# Continuous Inference for Aggregated Point Process Data

## TL;DR

This paper proposes continuous spatiotemporal models for aggregated count data, improving inference accuracy over traditional discrete models, with applications in epidemiology and political boundary analysis.

## Contribution

It introduces novel methods for continuous inference on aggregated counts, accommodating changing and uncertain aggregation units over time.

## Key findings

- Enhanced spatial prediction of malaria incidence in Namibia.
- Improved forecasting of voting patterns under boundary changes.
- Demonstrated advantages over traditional discrete models.

## Abstract

This article introduces new methods for inference with count data registered on a set of aggregation units. Such data are omnipresent in epidemiology due to confidentiality issues: it is much more common to know the county in which an individual resides, say, than know their exact location in space. Inference for aggregated data has traditionally made use of models for discrete spatial variation, for example conditional autoregressive models (CAR). We argue that such discrete models can be improved from both a scientific and inferential perspective by using spatiotemporally continuous models to directly model the aggregated counts. We introduce methods for delivering (limiting) continuous inference with spatitemporal aggregated count data in which the aggregation units might change over time and are subject to uncertainty. We illustrate our methods using two examples: from epidemiology, spatial prediction malaria incidence in Namibia; and from politics, forecasting voting under the proposed changes to parlimentary boundaries in the United Kingdom.