Reducing estimation bias in adaptively changing monitoring networks with preferential site selection

This paper explores the topic of preferential sampling, specifically situations where monitoring sites in environmental networks are preferentially located by the designers. This means the data arising from such networks may not accurately characterize the spatio-temporal field they intend to monitor. Approaches that have been developed to mitigate the effects of preferential sampling in various contexts are reviewed and, building on these approaches, a general framework for dealing with the effects of preferential sampling in environmental monitoring is proposed. Strategies for implementation are proposed, leading to a method for improving the accuracy of official statistics used to report trends and inform regulatory policy. An essential feature of the method is its capacity to learn the preferential selection process over time and hence to reduce bias in these statistics. Simulation studies suggest dramatic reductions in bias are possible. A case study demonstrates use of the method in assessing the levels of air pollution due to black smoke in the UK over an extended period (1970-1996). In particular, dramatic reductions in the estimates of the number of sites out of compliance are observed.

The Bloch-Okounkov correlation functions, a classical half-integral case

Bloch and Okounkovs correlation function on the infinite wedge space has connections to Gromov-Witten theory, Hilbert schemes, symmetric groups, and certain character functions of $hgl_infty$-modules of level one. Recent works have calculated these character functions for higher levels for $hgl_infty$ and its Lie subalgebras of classical type. Here we obtain these functions for the subalgebra of type $D$ of half-integral levels and as a byproduct, obtain $q$-dimension formulas for integral modules of type $D$ at half-integral level.

The Bloch-Okounkov correlation functions of negative levels

Bloch and Okounkov introduced an $n$-point correlation function on the fermionic Fock space and found a closed formula in terms of theta functions. This function affords several distinguished interpretations and in particular can be formulated as correlation functions on irreducible $hat{gl}_infty$-modules of level one. These correlation functions have been generalized for irreducible integrable modules of $hat{gl}_infty$ and its classical Lie subalgebras of positive levels by the authors. In this paper we extend further these results and compute the correlation functions as well as the $q$-dimensions for modules of $hat{gl}_infty$ and its classical subalgebras at negative levels.