Bayesian factor analysis for spatially correlated data: application to cancer incidence data in Scotland 2012

A hierarchical Bayesian factor model for multivariate spatially correlated data is proposed. Multiple cancer incidence data in Scotland are jointly analyzed, looking for common components, able to detect etiological factors of diseases hidden behind the data. The proposed method searches factor scores incorporating a dependence within observations due to a geographical structure. The great flexibility of the Bayesian approach allows the inclusion of prior opinions about adjacent regions having highly correlated observable and latent variables. The proposed model is an extension of a model proposed by Rowe (2003a) and starts from the introduction of separable covariance matrix for the observations. A Gibbs sampling algorithm is implemented to sample from the posterior distributions

The Local Galaxy Density and the Arm Class of Spiral Galaxies

We have examined the effect of the environmental density on the arm classification of an extensive sample of spiral galaxies included in the Nearby Galaxy Catalog (Tully, 1988a). We have also explored the dependence of the arm class of a galaxy on other factors, such as its blue absolute magnitude and its disk-to-total mass ratio, inferred in the literature either from the gradient of a good galaxy rotation curve or from a photometric mass decomposition method. We have found that the arm class is strongly related to the absolute magnitude in the mid-type spirals (in the sense that grand design galaxies are, on average, more luminous than flocculent objects), whilst this relation is considerably weaker in the early and late types. In general the influence of the local density on the arm structure appears to be much weaker than that of the absolute magnitude. The local density acts essentially in strengthening the arm class--absolute magnitude relation for the mid types, whereas no environmental density effects are observed in the early and late types. Using the most recent estimates of the disk-to-total mass ratio, we do not confirm this ratio to be a significant factor which affects the arm class; nevertheless, owing to poor statistics and large uncertanties, the issue remains open. Neither a local density effect nor an unambiguous bar effect on the disk-to-total mass ratio is detectable; the latter finding may challenge some theoretical viewpoints on the formation of bar structures.Comment: 15 pages, Latex, SISSA 102/93/A openbib.sty and 4 POSTSCRIPT figures appende

Galaxies in group and field environments: a comparison of optical-NIR luminosities and colors

We compare properties of galaxies in loose groups with those in field environment by analyzing the Nearby Optical Galaxy (NOG) catalog of galaxy systems. We consider as group galaxies, objects belonging to systems with at least five members identified by means of the "friends of friends method", and, as field galaxies, all galaxies with no companions. We analyze both a magnitude--limited sample of 959 and 2035 galaxies (groups vs. field galaxies, respectively, B<14 mag, and 2000<cz<6000 km/s) and a volume-limited sample (M_B <-19.01 mag, 2000<cz<4000 km/s 369 group and 548 field galaxies). For all these galaxies, blue corrected magnitudes and morphological types are available. The cross-correlation of NOG with the 2MASS second release allow us to assign K magnitudes and obtain B-K colors for about half of the galaxies in our samples. We analyze luminosity and color segregation-effects in relation with the morphological segregation. For both B and K bands, we find that group galaxies are, on average, more luminous than field galaxies and this effect is not entirely a consequence of the morphological segregation. After taking into account the morphological segregation, the luminosity difference between group and field galaxies is about 10%. When considering only very early-type galaxies (T<-2) the difference is larger than 30%. We also find that group galaxies are redder than field galaxies, Delta(B-K) about 0.4 mag. However, after taking into account the morphological segregation, we find a smaller B-K difference, poorly significant (only at the c.l. of about 80%).Comment: 11 pages, 10 eps figures, A&A in pres

The Mass Function of Nearby Galaxy Clusters

We present the distribution of virial masses for nearby galaxy clusters, as obtained from a data-set of 75 clusters, each having at least 20 galaxy members with measured redshifts within 1 Abell radius. After having accounted for problems of incompleteness of the data-set, we fitted a power-law to the cluster mass distribution.Comment: 10 pages (2 figures not included, available upon request), LATEX, Ref.SISSA 54/93/

Evolution of the Internal Dynamics of Galaxy Clusters

We consider a sample of 51 distant galaxy clusters at 0.15 about 0.3), each cluster having at least 10 galaxies with available redshift in the literature. We select member galaxies, analyze the velocity dispersion profiles, and evaluate in a homogeneous way cluster velocity dispersions and virial masses. We apply the same procedures already recently applied on a sample of nearby clusters (z<0.15, Girardi et al. 1998b) in order to properly analyze the possible dynamical evolution of galaxy clusters. We remark problems induced by the poor sampling and the small spatial extension of the sampled cluster region in the computation of velocity dispersion. We do not find any significant difference between nearby and distant clusters. In particular, we consider the galaxy spatial distribution, the shape of the velocity dispersion profile, and the relations between velocity dispersion and X-ray luminosity and temperature. Our results imply little dynamical evolution in the range of redshift spanned by our cluster sample, and suggest that the typical redshift of cluster formation is higher than that of the sample we analyze

Congruences of lines in P5\mathbb{P}^5, quadratic normality, and completely exceptional Monge-Amp\`ere equations

The existence is proved of two new families of locally Cohen-Macaulay sextic threefolds in $\mathbb{P}^5$, which are not quadratically normal. These threefolds arise naturally in the realm of first order congruences of lines as focal loci and in the study of the completely exceptional Monge-Amp\`ere equations. One of these families comes from a smooth congruence of multidegree $(1,3,3)$ which is a smooth Fano fourfold of index two and genus 9.Comment: 16 page

Bayesian correlated factor analysis of socio-demographic indicators

Recent changes in European family dynamics are often linked to common latent trends of economic and ideational change. Using Bayesian factor analysis, we extract three latent variables from eight socio-demographic indicators related to family formation, dissolution, and gender system and collected on 19 European countries within four periods (1970, 1980, 1990, 1998). The flexibility of the Bayesian approach allows us to introduce an innovative temporal factor model, adding the temporal dimension to the traditional factorial analysis. The underlying structure of the Bayesian factor model proposed reflects our idea of an autoregressive pattern in the latent variables relative to adjacent time periods. The results we obtain are consistent with current interpretations in European demographic trends

A Bayesian Factor Model for Spatial Panel Data with a Separable Covariance Approach

A hierarchical Bayesian factor model for multivariate spatially and temporally correlated data is proposed. This method searches factor scores incorporating a dependence within observations due to both a geographical and a temporal structure and it is an extension of a model proposed by Mezzetti (2012) using the results of a separable covariance matrix for the spatial panel data as in Leorato and Mezzetti (2016). A Gibbs sampling algorithm is implemented to sample from the posterior distributions. We illustrate the benefit and the performance of our model by analyzing death rates for different diseases together with some socio-economical and behavioural indicators and by analyzing simulated data