Summary Factorization models express a statistical object of interest in terms of a collection of simpler objects. For example, a matrix or tensor can be expressed as a sum of rank-one components. However, in practice, it can be challenging to infer the relative impact of the different components as well as the number of components. A popular idea is to include infinitely many components having impact decreasing with the component index. This article is motivated by two limitations of existing methods: (i) the lack of careful consideration of the within component sparsity structure; and (ii) no accommodation for grouped variables and other non-exchangeable structures. We propose a general class of infinite factorization models that address these limitations. Theoretical support is provided, practical gains are shown in simulation studies, and an ecology application focusing on modelling bird species occurrence is discussed.

The number of latent factors, in factor analysis, is typically unknown and motivated by a rich literature on priors distributions, which progressively penalize the number of factors in infinite factor models. Adaptive Gibbs samplers that truncate the infinite factor models are typically used for posterior inference. In this paper, we introduce a novel strategy to adaptively truncate the number of factors that is more interpretable, stable and consistent, with respect to standard approaches.

Introduction: Several investigations have argued for a strong relationship between neuroinflammation and amyloid metabolism but it is still unclear whether inflammation exerts a pro-amyloidogenic effect, amplifies the neurotoxic effect of amyloid, or is protective.Methods: Forty-two patients with acute encephalitis (ENC) and 18 controls underwent an extended cerebrospinal fluid (CSF) panel of inflammatory, amyloid (Aβ40, 42, and 38, sAPP-α, sAPP-β), glial, and neuronal biomarkers. Linear and non-linear correlations between CSF biomarkers were evaluated studying conditional independence relationships.Results: CSF levels of inflammatory cytokines and neuronal/glial markers were higher in ENC compared to controls, whereas the levels of amyloid-related markers did not differ. Inflammatory markers were not associated with amyloid markers but exhibited a correlation with glial and neuronal markers in conditional independence analysis.Discussion: By an extensive CSF biomarkers analysis, this study showed that an acute neuroinflammation state, which is associated with glial activation and neuronal damage, does not influence amyloid homeostasis.

The approaches commonly used to model the number of goals in a football match are characterised by strong assumptions about the dependence between the number of goals scored by the two competing teams and about their marginal distribution. In this work, we argue that the assumptions traditionally made are not always based on solid arguments and sometimes they can be hardly justified. In light of this, we propose a modification of the Dixon and Coles (1997) model by relaxing the assumption of Poisson-distributed marginal variables and by introducing an innovative dependence structure. Specifically, we define the joint distribution of the number of goals scored during a match by means of thoroughly chosen marginal (Mar-) and conditional distributions (-Co). The resulting Mar-Co model is able to balance flexibility and conceptual simplicity. A real data application involving five European leagues suggests that the introduction of the novel dependence structure allows to capture and interpret fundamental league-specific dynamics. In terms of betting performance, the newly introduced Mar-Co model does not perform worse than the Dixon and Coles one in a traditional framework (i.e. 1-X-2 bet) and it outperforms the competing model when a more comprehensive dependence structure is needed (i.e. Under/Over 2.5 bet).

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