Eva Riccomagno

Causal analysis with Chain Event Graphs

As the Chain Event Graph (CEG) has a topology which represents sets of conditional independence statements, it becomes especially useful when problems lie naturally in a discrete asymmetric non-product space domain, or when much context-specific information is present. In this paper we show that it can also be a powerful representational tool for a wide variety of causal hypotheses in such domains. Furthermore, we demonstrate that, as with Causal Bayesian Networks (CBNs), the identifiability of the effects of causal manipulations when observations of the system are incomplete can be verified simply by reference to the topology of the CEG. We close the paper with a proof of a Back Door Theorem for CEGs, analogous to Pearls Back Door Theorem for CBNs.

The Geometry of Causal Probability Trees that are Algebraically Constrained

Algebraic geometry is used to study properties of a class of discrete distributions defined on trees and called algebraically constrained statistical models. This structure has advantages in studying marginal models as it is closed under learning marginal mass functions. Furthermore, it allows a more expressive and general definition of causal relationships and probabilistic hypotheses than some of those currently in use. Simple examples show the flexibility and expressiveness of this model class which generalizes discrete Bayes networks.

Algebraic Representation of Gaussian Markov Combinations

Markov combinations for structural meta-analysis problems provide a way of constructing a statistical model that takes into account two or more marginal distributions by imposing conditional independence constraints between the variables that are not jointly observed. This paper considers Gaussian distributions and discusses how the covariance and concentration matrices of the different combinations can be found via matrix operations. In essence all these Markov combinations correspond to finding a positive definite completion of the covariance matrix over the set of random variables of interest and respecting the constraints imposed by each Markov combination. The paper further shows the potential of investigating the properties of the combinations via algebraic statistics tools. An illustrative application will motivate the importance of solving problems of this type.

Modelling of Fault Detection and Diagnostics for Hybrid Bus Using Chain Graph Models

Graphical models are statistical models supported on a graph structure: nodes represent random variables, and missing edges represent probabilistic relationship of conditional independence. This makes them suited to model the behavior of complex systems that are difficult to model through mathematical equations. In this work, this possibility is exploited in a context of diagnostics and fault detection. Specifically, the fault detection problem is reduced to the evaluation of a conditional probability. The relevant conditional distribution is derived from the analysis of a suitable graphical model taking advantage of the so-called Markov properties. As a case study, we consider diagnostics of a hybrid bus, characterized by the combined use of a diesel engine and an electrical engine. The aim of the study is to verify the correct operation of the electrical system, in particular the status of the battery. Copyright

Long-range dependence in earthquake-moment release and implications for earthquake occurrence probability

Since the beginning of the 1980s, when Mandelbrot observed that earthquakes occur on ‘fractal’ self-similar sets, many studies have investigated the dynamical mechanisms that lead to self-similarities in the earthquake process. Interpreting seismicity as a self-similar process is undoubtedly convenient to bypass the physical complexities related to the actual process. Self-similar processes are indeed invariant under suitable scaling of space and time. In this study, we show that long-range dependence is an inherent feature of the seismic process, and is universal. Examination of series of cumulative seismic moment both in Italy and worldwide through Hurst’s rescaled range analysis shows that seismicity is a memory process with a Hurst exponent H ≈ 0.87. We observe that H is substantially space- and time-invariant, except in cases of catalog incompleteness. This has implications for earthquake forecasting. Hence, we have developed a probability model for earthquake occurrence that allows for long-range dependence in the seismic process. Unlike the Poisson model, dependent events are allowed. This model can be easily transferred to other disciplines that deal with self-similar processes.

Discovery of statistical equivalence classes using computer algebra

Abstract Discrete statistical models supported on labeled event trees can be specified using so-called interpolating polynomials which are generalizations of generating functions. These admit a nested representation which is a notion formalized in this paper. A new algorithm exploits the primary decomposition of monomial ideals associated with an interpolating polynomial to quickly compute all nested representations of that polynomial. It hereby determines an important subclass of all trees representing the same statistical model. To illustrate this method we analyze the full polynomial equivalence class of a staged tree representing the best fitting model inferred from a real-world dataset.

A symbolic algebra for the computation of expected utilities in multiplicative influence diagrams

Influence diagrams provide a compact graphical representation of decision problems. Several algorithms for the quick computation of their associated expected utilities are available in the literature. However, often they rely on a full quantification of both probabilistic uncertainties and utility values. For problems where all random variables and decision spaces are finite and discrete, here we develop a symbolic way to calculate the expected utilities of influence diagrams that does not require a full numerical representation. Within this approach expected utilities correspond to families of polynomials. After characterizing their polynomial structure, we develop an efficient symbolic algorithm for the propagation of expected utilities through the diagram and provide an implementation of this algorithm using a computer algebra system. We then characterize many of the standard manipulations of influence diagrams as transformations of polynomials. We also generalize the decision analytic framework of these diagrams by defining asymmetries as operations over the expected utility polynomials.

An Online Algorithm for Online Fraud Detection: Definition and Testing

Abstract Detecting anomalous pattern and data points when collecting information from online mobile devices is as important as doing it fast, reliably, online, and real time for a number of reasons including fraud detection and anomalous software behavior. We present a general-purpose (that is not context specific) strategy and develop an algorithm to address this. It is based on data-mining techniques and in crude essence, it is a statistical classifier for which the characteristics of the clusters need not to be determined stored.Detecting anomalous pattern and data points when collecting information from online mobile devices is as important as doing it fast, reliably, online, and real time for a number of reasons including fraud detection and anomalous software behavior. We present a general-purpose (that is not context specific) strategy and develop an algorithm to address this. It is based on data-mining techniques and in crude essence, it is a statistical classifier for which the characteristics of the clusters need not to be determined stored.