Replicated INAR(1) processes

Replicated time series are a particular type of repeated measures, which consist of time-sequences of measurements taken from several subjects (experimental units). We consider independent replications of count time series that are modelled by first-order integer-valued autoregressive processes, INAR(1). In this work, we propose several estimation methods using the classical and the Bayesian approaches and both in time and frequency domains. Furthermore, we study the asymptotic properties of the estimators. The methods are illustrated and their performance is compared in a simulation study. Finally, the methods are applied to a set of observations concerning sunspot data.PRODEP II

On the Graded Identities for Elementary Gradings in Matrix Algebras over Infinite Fields

We find a basis for the $G$-graded identities of the $n\times n$ matrix algebra $M_n(K)$ over an infinite field $K$ of characteristic $p>0$ with an elementary grading such that the neutral component corresponds to the diagonal of $M_n(K)$

Estimation and forecasting in SUINAR(1) model

This work considers a generalization of the INAR(1) model to the panel data first order Seemingly Unrelated INteger AutoRegressive Poisson model, SUINAR(1). It presents Bayesian and classical methodologies to estimate the parameters of Poisson SUINAR(1) model and to forecast future observations of the process. In particular, prediction intervals for forecasts - classical approach - and HPD prediction intervals - Bayesian approach - are derived. A simulation study is provided to give additional insight into the finite sample behaviour of the parameter estimates and forecasts

John Polkinghorne on Divine Action: a Coherent Theological Evolution

I examine John Polkinghorne's account of how God acts in the world, focusing on how his ideas developed with the consideration of the notion of kenosis, and how this development was not a rejection of his previous ideas, but on the contrary a fulfilling of his own personal philosophical and theological insights. Polkinghorne's thought can be distinguished in three different periods:1) divine action as input of active information (1988-2000/2001);2) Polkinghorne's reception of the notion of kenosis (2000-2004);3) Polkinghorne's "thought experiment" approach to his ideas on divine action (2004- ). Finally, I consider the question of internal coherence of this theological development, focusing on the transition from the first to the second period, which I believe to be the most significant

From Extrinsic Design to Intrinsic Teleology

In this paper I offer a distinction between design and teleology, referring mostly to thehistory of these two terms, in order to suggest an alternative strategy for arguments thatintend to demonstrate the existence of the divine. I do not deal with the soundness ofeither design or teleological arguments. I rather emphasise the differences between thesetwo terms, and how these differences involve radically different arguments for the existence of the divine. I argue that the term „design‟ refers to an extrinsic feature that was in history understood to be imposed by God in nature, while one may argue for an internal tendency, what I call „teleology‟. I first offer a historical tour of design arguments and how the basic notion of design was understood in extrinsic terms. I then briefly present three kinds of objections available in history to these arguments: philosophical, scientific, and theological. I finally move to discussing an intrinsicunderstanding of teleology, and how this notion differs from that of extrinsic design. Iend the paper showing how this notion could be useful in interpreting processes innature, in particular the reproductive tendencies in living beings