# Multi-level methods for discrete state modelling of chemical systems

**Ruth Baker
**

Mathematical Institute

University of Oxford

Oxford, United Kingdom

### Abstract:

The multi-level method for discrete state systems, first introduced by Anderson and Higham in 2012 is a highly efficient simulation technique that can be used to elucidate statistical characteristics of biochemical reaction networks. A single point estimator is produced in a cost-effective manner by combining a number of estimators of differing accuracy in a telescoping sum. The first term in the sum is calculated using an approximate stochastic simulation algorithm, and can be calculated quickly but is of significant bias. Subsequent terms successively correct this bias by combining estimators from approximate stochastic simulations algorithms of increasing accuracy, until a desired level of accuracy is reached. In this talk I will present several significant refinements of the multi-level method that render it easier to understand and implement, and, importantly, make it more efficient.