BSTPP 0.1

Bayesian Spatiotemporal Point Process

## Bayesian Spatiotemporal Point Process

This package provides bayesian inference for three spatiotemporal point process models with or without spatial covariates: - Log Gaussian Cox Process (lgcp) - Hawkes Process - Cox Hawkes Process

### Usage

Install with `pip install git+https://github.com/imanring/BSTPP.git`

API documentation is in `bstpp_API_doc.pdf`.

See `demo.ipynb` for a demo.

### Model Details

The full Cox Hawkes Model is formulated as follows,

$lambda(t,s) = mu(t,s) + sum_{i:t_i < t}{alpha f(t-t_i;beta) varphi(s-s_i;sigma)}$

$f$ by default is the exponential density and $varphi$ by default is the normal density.

$mu(t,s) = exp(a_0 + X(s)w + f_s(s) + f_t(t))$

$X(s)$ is the spatial covariate matrix, and $f_s$ and $f_t$ are gaussian processes.

The Hawkes process is the same with the as the Cox Hawkes, except the background is

$mu(t,s) = exp(a_0 + X(s)w)$

Finally, the Log Gaussian Cox Process is the same as Cox Hawkes except without the self-exciting summation,

$lambda(t,s) = exp(a_0 + X(s)w + f_s(s) + f_t(t))$

### Acknowledgements

This repo is based on code from [1]. The trained decoders and encoder/decoder functions are provided by Dr Elisaveta Semenova following the proposals in [2].

[1] X. Miscouridou, G. Mohler, S. Bhatt, S. Flaxman, S. Mishra, Cox-Hawkes: Doubly stochastic spatiotemporal poisson point process, Transaction of Machine Learning Research, 2023

[2] Elizaveta Semenova, Yidan Xu, Adam Howes, Theo Rashid, Samir Bhatt, B. Swapnil Mishra, and Seth R. Flaxman. Priorvae: encoding spatial priors with variational autoencoders for small-area estimation. Royal Society Publishing, pp. 73–80, 2022