimensionality of the parameter of the Hawkes process, and is partially robust to some type of model mis-specification

Bayesian estimation of nonlinear Hawkes process

Multivariate point processes (MPPs) are widely applied to model the occurrences of events, e.g., natural disasters, online message exchanges, financial transactions or neuronal spike trains. In the Hawkes process model, the probability of occurrences of future events depend on the past of the process. This model is particularly popular for modelling interactive phenomena such as disease expansion. In this work we consider the nonlinear multivariate Hawkes model, which allows to account for excitation and inhibition between interacting entities. We provide theoretical guarantees for applying nonparametric Bayesian estimation methods in this context. In particular, we obtain concentration rates of the posterior distribution on the parameters, under mild assumptions on the prior distribution and the model. These results also lead to convergence rates of Bayesian estimators. Another object of interest in event-data modelling is to infer the graph of interaction - or Granger causal graph. In this case, we provide consistency guarantees; in particular, we prove that the posterior distribution is consistent on the graph adjacency matrix of the process, as well as a Bayesian estimator based on an adequate loss function