Moment Priors for Bayesian Model Choice with Applications to Directed Acyclic Graphs

We propose a new method for the objective comparison of two nested models based on non-local priors. More specifically, starting with a default prior under each of the two models, we construct a moment prior under the larger model, and then use the fractional Bayes factor for a comparison. Non-local priors have been recently introduced to obtain a better separation between nested models, thus accelerating the learning behaviour, relative to currently used local priors, when the smaller model holds. Although the argument showing the superior performance of non-local priors is asymptotic, the improvement they produce is already apparent for small to moderate samples sizes, which makes them a useful and practical tool. As a by-product, it turns out that routinely used objective methods, such as ordinary fractional Bayes factors, are alarmingly slow in learning that the smaller model holds. On the downside, when the larger model holds, non-local priors exhibit a weaker discriminatory power against sampling distributions close to the smaller model. However, this drawback becomes rapidly negligible as the sample size grows, because the learning rate of the Bayes factor under the larger model is exponentially fast, whether one uses local or non-local priors. We apply our methodology to directed acyclic graph models having a Gaussian distribution. Because of the recursive nature of the joint density, and the assumption of global parameter independence embodied in our prior, calculations need only be performed for individual vertices admitting a distinct parent structure under the two graphs; additionally we obtain closed-form expressions as in the ordinary conjugate case. We provide illustrations of our method for a simple three-variable case, as well as for a more elaborate seven-variable situation. Although we concentrate on pairwise comparisons of nested models, our procedure can be implemented to carry-out a search over the space of all models.Fractional Bayes factor; Gaussian graphical model; Non-local prior; Objective Bayes network; Stochastic search; Structural learning.

Objective Bayes Factors for Gaussian Directed Acyclic Graphical Models

We propose an objective Bayesian method for the comparison of all Gaussian directed acyclic graphical models defined on a given set of variables. The method, which is based on the notion of fractional Bayes factor, requires a single default (typically improper) prior on the space of unconstrained covariance matrices, together with a prior sample size hyper-parameter, which can be set to its minimal value. We show that our approach produces genuine Bayes factors. The implied prior on the concentration matrix of any complete graph is a data-dependent Wishart distribution, and this in turn guarantees that Markov equivalent graphs are scored with the same marginal likelihood. We specialize our results to the smaller class of Gaussian decomposable undirected graphical models, and show that in this case they coincide with those recently obtained using limiting versions of hyper-inverse Wishart distributions as priors on the graph-constrained covariance matrices.Bayes factor; Bayesian model selection; Directed acyclic graph; Exponential family; Fractional Bayes factor; Gaussian graphical model; Objective Bayes;Standard conjugate prior; Structural learning. network; Stochastic search; Structural learning.

Objective Bayesian Search of Gaussian DAG Models with Non-local Priors

Directed Acyclic Graphical (DAG) models are increasingly employed in the study of physical and biological systems, where directed edges between vertices are used to model direct influences between variables. Identifying the graph from data is a challenging endeavor, which can be more reasonably tackled if the variables are assumed to satisfy a given ordering; in this case, we simply have to estimate the presence or absence of each possible edge, whose direction is established by the ordering of the variables. We propose an objective Bayesian methodology for model search over the space of Gaussian DAG models, which only requires default non-local priors as inputs. Priors of this kind are especially suited to learn sparse graphs, because they allow a faster learning rate, relative to ordinary local priors, when the true unknown sampling distribution belongs to a simple model. We implement an efficient stochastic search algorithm, which deals effectively with data sets having sample size smaller than the number of variables. We apply our method to a variety of simulated and real data sets.Fractional Bayes factor; High-dimensional sparse graph; Moment prior; Non-local prior; Objective Bayes; Pathway based prior; Regulatory network; Stochastic search; Structural learning.

Objective Bayesian Search of Gaussian DAG Models with Non-local Priors

Directed Acyclic Graphical (DAG) models are increasingly employed in the study of physical and biological systems, where directed edges between vertices are used to model direct influences between variables. Identifying the graph from data is a challenging endeavor, which can be more reasonably tackled if the variables are assumed to satisfy a given ordering; in this case, we simply have to estimate the presence or absence of each possible edge, whose direction is established by the ordering of the variables. We propose an objective Bayesian methodology for model search over the space of Gaussian DAG models, which only requires default non-local priors as inputs. Priors of this kind are especially suited to learn sparse graphs, because they allow a faster learning rate, relative to ordinary local priors, when the true unknown sampling distribution belongs to a simple model. We implement an efficient stochastic search algorithm, which deals effectively with data sets having sample size smaller than the number of variables. We apply our method to a variety of simulated and real data sets

On the comparison of regression coefficients across multiple logistic models with binary predictors

In many applied contexts, it is of interest to identify the extent to which a given association measure changes its value as different sets of variables are included in the analysis. We consider logistic regression models where the interest is for the effect of a focal binary explanatory variable on a specific response, and a further collection of binary covariates is available. We provide a methodological framework for the joint analysis of the full set of coefficients of the focal variable computed across all the models obtained by adding or removing predictors from the set of covariates. The result is obtained by applying a specific log-hybrid linear expansion of the joint distribution of the variables that implicitly comprises all the regression coefficients of interest. In this way, we obtain a method that allows one to verify, in a flexible way, a wide range of scientific hypotheses involving the comparison of multiple logistic regression coefficients both in nested and in non-nested models. The proposed methodology is illustrated through a test bed example and an empirical application

Dynamical Criticality in Gene Regulatory Networks

A well-known hypothesis, with far-reaching implications, is that biological evolution should preferentially lead to states that are dynamically critical. In previous papers, we showed that a well-known model of genetic regulatory networks, namely, that of random Boolean networks, allows one to study in depth the relationship between the dynamical regime of a living being's gene network and its response to permanent perturbations. In this paper, we analyze a huge set of new experimental data on single gene knockouts in S. cerevisiae, laying down a statistical framework to determine its dynamical regime. We find that the S. cerevisiae network appears to be slightly ordered, but close to the critical region. Since our analysis relies on dichotomizing continuous data, we carefully consider the issue of an optimal threshold choice

Unlocking Onboard SAR Processing: Focusing and Ship Detection on Sentinel-1 IW Data

This work demonstrates the possibility of enabling onboard processing of SAR data in real-time through the adoption of an innovative focusing technology coupled with object detection, using limited computational resources. Our approach aims to provide a coarse focused product onboard to unlock real-time monitoring capabilities, complementing the ground-based detailed focusing algorithms. The focusing algorithm transforms the Level-0 raw signal into Level-1 Single-Look-Complex (SLC) data. It consists of a two-layers hybrid architecture: a traditional Fast-Fourier Transform (FFT) algorithm for range processing and a Deep Neural Network (DNN), trained to solved the azimuth processing task, which provides scalability and modularity benefits. After focusing, an object detection network is trained to detect the presence of ships in the SLC data. The whole processing chain has been optimized and deployed on different embedded devices, including NVIDIA Jetson Nano, and NVIDIA Jetson Xavier, to demonstrate the feasibility of running the overall pipeline onboard the future generations of SAR missions

Growth and Photosynthetic Efficiency of Microalgae and Plants with Different Levels of Complexity Exposed to a Simulated M-Dwarf Starlight

Oxygenic photosynthetic organisms (OPOs) are primary producers on Earth and generate surface and atmospheric biosignatures, making them ideal targets to search for life from remote on Earth-like exoplanets orbiting stars different from the Sun, such as M-dwarfs. These stars emit very low light in the visible and most light in the far-red, an issue for OPOs, which mostly utilize visible light to photosynthesize and grow. After successfully testing procaryotic OPOs (cyanobacteria) under a simulated M-dwarf star spectrum (M7, 365-850 nm) generated through a custom-made lamp, we tested several eukaryotic OPOs: microalgae (Dixoniella giordanoi, Microchloropsis gaditana, Chromera velia, Chlorella vulgaris), a non-vascular plant (Physcomitrium patens), and a vascular plant (Arabidopsis thaliana). We assessed their growth and photosynthetic efficiency under three light conditions: M7, solar (SOL) simulated spectra, and far-red light (FR). Microalgae grew similarly in SOL and M7, while the moss P. patens showed slower growth in M7 with respect to SOL. A. thaliana grew similarly in SOL and M7, showing traits typical of shade-avoidance syndrome. Overall, the synergistic effect of visible and far-red light, also known as the Emerson enhancing effect, could explain the growth in M7 for all organisms. These results lead to reconsidering the possibility and capability of the growth of OPOs and are promising for finding biosignatures on exoplanets orbiting the habitable zone of distant stars