Efficient Parameter Inference for Stochastic Chemical Kinetics

Sammanfattning: Parameter inference for stochastic systems is considered as one of the fundamental classical problems in the domain of computational systems biology. The problem becomes challenging and often analytically intractable with the large number of uncertain parameters. In this scenario, Markov Chain Monte Carlo (MCMC) algorithms have been proved to be highly effective. For a stochastic system, the most accurate description of the kinetics is given by the Chemical Master Equation (CME). Unfortunately, analytical solution of CME is often intractable even for considerably small amount of chemically reacting species due to its super exponential state space complexity. As a solution, Stochastic Simulation Algorithm (SSA) using Monte Carlo approach was introduced to simulate the chemical process defined by the CME. SSA is an exact stochastic method to simulate CME but it also suffers from high time complexity due to simulation of every reaction. Therefore computation of likelihood function (based on exact CME) in MCMC becomes expensive which alternately makes the rejection step expensive. In this generic work, we introduce different approximations of CME as a pre-conditioning step to the full MCMC to make rejection cheaper. The goal is to avoid expensive computation of exact CME as far as possible. We show that, with effective pre-conditioning scheme, one can save a considerable amount of exact CME computations maintaining similar convergence characteristics. Additionally, we investigate three different sampling schemes (dense sampling, longer sampling and i.i.d sampling) under which convergence for MCMC using exact CME for parameter estimation can be analyzed. We find that under i.i.d sampling scheme, better convergence can be achieved than that of dense sampling of the same process or sampling the same process for longer time. We verify our theoretical findings for two different processes: linear birth-death and dimerization.Apart from providing a framework for parameter inference using CME, this work also provides us the reasons behind avoiding CME (in general) as a parameter estimation technique for so long years after its formulation