Monte Carlo algorithms often aim to draw from a distribution π by simulating a Markov chain with transition kernel P such that π is invariant under P . However, there are many situations for which it is impractical or impossible to draw from the transition kernel P . For instance, this is the case with massive datasets, where is it prohibitively expensive to calculate the likelihood and is also the case for intractable likelihood models arising from, for example, Gibbs random fields, such as those found in spatial statistics and network analysis. A natural approach in these cases is to replace P by an approximationP . Using theory from the stability of Markov chains we explore a variety of situations where it is possible to quantify how 'close' the chain given by the transition kernelP is to the chain given by P . We apply these results to several examples from spatial statistics and network analysis.
Bayesian inference of Gibbs random fields (GRFs) is often referred to as a doubly intractable problem, since the likelihood function is intractable. The exploration of the posterior distribution of such models is typically carried out with a sophisticated Markov chain Monte Carlo (MCMC) method, the exchange algorithm (Murray et al., 2006), which requires simulations from the likelihood function at each iteration. The purpose of this paper is to consider an approach to dramatically reduce this computational overhead. To this end we introduce a novel class of algorithms which use realizations of the GRF model, simulated offline, at locations specified by a grid that spans the parameter space. This strategy speeds up dramatically the posterior inference, as illustrated on several examples. However, using the pre-computed graphs introduces a noise in the MCMC algorithm, which is no longer exact. We study the theoretical behaviour of the resulting approximate MCMC algorithm and derive convergence bounds using a recent theoretical development on approximate MCMC methods.
BackgroundDocetaxel based therapy is one of the first line chemotherapeutic agents for the treatment of metastatic castrate-resistant prostate cancer. However, one of the major obstacles in the treatment of these patients is docetaxel-resistance. Defining the mechanisms of resistance so as to inform subsequent treatment options and combinations represents a challenge for clinicians and scientists.Previous work by our group has shown complex changes in pro and anti-apoptotic proteins in the development of resistance to docetaxel. Targeting these changes individually does not significantly impact on the resistant phenotype but understanding the central signalling pathways and transcription factors (TFs) which control these could represent a more appropriate therapeutic targeting approach.MethodsUsing a number of docetaxel-resistant sublines of PC-3 cells, we have undertaken a transcriptomic analysis by expression microarray using the Affymetrix Human Gene 1.0 ST Array and in conjunction with bioinformatic analyses undertook to predict dysregulated TFs in docetaxel resistant prostate cancer. The clinical significance of this prediction was ascertained by performing immunohistochemical (IHC) analysis of an identified TF (SRF) in the metastatic sites from men who died of advanced CRPC. Investigation of the functional role of SRF was examined by manipulating SRF using SiRNA in a docetaxel-resistant PC-3 cell line model.ResultsThe transcription factors identified include serum response factor (SRF), nuclear factor kappa-B (NFκB), heat shock factor protein 1 (HSF1), testicular receptor 2 & 4 (TR2 &4), vitamin-D and retinoid x receptor (VDR-RXR) and oestrogen-receptor 1 (ESR1), which are predicted to be responsible for the differential gene expression observed in docetaxel-resistance. IHC analysis to quantify nuclear expression of the identified TF SRF correlates with both survival from date of bone metastasis (p = 0.003), survival from androgen independence (p = 0.00002), and overall survival from prostate cancer (p = 0.0044). Functional knockdown of SRF by siRNA demonstrated a reversal of apoptotic resistance to docetaxel treatment in the docetaxel-resistant PC-3 cell line model.ConclusionsOur results suggest that SRF could aid in treatment stratification of prostate cancer, and may also represent a therapeutic target in the treatment of men afflicted with advanced prostate cancer.Electronic supplementary materialThe online version of this article (doi:10.1186/s12885-017-3100-4) contains supplementary material, which is available to authorized users.
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