On the density distribution across space: a probabilistic approach

This paper aims at providing a Bayesian parametric framework to tackle the accessibility problem across space in urban theory. Adopting continuous variables in a probabilistic setting we are able to associate with the distribution density to the Kendall's tau index and replicate the general issues related to the role of proximity in a more general context. In addition, by referring to the Beta and Gamma distribution, we are able to introduce a differentiation feature in each spatial unit without incurring in any a-priori definition of territorial units. We are also providing an empirical application of our theoretical setting to study the density distribution of the population across Massachusetts.Agglomerations, Bayesian inference, Distance, Gibbs sampling, Kendall's tau index, Population density.

Nonparametric Priors for Vectors of Survival Functions

The paper proposes a new nonparametric prior for two–dimensional vectors of survival functions (S1, S2). The definition we introduce is based on the notion of L´evy copula and it will be used to model, in a nonparametric Bayesian framework, two–sample survival data. Such an application will yield a natural extension of the more familiar neutral to the right process of Doksum (1974) adopted for drawing inferences on single survival functions. We, then, obtain a description of the posterior distribution of (S1, S2), conditionally on possibly right–censored data. As a by–product of our analysis, we find out that the marginal distribution of a pair of observations from the two samples coincides with the Marshall–Olkin or the Weibull distribution according to specific choices of the marginal L´evy measures.Bayesian nonparametrics, Completely random measures, Dependent stable processes, L´evy copulas, Posterior distribution, Right–censored data, Survival function

Nonparametric priors for vectors of survival functions

The paper proposes a new nonparametric prior for two-dimensional vectors of survival functions (S1,S2). The definition we introduce is based on the notion of Lévy copula and it will be used to model, in a nonparametric Bayesian framework, two-sample survival data. Such an application will yield a natural extension of the more familiar neutral to the right process of Doksum (1974) adopted for drawing inferences on single survival functions. We, then, obtain a description of the posterior distribution of (S1,S2), conditionally on possibly right-censored data. As a by-product of our analysis, we find out that the marginal distribution of a pair of observations from the two samples coincides with the Marshall-Olkin or the Weibull distribution according to specific choices of the marginal Lévy measures.Bayesian nonparametrics; Completely random measures; Dependent stable processes; Lévy copulas; Posterior distribution; Right-censored data; Survival function

Case-deletion importance sampling estimators: Central limit theorems and related results

Case-deleted analysis is a popular method for evaluating the influence of a subset of cases on inference. The use of Monte Carlo estimation strategies in complicated Bayesian settings leads naturally to the use of importance sampling techniques to assess the divergence between full-data and case-deleted posteriors and to provide estimates under the case-deleted posteriors. However, the dependability of the importance sampling estimators depends critically on the variability of the case-deleted weights. We provide theoretical results concerning the assessment of the dependability of case-deleted importance sampling estimators in several Bayesian models. In particular, these results allow us to establish whether or not the estimators satisfy a central limit theorem. Because the conditions we derive are of a simple analytical nature, the assessment of the dependability of the estimators can be verified routinely before estimation is performed. We illustrate the use of the results in several examples.Comment: Published in at http://dx.doi.org/10.1214/08-EJS259 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

Bayesian estimation for a parametric Markov renewal model applied to seismic data.

This paper presents a complete methodology for Bayesian inference on a semi-Markov process, from the elicitation of the prior distribution, to the computation of posterior summaries, including a guidance for its JAGS implementation. The holding times (conditional on the transition between two given states) are assumed to be Weibull-distributed. We examine the elicitation of the joint prior density of the shape and scale parameters of the Weibull distributions, deriving a specific class of priors in a natural way, along with a method for the determination of hyperparameters based on ``learning data'' and moment existence conditions. This framework is applied to data of earthquakes of three types of severity (low, medium and high size) that occurred in the central Northern Apennines in Italy and collected by the \cite{CPTI04} catalogue. Assumptions on two types of energy accumulation and release mechanisms are evaluated

BankSealer: An Online Banking Fraud Analysis and Decision Support System

Part 9: Malicious Behavior and FraudInternational audienceWe propose a semi-supervised online banking fraud analysis and decision support approach. During a training phase, it builds a profile for each customer based on past transactions. At runtime, it supports the analyst by ranking unforeseen transactions that deviate from the learned profiles. It uses methods whose output has a immediate statistical meaning that provide the analyst with an easy-to-understand model of each customer’s spending habits. First, we quantify the anomaly of each transaction with respect to the customer historical profile. Second, we find global clusters of customers with similar spending habits. Third, we use a temporal threshold system that measures the anomaly of the current spending pattern of each customer, with respect to his or her past spending behavior. As a result, we mitigate the undertraining due to the lack of historical data for building of well-trained profiles (of fresh users), and the users that change their (spending) habits over time. Our evaluation on real-world data shows that our approach correctly ranks complex frauds as “top priority”

On the density distribution across space : a probabilistic approach

This paper aims at providing a Bayesian parametric framework to tackle the accessibility problem across space in urban theory. Adopting continuous variables in a probabilistic setting we are able to associate with the distribution density to the Kendall's tau index and replicate the general issues related to the role of proximity in a more general context. In addition, by referring to the Beta and Gamma distribution, we are able to introduce a differentiation feature in each spatial unit without incurring in any a-priori definition of territorial units. We are also providing an empirical application of our theoretical setting to study the density distribution of the population across Massachusetts

Interval Change-Point Detection for Runtime Probabilistic Model Checking

Recent probabilistic model checking techniques can verify reliability and performance properties of software systems affected by parametric uncertainty. This involves modelling the system behaviour using interval Markov chains, i.e., Markov models with transition probabilities or rates specified as intervals. These intervals can be updated continually using Bayesian estimators with imprecise priors, enabling the verification of the system properties of interest at runtime. However, Bayesian estimators are slow to react to sudden changes in the actual value of the estimated parameters, yielding inaccurate intervals and leading to poor verification results after such changes. To address this limitation, we introduce an efficient interval change-point detection method, and we integrate it with a state-of-the-art Bayesian estimator with imprecise priors. Our experimental results show that the resulting end-to-end Bayesian approach to change-point detection and estimation of interval Markov chain parameters handles effectively a wide range of sudden changes in parameter values, and supports runtime probabilistic model checking under parametric uncertainty