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Register a new userSynthetic likelihood method for reaction network inference
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Added by
Grzegorz A Rempala
Publication date
2018
fields
Mathematical Statistics
and research's language is
English
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We propose a novel Markov chain Monte-Carlo (MCMC) method for reverse engineering the topological structure of stochastic reaction networks, a notoriously challenging problem that is relevant in many modern areas of research, like discovering gene regulatory networks or analyzing epidemic spread. The method relies on projecting the original time series trajectories onto information rich summary statistics and constructing the appropriate synthetic likelihood function to estimate reaction rates. The resulting estimates are consistent in the large volume limit and are obtained without employing complicated tuning strategies and expensive resampling as typically used by likelihood-free MCMC and approximate Bayesian methods. To illustrate run time improvements that can be achieved with our approach, we present a simulation study on inferring rates in a stochastic dynamical system arising from a density dependent Markov jump process. We then apply the method to two real data examples: the RNA-seq data from zebrafish experiment and the incidence data from 1665 plague outbreak at Eyam, England.
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We derive Laplace-approximated maximum likelihood estimators (GLAMLEs) of parameters in our Graph Generalized Linear Latent Variable Models. Then, we study the statistical properties of GLAMLEs when the number of nodes $n_V$ and the observed times of a graph denoted by $K$ diverge to infinity. Finally, we display the estimation results in a Monte Carlo simulation considering different numbers of latent variables. Besides, we make a comparison between Laplace and variational approximations for inference of our model.
High-dimensional statistical inference with general estimating equations are challenging and remain less explored. In this paper, we study two problems in the area: confidence set estimation for multiple components of the model parameters, and model specifications test. For the first one, we propose to construct a new set of estimating equations such that the impact from estimating the high-dimensional nuisance parameters becomes asymptotically negligible. The new construction enables us to estimate a valid confidence region by empirical likelihood ratio. For the second one, we propose a test statistic as the maximum of the marginal empirical likelihood ratios to quantify data evidence against the model specification. Our theory establishes the validity of the proposed empirical likelihood approaches, accommodating over-identification and exponentially growing data dimensionality. The numerical studies demonstrate promising performance and potential practical benefits of the new methods.
There have been controversies among statisticians on (i) what to model and (ii) how to make inferences from models with unobservables. One such controversy concerns the difference between estimation methods for the marginal means not necessarily having a probabilistic basis and statistical models having unobservables with a probabilistic basis. Another concerns likelihood-based inference for statistical models with unobservables. This needs an extended-likelihood framework, and we show how one such extension, hierarchical likelihood, allows this to be done. Modeling of unobservables leads to rich classes of new probabilistic models from which likelihood-type inferences can be made naturally with hierarchical likelihood.
Rejoinder to Likelihood Inference for Models with Unobservables: Another View by Youngjo Lee and John A. Nelder [arXiv:1010.0303]
Applying standard statistical methods after model selection may yield inefficient estimators and hypothesis tests that fail to achieve nominal type-I error rates. The main issue is the fact that the post-selection distribution of the data differs from the original distribution. In particular, the observed data is constrained to lie in a subset of the original sample space that is determined by the selected model. This often makes the post-selection likelihood of the observed data intractable and maximum likelihood inference difficult. In this work, we get around the intractable likelihood by generating noisy unbiased estimates of the post-selection score function and using them in a stochastic ascent algorithm that yields correct post-selection maximum likelihood estimates. We apply the proposed technique to the problem of estimating linear models selected by the lasso. In an asymptotic analysis the resulting estimates are shown to be consistent for the selected parameters and to have a limiting truncated normal distribution. Confidence intervals constructed based on the asymptotic distribution obtain close to nominal coverage rates in all simulation settings considered, and the point estimates are shown to be superior to the lasso estimates when the true model is sparse.
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