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When intrinsic Gaussian random Markov field (IGRMF) priors are assumed for random effects of a latent Gaussian model, a notable issue concerns prior elicitation for the precision hyperparameters. In fact, the structure of the precision matrix could lead to the undesired feature that the same prior for different precisions imply different marginal priors for the random effects. The work is aimed at investigating this problem following a rigorous mathematical procedure, in order to propose a new strategy and compare it to a widespread solution based on matrix scaling. Finally, an application of the proposed method to a real data problem is presented.

Biological processes involve complex interactions between genes. Such interactions may be represented employing a conditional independence graph. Here, we propose the use of a PC-stable algorithm to estimate the neighbourhood of each node in the graph, thus learning its structure. We apply our algorithm to two single- cell RNA sequencing datasets, demonstrating that we can identify important genes as hub nodes in the networks.

We propose a sequential hypothesis test for the process capability index Cpmk. We compare the performance of the proposed test with the properties of the most used non-sequential test by performing a simulation study. The results indicate that the sequential test has best results in terms of power function and makes it possible to save a not negligible amount of sample size.

Bissiri et al. (2016) present a general Bayesian approach where the like- lihood is replaced more generally by a loss function, which is used to derive the posterior distribution from the prior. In this paper, we exploit this idea for learning the structure of undirected graphical models over discrete variables.

This paper proposes a comparison between uni- and multidimesional approaches to the measurement of poverty. Traditional uni-, fuzzy uni- and fuzzy multidimensional indicators are compared by means of a rank correlation analysis. The robustness of the comparison is ensured by a simulation study. Our results stress that unidimensional indicators provide partial information on the poverty condition.