# Maximum Likelihood Estimation for Stochastic Differential Equations Using Sequential Kriging-Based Optimization

arXiv: https://arxiv.org/abs/1408.2441 · HTML: https://mlsanity.com/paper/1408.2441/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Aug 2014.

## Built on by (most cited first, 2 of 2)

- [GFINNs: GENERIC Formalism Informed Neural Networks for Deterministic and Stochastic Dynamical Systems](https://mlsanity.com/paper/2109.00092/) (2021)
- [Efficient CNN-LSTM based Parameter Estimation of Levy Driven Stochastic Differential Equations](https://mlsanity.com/paper/2403.04246/) (2024)

## Abstract (arXiv)

Stochastic Differential Equations (SDEs) are used as statistical models in many disciplines. However, intractable likelihood functions for SDEs make inference challenging, and we need to resort to simulation-based techniques to estimate and maximize the likelihood function. While sequential Monte Carlo methods have allowed for the accurate evaluation of likelihoods at fixed parameter values, there is still a question of how to find the maximum likelihood estimate. In this article we propose an efficient Gaussian-process-based method for exploring the parameter space using estimates of the likelihood from a sequential Monte Carlo sampler. Our method accounts for the inherent Monte Carlo variability of the estimated likelihood, and does not require knowledge of gradients. The procedure adds potential parameter values by maximizing the so-called expected improvement, leveraging the fact that the likelihood function is assumed to be smooth. Our simulations demonstrate that our method has significant computational and efficiency gains over existing grid- and gradient-based techniques. Our method is applied to modeling the closing stock price of three technology firms.