# Bayesian estimation of the functional spatial lag model

## TL;DR

This paper introduces a Bayesian estimation approach for the functional spatial lag model, extending traditional spatial models to a functional framework and demonstrating its effectiveness through simulations and real data analysis.

## Contribution

It proposes a novel Bayesian MCMC estimation method for the functional spatial lag model, improving upon existing truncated maximum likelihood techniques.

## Key findings

- Bayesian method performs well in simulations.
- Application to Senegal data reveals meaningful spatial relationships.
- Bayesian approach offers a flexible alternative for functional spatial models.

## Abstract

The spatial lag model (SLM) has been widely studied in the literature for spatialised data modeling in various disciplines such as geography, economics, demography, regional sciences, etc. This is an extension of the classical linear model that takes into account the proximity of spatial units in modeling. The extension of the SLM model in the functional framework (the FSLM model) as well as its estimation by the truncated maximum likelihood technique have been proposed by \cite{Ahmed}. In this paper, we propose a Bayesian estimation of the FSLM model. The Bayesian MCMC technique is used as estimation methods of the parameters of the model. A simulation study is conducted in order to compare the results of the Bayesian estimation method with the truncated maximum likelihood method. As an illustration, the proposed Bayesian method is used to establish a relationship between the unemployment rate and the curves of illiteracy rate observed in the 45 departments of Senegal.