Room impulse response estimation is essential for tasks like speech dereverberation, which improves automatic speech recognition. Most existing methods rely on either statistical signal processing or deep neural networks designed to replicate signal processing principles. However, combining statistical and physical modeling for RIR estimation remains largely unexplored. This paper proposes a novel approach integrating both aspects through a theoretically grounded model. The RIR is decomposed into interpretable parameters: white Gaussian noise filtered by a frequency-dependent exponential decay (e.g. modeling wall absorption) and an autoregressive filter (e.g. modeling microphone response). A variational free-energy cost function enables practical parameter estimation. As a proof of concept, we show that given dry and reverberant speech signals, the proposed method outperforms classical deconvolution in noisy environments, as validated by objective metrics.