Speaker:  Antal A. Járai (Carleton)

Title:  A forest-fire model (joint work with J. van den Berg, CWI, Amsterdam)

Abstract: Various natural phenomena produce self-similar structures characterized by probability distributions whose tail falls off as a power. It is a challenge to look for natural mechanisms that can explain the widespread occurrence of such power laws. The concept of self-organized criticality, and within that a forest-fire model proposed by physicists is an attempt in this direction. I will introduce the forest-fire model, and discuss the mathematical challenges it presents. I will discuss results for the one-dimensional model, which currently represents the only case where rigorous results have been obtained.

Speaker:   Raluca Balan (University of Ottawa)

Title:  A new class of prior distributions

Abstract:  We consider the class of random distribution functions (on the real line) which satisfy the Markov property. This class includes the neutral to the right (NR) processes and it was recently proved to be closed in the Bayesian sense. In particular, the subclass of Markov jump random distribution functions turns out to be also closed.

Speaker:   Mona Zamfirescu (Baruch College, City Univeristy of New York)

Title:  Game Approach To The Optimal Stopping Problem

Abstract:  The game approach to the theory of optimal stopping assumes there are two players, the ``controller'' and the ``stopper''. The reward of the game is a nonnegative process $Y$ with RCLL paths on a time-horizon $[0,T]$ of finite length, adapted to a filtration $\mathbf{F} = \{{\cal F}_t\}_{0 \le t \le T}$ that satisfies the ``usual conditions''. The ``controller'' is given a choice from a set of possible models in the form of a family ${\cal P}$ of probability measures, equivalent to a reference probability $Q$ on a given measurable space $(\Omega, {\cal F})$. The ``stopper'' can maximize his expected reward by choosing the optimal stopping time from the family ${\cal S}$ of all $\mathbf{F}-$stopping times. We explore two types of problems, a cooperative and a noncooperative game, as the ``controller'' may work in collaboration or in competition with the ``stopper'' and also present an application of these games in pricing American options under constraints.

Speaker:   Rafal Kulik (Univesrity of Ottawa, Postdoctoral Fellow)

Title:  Limit theorems for solution of stochastic recurrence equations with heavy tailed noise

Abstract:  We consider a stochastic recurrence equation $X_t=X_{t-1}Y_{t}+Z_{t}$ driven by i.i.d. random pairs $(Y_t,Z_t)$ under assumption that $Z_t$ is heavy tailed. We study a tail behaviour for stationary solution of this equation and a limit for corresponding point process. As a corollary, we obtain result for bilinear process considered in Davis and Resnick (1996). We mention some interesting phenomena comparing it with pure AR(1) model, i.e. $x_t=aX_{t-1}+Z_{t}$, $a$ - constant. Some generalizations to matrix recurrence equations are also given.

Speaker:   Subhash Kochar (Indian Statistical Institute, New Delhi)

Title:  Dependence orderings for order statistic and records

Abstract:  in PDF

Speaker:   Takis Merkouris (Statistics Canada)

Title:  Combining information from multiple surveys for small area estimation using generalized and optimal regression

Abstract:  There is growing interest within statistical organizations in combining comparable information from independent multiple surveys of the same population for more efficient estimation of common survey characteristics. In particular, it has been recently suggested (e.g., Rao 2003) that integration of harmonized surveys leads to increased effective sample size for the harmonized items, and, hence, to improved direct estimates for small areas. Recently developed regression techniques (Zieschang, 1990; Renssen and Nieuwenbroek, 1997; Merkouris, to appear), as well as an empirical likelihood method (Wu 2004), can produce efficient composite estimators of totals for common survey characteristics for the total population of interest. These techniques can be adapted to small area estimation. In this talk

I will outline how optimal or nearly optimal small area composite regression estimators for common survey characteristics can be constructed. Substantive issues in such combination of comparable information from independent multiple surveys will be highlighted and illustrated by examples.