Stochastic Modelling for Systems Biology

By Darren J. Wilkinson. 2006

1,035 citations recorded by the source corpus.

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In Molecular Biology

Citations in the corpus

Causal Models for Dynamical Systems (2020, background): “Formally, a general reaction [e.g. Wilkinson, 2006] takes the form where r is the number of reactants and p the number of products.”
Causal interpretation of stochastic differential equations (2013, methodology): “The first result, Lemma A.1, is an elementary yet crucial result about interventions in discrete time Markov chains, allowing us to use the Euler scheme to prove Theorem 5.3.”
Deep and Hierarchical Implicit Models (2017, positive): “We use variational inference (Jordan et al., 1999).”
Bayesian computation: a perspective on the current state, and sampling backwards and forwards (2015, methodology): “Now, reﬂecting upon the evolution of MCMC meth-ods over the 25 or so years they have been at the fore-front of Bayesian inference, the focus has evolved a long way, from hierarchical models that extended the linear, mixed and generalised linear models (Albert 1988; Carlin et al. 1992; Bennett et al.”
Stability analysis for stochastic hybrid systems: A survey (2014, neutral): “, 2013a; Bohacek, Hespanha, Lee, & Obraczka, 2003; Donkers, Heemels, Van De Wouw, & Hetel, 2011; Hespanha, 2004, 2005, 2007; Hespanha, Bohacek, Obraczka, & Lee, 2001; Tabbara & Nesic, 2008), biological systems (Batt et al., 2005; De Jong et al., 2003; Ghosh & Tomlin, 2001; Hu, Wu, & Sastry, 2004; Kæ”
Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows (2018, methodology): “3 Lotka–Volterra population model The Lotka–Volterra model [10] is a Markov jump process describing the evolution of a population of predators interacting with a population of prey, and has four parameters θ = (θ1, .”
Quantifying intrinsic and extrinsic noise in gene transcription using the linear noise approximation: An application to single cell data (2013, methodology): “However, here we give a simplified derivation of the LNA by Wallace (2010) [see also Wilkinson (2011)] which is less general than Kurtz (1971) but more intuitive, as it treats births and deaths separately.”
Network Inference and Biological Dynamics (2011, background): “On the other hand, Wilkinson (2006); Wilkinson (2009) discusses a number of general issues relating to stochastic modeling for systems biology, but does not discuss network inference per se in detail.”
Relativistic Brownian Motion (2008, background): “A few recent papers [22, 195, 196, 197, 198, 199, 200] have raised doubts about the correctness of Jüttner’s results [186, 194], but relativistic molecular dynamics simulations confirm Jüttner’s prediction [201, 202], cf. discussion in Sections 3.2.2 and 4.3 below.”
Hierarchical Implicit Models and Likelihood-Free Variational Inference (2017, methodology): “For example, in population ecology, the Lotka-Volterra model simulates predator-prey populations over time via a stochastic differential equation [55].”
Learning Large Scale Ordinary Differential Equation Systems (2017, background): “This setting arises for instance in systems biology with biochemical reactions and molecular networks (Wilkinson 2006, Oates & Mukherjee 2012, Babtie et al. 2014, Hill et al. 2016), where a reaction network or a gene regulatory network may either be partially known or completely unknown.”
A Continuous Time Framework for Discrete Denoising Models (2022, methodology): “by using Gillespie’s Algorithm [21, 22, 23]) would be inefficient for large D, because we would need to step through each transition individually and so only one dimension would change for each simulation step.”
BayesFlow: Learning Complex Stochastic Models With Invertible Neural Networks (2020, background): “The LV model describes the dynamics of biological systems in which a population of predators interacts with a population of prey [55].”
An introduction to sampling via measure transport (2016, background): “This is a common scenario in Bayesian inference problems with intractable likelihoods [92, 52, 23].”
Statistical inference for dynamical systems: A review (2012, methodology): “The underlying model often favored by biologists consists of a system of ordinary differential equations, with each variable in the state vector representing the expression level of a particular gene in the network [5, 171].”
Likelihood-free MCMC with Approximate Likelihood Ratios (2019, methodology): “The Lotka-Volterra model [19] describes the evolution of predator and prey populations over time.”
Likelihood-free MCMC with Amortized Approximate Ratio Estimators (2019, background): “ed on pre-simulated datasets (common in many scientiﬁc ﬁelds), thereby limiting the reliance on expensive simulator calls during training. 4.2 Lotka-Volterra population model The Lotka-Volterra model [19] describes the evolution of predator and prey populations over time. The population dynamics are”