Marked doubly stochastic Poisson processes are a particular type of marked point processes that are characterized by the number of events in any time interval as being conditionally Poisson distributed, given another positive stochastic process called intensity. Here we consider a subclass of these processes in which the intensity is assumed to be a deterministic function of another nonexplosive marked point process. In particular, we will investigate an intensity jump process with an exponential decay having an analytic form for the distribution of the times and sizes of the jumps, which can be seen as a generalization of the classical shot noise process. Assuming that the intensity is unobservable, interest here is in its filtering, that is, in the computation of its conditional distribution, over a whole time interval, given an observed trajectory of realized events. Because, in general, this computation cannot be performed analytically, we propose a simulation method that provides an approximate solution, which relies on the reversible-jump Markov chain Monte Carlo algorithm. Interestingly, the proposed filtering algorithm also allows the setup of a likelihood-based procedure for the estimation of the parameters of the model based on stochastic versions of the expectation-maximization (EM) algorithm. The potential of the filtering and estimation methods proposed are illustrated through some simulation experiments as well as on a financial ultra-high-frequency dataset of intraday S&P500 futures prices.

Purpose – The purpose of this paper is to evaluate connections between the practice of mindfulness meditation and individual and organisational well-being. Design/methodology/approach – A direct randomised study conducted on a groups of persons involved in various work activities through a programme of Zen meditation courses and a comparison between the situation of well-being found before and after taking part in the courses, assessed in the light of results obtained from a control group that had not taken part in the courses. Findings – The comparison and analysis of results showed that the group of participants taking part in the meditation training obtained a significant increase in certain indicators relating in particular to subjectively perceived well-being, as regards attention and concentration as well as in a physiological indicator measuring stress reduction. Originality/value – The study brought to the place of business a tool traditionally used almost exclusively in relation to the personal sphere, evaluating its potential in terms not only of individual well-being but also in terms of efficiency and productivity.

We propose a modeling framework for ultra-high-frequency data on financial asset price movements. The models proposed belong to the class of the doubly stochastic Poisson processes with marks and allow an interpretation of the changes in price volatility and trading activity in terms of news or information arrival. Assuming that the intensity process underlying event arrivals is unobserved by market agents, we propose a signal extraction (filtering) method based on the reversible jump Markov chain Monte Carlo algorithm. Moreover, given a realization of the price process, inference on the parameters can be performed by appealing to stochastic versions of the expectation-maximization algorithm. The simulation methods proposed will be applied to the computation of hedging strategies and derivative prices.

For stationary second-order autoregressive normal processes, the conjecture of uniqueness of the solution of the exact likelihood equations is examined. A sufficient condition for uniqueness is given; this condition is satisfied with very high probability if the number of observations is not extremely small. Moreover, it is shown that not more than two maxima may exist. Examples of data which actually produce a likelihood function with two local maxima are given. Keywords. Autoregressive model; first-order autoregression, maximum likelihood; second-order autoregression; uniqueness of the maximum likelihood estimate.

SUMMARYThe investigation of spatial variation in disease rates is a standard epidemiological practice used to describe the geographic clustering of diseases which is helpful for making hypotheses about the possible 'factors' responsible for differences in risk. Up to the most recent statistical and computational developments, studies have almost entirely focused on the spatial modeling of univariate distributions of cases, that is, on the spatial modeling of single diseases. However, many diseases show similar patterns of geographical variation which may suggest the existence of common underlying risk factors, whether these are related to the environment, to particular local food habits, or to the clustering of a particular population (genetic origin). In this work, for multivariate categorical data pointwise geo-referenced in a 'geostatistical' fashion, we propose a model for the study of the joint spatial variation of more diseases. Our approach is based on a hierarchical (generalized linear mixed) multivariate model where the underlying latent structure is given by a Gaussian geostatistical spatial factor model. The methodology proposed can be seen as an extension of the geostatistical linear model of coregionalization, and of the related 'factorial kriging analysis', to the case of geo-referenced, in general multi-way, contingency tables. An application of the proposed methodology is shown on an epidemiological data set coming from an extensive survey on diabetes mellitus patients which involved the majority of the family practitioners of the region of Umbria in central Italy in 1990. Attention is centered on the study of nephropathy and retinopathy, two of the chronic diabetic complications affecting life quality and expectancy.