Presentation Details 

Andrieu, Christophe 
Stability and stabilisation of controlled Markov chains and their applications in statistics 
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The initial motivation for the work presented was to understand the behaviour of popular algorithms used for statistical inference, such as Monte Carlo approximations of the EM (expectation maximisation) algorithm or adaptive Markov chain Monte Carlo methods which fall in the category of controlled Markov chain processes. Informally, given a family of Markov transition probabilities indexed by a parameter, such processes correspond, at a given time instant, to updating the state of the process with one of those transition probabilities whose indexing parameter is chosen according to a rule which may depend on the whole past of the process. Such processes can be particularly unstable when the indexing parameter approaches a set of critical values. The aim of the presentation is to provide some insights into the observed stability of some controlled Markov chains of interest and present some stabilisation techniques which are designed to ensure the stability of the process. As we shall see some of the aforementioned algorithms used in statistics possess natural "strong" stability properties, while others may require the use of stabilisation techniques. 
Atchade, Yves 
Computing Bayes factors with confidence 
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The talk will present a flexible implementation of the path sampling identity using nonhomogeneous Markov chains. This allows for rigorous confidence interval estimation for ratio of normalizing constants. 
Beskos, Alexandros 
Hamiltonian dynamics in high dimensions 
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We look at the behavior of Hybrid MonteCarlo methods in high dimensions, and illustrate results designating an asymptotically optimal acceptance probability of 0.651. We also present an "advanced" version of Hybrid MonteCarlo on Hilbert spaces, for target distributions defined as change of measures from Gaussian laws arising in applications. Analytical and experimental results will illustrate the superiority of advanced Hybrid MonteCarlo over alternative "standard" MCMC methods. 
Byrne, Simon 
Orthogonal foliations for graphical models (Joint presentation with Frank Critchley, Open University) 
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Bayesian hierarchical models are one of the most common applications of MCMC, but can be still quite difficult to implement effectively. Conditional independence means that simple methods such as Gibbs sampling often work quite well for the lowerlevel parameters, however the high correlation between levels means that it can be difficult to construct efficient proposal schemes for the higherlevel parameters.
The geometry of such models suggests that these updates should be done in a manner that is geometrically orthogonal to the lowerlevel updates. This defines a "foliation": a partition of the model into locally parallel submanifolds. In order to efficiently sample from this submanifold, we can adapt the Riemannian manifold Hamiltonian Monte Carlo (RMHMC) algorithm to utilise constrained Hamiltonian dynamics. 
Chopin, Nicolas 
My memory is long, my patience is not: how not to use MCMC for Bayesian spectral density estimation for longmemory processes 
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Longmemory or shortmemory Gaussian timeseries models are often specified through their spectral density. Such models pose several computational challenges, such as the nonsparseness of the covariance matrix, which makes the likelihood expensive to compute, and the absence of any structure in the likelihood, which prevents a Gibbs sampling implementation. The first part of this work develops a fast approximation of the likelihood, which can be computed in O(n) time. It is shown that the variance of the weights of an importance sampling step, from the approximate to the true likelihood, goes to zero as the sample size goes to infinity. The second part of this work uses a tempering version of Sequential Monte Carlo to sample from the approximate posterior (i.e. the prior times the approximate likelihood). We show that this SMC sampler is faster, and, more importantly, more robust to multimodality than plain MCMC. 
De Iorio, Maria 
A Bayesian model of NMR spectra for the deconvolution andquantification of metabolites in complex biological mixtures 
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Nuclear Magnetic Resonance (NMR) spectra are widely used in metabolomics to obtain profiles of metabolites dissolved in biofluids such as cell supernatants. Methods for estimating metabolite concentrations from these spectra are presently confined to manual peak fitting and to binning procedures for integrating resonance peaks. Extensive information on the patterns of spectral resonance generated by human metabolites is now available in online databases. By incorporating this information into a Bayesian model we can deconvolve resonance peaks from a spectrum and obtain explicit concentration estimates for the corresponding metabolites. Spectral resonances that cannot be deconvolved in this way may also be of scientific interest so we model them using wavelets. We describe a Markov chain Monte Carlo algorithm which allows us to sample from the joint posterior distribution of the model parameters, using specifically designed block updates to improve mixing. We assess our method for peak alignment and concentration estimation and find that alignment is unbiased and precise. Moreover, our concentration estimates significantly reduce mean estimation error when compared to conventional numerical integration methods. Finally, we apply our method to a spectral dataset taken from an investigation of the metabolic response of yeast to recombinant protein expression. 
Fort, Gersende 
Stochastic approximation for adaptive interacting MCMC samplers 
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Interacting MCMC samplers are based on the construction of K parallel processes targeting different distributions. For example, the K limiting distributions can be chosen as tempered version of the target density. These parallel processes are defined so that interaction with the whole past of a neighboring process is allowed thus improving the convergence properties of the sampler. In this context, the parallel processes are no more a Markov chain.
Among Interacting MCMC samplers, the EquiEnergy sampler (Kou et al 2006) is a powerful algorithm for sampling multimodal distributions. In this algorithm, interactions only involve points with the same energy level. This algorithm depends on many design parameters such as the number of parallel processes K and number of rings, the probability of interaction, the choice of the energy rings. In this talk, I will first propose and Adaptive EquiEnergy sampler, in which the energy rings are adapted on the fly based on the history of the parallel processes.
When deriving convergence results for this adaptive EquiEnergy sampler, we are faced to challenging problems about stability and convergence of stochastic approximation schemes with discontinuous dynamics, when the mean field is approximated by Interacting MCMC samples. I will discuss recent results on these problems, and will show how they are used to prove ergodicity and law of large numbers for the Adaptive EquiEnergy sampler. This is a joint work with A. Garivier, E. Moulines, A. Schreck  from LTCI, France; and M. Vihola  from Jyvaskyla, Finland 
Friel, Nial 
Estimating the evidence for doubly intractable distributions 
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There has been considerable interest in the literature in parameter estimation for doubly intractable distributions. Posterior distributions arising from Markov random fields, such as those found in spatial statistics and social network analysis, are examples of this intractability. This talk will illustrate an approach, extending this methodology, to allow one estimate the evidence for this class of statistical models, thereby facilitating model choice. 
Golightly, Andrew 
Exact inference for stochastic kinetic models via a linear noise approximation 
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Recently proposed particle MCMC methods provide a flexible way of performing Bayesian inference for parameters governing stochastic kinetic models defined as Markov (jump)
processes (MJPs). Each iteration of the scheme requires an estimate of marginal likelihood calculated from the output of a sequential Monte Carlo scheme (also known as a particle filter). Consequently, the method can be extremely computationally intensive. We therefore aim to negate the expensive likelihood calculation through use of a fast approximation, or `emulator'. We use the tractable marginal likelihood under a linear noise approximation of the MJP to calculate a first step acceptance probability. If a proposal is accepted under the approximation, we then run a sequential Monte Carlo scheme to compute an estimate of the marginal likelihood under the MJP and construct a second stage acceptance probability that permits exact (simulation based) inference for the MJP. We therefore avoid expensive calculations for proposals that are likely to be rejected. We illustrate the method by considering inference for parameters governing a LotkaVolterra system. 
Griffin, Jim 
Adaptive Monte Carlo methods for variable selection 
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The Bayesian approach to variable selection in regression models is wellestablished with a prior placed on the space of all possible regression models and their parameters. The posterior distribution is often hard to simulate using MetroplisHastings methods since it can have multiple, wellseparated modes leading to low acceptance rates for between model moves. If our data include many potential regressors but few observations, the posterior distribution often becomes flatter and the acceptance rate for between model moves can become large. The high acceptance rates suggests that more efficient algorithms can be obtained by proposing ``bigger'' between model moves. This talk will discuss how such moves can be constructed and how the ideas of adaptive Monte Carlo can be used to tune them to give efficient methods. The methods will be illustrated on examples in both linear and binary regression problems. 
Haario, Heikki 
State and parameter estimation for large scale models 
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The Kalman Filter and nonlinear extensions of it provide a natural approach for data assimilation problems. But they are infeasible for large enough models. Here we discuss lowmemory approximations based on optimization algorithms. While MCMC can be technically performed even for such large systems, and an additional challenge is due to chaoticity: small parameter changes may lead to large 'random' variations of the likelihood. As a remedy, we propose the use of filteringbased likelihoods. Finally, we discuss an approach where an operational ensemble weather prediction system is slighly modified for parameter estimation purposes, with practically no additional CPU cost. 
Hobert, Jim 
Convergence rate results for two Gibbs samplers 
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After a brief review of Markov chain CLTs, geometric ergodicity and geometric drift conditions, I will describe new convergence rate results for two block Gibbs samplers. The first is a recently developed algorithm for exploring the intractable posterior density associated with a Bayesian quantile regression model. The second is a wellknown Gibbs sampler for the Bayesian version of the general linear mixed model with improper priors. (This is joint work with K Khare and J Roman) 
Imparato, Daniele 
Density estimators through zero variance Markov Chain Monte Carlo 
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A Markov Chain Monte Carlo method is proposed for the pointevaluation of a density whose normalization constant is not known. This method was introduced in the physics literature by Assaraf et al. (2007). Conditions for unbiasedness of the estimator and for central limit theorem are derived in this context. The new idea is tested on some toyexamples. 
Laine, Marko 
Efficient adaptive MCMC for complex models 
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In multi scale dynamical process models, such as those used for weather prediction and climate studies, subgrid scale processes must be replaced by physical parameterization schemes. Tuning and uncertainty analysis of closure parameters related to these schemes is complicated by the high complexity and computational burden of the models.
We review some efficient MCMC techniques for performing statistical inference for computationally highly complex models: adaptation, parallel chains and early rejection. The examples describe our analysis of ECHAM5 climate model. We discuss our MCMC experiments, specification of cost function, parameter identification, and some alternative Monte Carlo techniques based on ensemble model runs.
References:
A. Solonen, P. Ollinaho, M. Laine, H. Haario, J. Tamminen, H. Järvinen: Efficient MCMC for climate model parameter estimation: parallel adaptive chains and early rejection, Bayesian Analysis, accepted, 2012.
J. Hakkarainen, A. Ilin, A. Solonen, M. Laine, H.Haario, J. Tamminen, E. Oja, H. Järvinen: On closure parameter estimation in chaotic systems, Nonlinear Processes in Geophysics, accepted, 2012.
H. Järvinen, P. Räisänen, M. Laine, J. Tamminen, A. Ilin, E. Oja, A. Solonen, H. Haario: Estimation of ECHAM5 climate model closure parameters with adaptive MCMC, Atmospheric Chemistry and Physics, 10(1), pages 999310002, 2010. doi:10.5194/acp1099932010 
Latuszynski, Krzysztof 
Robustness of manifold MALA and related algorithms 
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The standard MALA algorithms generally have improved convergence properties over the Random Walk Metropolis, however they cannot be applied for target distributions with too heavy or too light tails. Motivated by this imperfection and inspired by the recent work on Manifold Monte Carlo Methods (Girolami and Calderhead 2011), we investigate properties of a more general version of MALA algorithms based on discretising a family of Langevin diffusions with local diffusion coefficient targeting the stationary measure. We analyse it for a benchmark family of targets and extend towards more general distributions.
This is joint work with Gareth O. Roberts and Katarzyna Wolny. 
Lawson, Dan 
The Dirichlet process in genetics 
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The Dirichlet Process is an extremely important and popular tool for a wide range of clustering problems. This computationally cheap Bayesian prior allows numerical integration over the assignment of samples to clusters, whilst also determining the number of clusters from the data. A mechanistic model for the data can still be placed within the Dirichlet Process Prior, making this a very flexible modelling framework. In this talk I'll give an introduction to the Dirichlet Process and discuss the MCMC moves needed for efficient mixing. I'll also give an overview of some interesting extensions used in the (genetics) literature. Finally, I'll conclude with my own research which maps an inherently complex problem down to a Dirichlet Process MCMC problem by careful exploitation of the approximate behaviour of the underlying "correct" model. This allows for very efficient and very precise population assignment of individuals using their genetics. 
Liang, Faming 
Bayesian subset modeling for high dimensional generalized linear models and its asymptotic properties 
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We propose a new prior setting for high dimensional generalized linear models (GLMs), which leads to a Bayesian subset regression (BSR) with the maximum a posteriori model coinciding with the minimum extended BIC model. We establish consistency of the posterior under mild conditions and sample from the posterior using the stochastic approximation Monte Carlo algorithm. Further, we propose a variable screening procedure based on the marginal inclusion probability and show that this procedure shares the same properties of sure screening and consistency with the existing sure independence screening (SIS) procedure. However, since the proposed procedure makes use of joint information of all predictors, it generally outperforms SIS and its improved version in real applications. For subject classification, we propose a selected Bayesian classifier based on the goodnessoffit test for the models sampled from the posterior. The new classifier is consistent and robust to the choice of priors. The numerical results indicate that the new classifier can generally outperform the Bayesian model averaging classifier and the classifier based on the high posterior probability models. We also made extensive comparisons of BSR with the popular penalized likelihood methods, including Lasso, elastic net, SIS and ISIS. The numerical results indicate that BSR can generally outperform the penalized likelihood methods: The models elected by BSR tend to be sparser and, more importantly, of higher generalization ability. In addition, we find that the performance of the penalized likelihood methods tend to deteriorate as the number of predictors increases, while this is not significant for BSR. 
Marin, JeanMichel 
Bayesian inference on a mixture model with spatial dependence 
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We introduce a new technique in order to select the number of components of a mixture model with spatial dependences. Typically, we consider an image field where the greyscale values are Gaussian random variables depending on the component of the associated pixel and the components are distributed according to a Potts model. Our approach is deduced from an approximation of the integrated completed likelihood and from the use of specific auxilliary variable MCMC algorithms which avoid the difficulty associated to the fact the normalizing constant of the Potts model is not available. 
Meng, XiaoLi 
Thank God that regressing Y on X is not the same as regressing X on Y: interweaving residual augmentations 
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What does regressing Y on X versus regressing X on Y have anything to do with MCMC? It turns out that many strategies for speeding up data augmentation type of algorithms intrinsically share the same principle as regression in the sense of fostering independence between a regression function and the corresponding residual, thereby reducing or even eliminating dependence among MCMC iterates. There are two general classes of algorithms, those corresponding to regressing parameters on augmented data/auxiliary variables and those the other way around. The interweaving strategy (Yu and Meng, 2011, JCGS) amounts to taking advantage of both, and it is the existence of two different types of residuals that makes the interweaving strategy seemingly magical in some cases and promising in general. This talk reports on the latest findings in the search for effective residual augmentations, as well as an intriguing phase transition type phenomenon that might provide general insight into constructing interweaving algorithms that meet the 3S criterion: simple, speedy, and stable. (This is joint work with Xiaojin Xu and Yaming Yu.) 
Murray, Iain 
Sampling hierarchical latent Gaussian models 
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Latent Gaussian models are a standard workhorse for statistical modelling. Applications are found in diverse areas such as astrophysics, and modelling sports outcomes. They are also a useful testbed for probabilistic inference methods, as several difficulties manifest themselves that are common to many inference problems. I'll outline some of my work on Markov chain Monte Carlo methods for simulating the posteriors of hierarchical latent Gaussian models. 
Papaspiliopoulos, Omiros 
Path augmentation 
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In this talk I will present a novel framework for data augmentation which considerably extends the ideas of noncentering and it is particularly attractive for inference for hierarchical models with latent stochastic processes. The framework, together with additional results which link continuous and discrete time approaches to inference for diffusions, provides a unification and theoretical justification of popular algorithms for inference for diffusions. 
Pillai, Natesh 
Recent advances in high dimensional covariance matrix estimation 
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We will present a brief overview of our recent work on high dimensional covariance estimation. Firstly,we will present a flexible class of models based on scale mixture of uniform distributions to construct shrinkage priors for covariance matrix estimation. This new class of priors enjoys a number of advantages over the traditional scale mixture of normal priors, including its simplicity and flexibility in characterizing the prior density. We also exhibit a simple, easy to implement Gibbs sampler for posterior simulation which leads to efficient estimation in high dimensional problems. Next we will present some recent theoretical results on factor models. 
Roberts, Gareth 
Why does the Gibbs sampler work on hierarchical models? 
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Contrary to common perception, the Gibbs sampler does not intrinsically break down the curse of dimensionality. However, as we know, it (and its generalisations) have been highly successful in Bayesian inference with highdimensional parameter spaces. So what is special about "statistical" highdimensional distributions that has facilitated this? This presentation will explore the links between hierarchical models and stability properties of the Gibbs sampler such as geometric ergodicity. Some general results will be given which have simple and practical implications for MCMC algorithm design. This is joint work with Omiros Papaspiliopoulos, Kryszof Latuszynski, and Natesh Pillai. 
Särkkä, Simo 
Posterior inference on parameters of stochastic differential equations via Gaussian process approximations 
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This talk is concerned with Bayesian estimation of parameters in stochastic differential equation (SDE) models occurring in physics, engineering and financial applications. In particular, we consider implementation of MCMC based sampling methods for partially observed irreducible Brownianmotiondriven nonlinear multivariate SDEs. For these kind of SDEs computation of the transition densities is not possible in closed form and thus the implementation of MCMC methods is not possible without additional approximations to them. In this talk we show how Taylor series and Gaussian cubature methods can be used for forming Gaussian approximations to the transition densities and how nonlinear Kalman filters can be used in efficient implementation of MCMC sampling. In addition to MCMC, we also discuss implementation of Laplace approximations and other types of methods for the posterior parameter inference by using similar approximations. 
Stuart, Andrew 
Random walk metropolis algorithms in high dimensions 
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I will describe recent theoretical developments which explain how to develop and analyze random walk type Metropolis algorithms in high dimensions. The setting is based on studying probability measures which have density with respect to a Gaussian random field, and their finite dimensional approximations. Diffusion limits to stochastic PDEs, and spectral gaps using the Wasserstein1 distance, are shown to provide effective and robust tools which quantify computational complexity in this scenario. Joint work with Martin Hairer, Jonathan Mattingly, Natesh Pillai, Alex Thiery and Sebastian Vollmer will be described. 
Tribello, Gareth 
Methods for surveying complex probability distributions 
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The probability of adopting a particular molecular configuration is given by the Boltzmann distribution and in physics we often use molecular dynamics (MD) to probe this distribution. However, when we discretize Newton's equations of motion in our MD simulation we are forced to use a very short timestep so we often do not see interesting, longtimescale chemical processes. For simple chemical processes it is straightforward to resolve this second problem using the wellestablished metadynamics [1] method. This method generates a history dependent bias that forces the system to move away from previously visited configurations and into unexplored parts of phase space. The problem with this method is that it is reliant on user defined collective variables (CVs). Suggesting such CVs is simple when the underlying physics is straightforward but is considerably more difficult for processes such as protein folding that have complex and less well understood mechanisms. Hence, the work I will present is concerned with finding CVs that can be used to accelerate sampling when the reaction mechanism is complicated and our understanding is limited.
The first method I will present is the well tempered ensemble [2], which uses the potential energy as a CV. It is possible to show that biasing the energy in this way enhances the fluctuations in the energy and thus increases sampling. However, problems occur for this method when there are multiple structures with similar energies as there is no bias present to force the system to travel between the different chemical states. Hence, the other methods I will show work by assuming that there are a small number of lowenergy configurations and that there are a small number of connections (transition pathways) between these low energy states. The interesting low energy parts of phase space will be highly populated in short MD trajectories so we can recognize energetic basins using a Gaussian Mixture model [3]. The fit obtained from this model can be used to generate a bespoke bias that can in turn be used to force a more rapid sampling of CV space.
A separate but related problem to the one of sampling is how to understand the data that we obtain from a thorough sampling of phase space. I will thus also show how we can use dimensionality reduction to understand MD trajectories [4] and how the lowdimensionality coordinates so obtained can be used to enhance the sampling of phase space [5].
[1] A. Laio and M. Parrinello Escaping free energy minima Proc. Natl. Acad. Sci. U.S.A.
99 1256212566 (2002)
[2] M. Bonomi and M. Parrinello Enhanced sampling in the welltempered ensemble Phys. Rev. Lett 104 190601 (2010)
[3] G. A. Tribello, M. Ceriotti and M. Parrinello A selflearning algorithm for biased molecular dynamics Proc. Natl. Acad. Sci. U.S.A 107 1750917514 (2010)
[4] M. Ceriotti, G. A. Tribello and M. Parrinello Simplifying the representation of complex free energy landscapes using sketchmap Proc. Natl. Acad. Sci. U.S.A. 108
1302313028 (2011)
[5] G. A. Tribello, M. Ceriotti and M. Parrinello Using sketchmap coordinates to analyze and bias molecular dynamics simulations Proc. Natl. Acad. Sci. U.S.A. 109 51965201 (2012) 
van Dyk, David 
Metropolis Hastings within partially collapsed Gibbs samplers, with application in highenergy astrophysics 
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The Partially Collapsed Gibbs (PCG) sampler offers a new strategy for improving the convergence of a Gibbs sampler. PCG achieves faster convergence by reducing the conditioning in some of the draws of its parent Gibbs sampler. Although this can significantly improve convergence, care must be taken to ensure the stationary distribution is preserved. The conditional distributions sampled in a PCG sampler may be functionally incompatible and permuting them may upset the station ary distribution. Extra care must be taken when Metropolis steps are used. Reducing the conditioning in an MH within Gibbs sampler can change the stationary distribution, even when the PCG sampler would work perfectly if all the conditional updates were available. We illustrate the challenges that may arise when using an MH within PCG sampler and develop a general strategy for using such updates while maintaining the stationary distribution. 
Whiteley, Nick 
Stability properties of particle filters 
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Particle filtering has become a very popular method for inferential computation in state space models. What arguably makes particle filters useful is that they exhibit some form of stability; it is commonly observed that the stochastic errors associated with the particle approximation do not explode over time, so that these algorithms can be applied successfully at a computational cost which scales slowly with the length of the data record under analysis.
Whilst there is now a rich literature on various theoretical properties of particle filters, most existing results which explain their stability properties rely on strong mixing assumptions which do not hold in typical applications. One of the main obstacles is dealing with a noncompact state space.
This talk will describe recent developments which allow some stability properties of particle filters to be verified when the state space is noncompact. 
Wilkinson, Darren 
Bayesian inference for Markov processes with application to biochemical network dynamics 
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A number of interesting statistical applications require the estimation of parameters underlying a nonlinear multivariate continuous time Markov process model, using partial and noisy discrete time observations of the system state. Bayesian inference for this problem is difficult due to the fact that the discrete time transition density of the Markov process is typically intractable and computationally intensive to approximate. It turns out to be possible to develop particle MCMC algorithms which are exact, provided that one can simulate exact realisations of the process forwards in time. Such algorithms, often termed "likelihood free" or "plugandplay" are very attractive, as they allow separation of the problem of model development and simulation implementation from the development of inferential algorithms. Such techniques break down in the case of perfect observation or highdimensional data, but more efficient algorithms can be developed if one is prepared to deviate from the likelihood free paradigm, at least in the case of diffusion processes. The methods will be illustrated using examples from population dynamics and stochastic biochemical network dynamics. 