efficient implementation of markov chain monte carlo when using an unbiased likelihood estimator summary when an unbiased estimator of the likelihood is used within a metropolis hastings chain it is necessary to trade off the number of monte carlo samples used to construct this estimator against the asymptotic variances of the averages computed under this chain using many monte carlo samples will typically result in metropolis hastings averages with lower asymptotic variances than the corresponding averages that use fewer samples however the computing time required to construct the likelihood estimator increases with the number of samples under the assumption that the distribution of the additive noise introduced by the loglikelihood estimator is gaussian with variance inversely proportional to the number of samples and independent of the parameter value at which it is evaluated we provide guidelines on the number of samples to select we illustrate our results by considering a stochastic volatility model applied to stock index returns

bayesian semiparametric wiener system identification we present a novel method for wiener system identication the method relies on a semiparametric i e a mixed parametric nonparametric model of a wiener system we use a state space model for the linear dynamical system and a nonparametric gaussian process model for the static nonlinearity we avoid making strong assumptions such as monotonicity on the nonlinear mapping stochastic disturbances entering both as measurement noise and as process noise are handled in a systematic manner the nonparametric nature of the gaussian process allows us to handle a wide range of nonlinearities without making problem specic parameterizations we also consider sparsity promoting priors based on generalized hyperbolic distributions to automatically infer the order of the underlying dynamical system we derive an inference algorithm based on an ecient particle markov chain monte carlo method referred to as particle gibbs with ancestor sampling the method is proled on two challenging identication problems with good results blind wiener system identication is handled as a special case

stopping time resampling for sequential monte carlo methods summary motivated by the statistical inference problem in population genetics we present a new sequential importance sampling with resampling strategy the idea of resampling is key to the recent surge of popularity of sequential monte carlo methods in the statistics and engineering communities but existing resampling techniques do not work well for coalescent based inference problems in population genetics we develop a new method called stopping time resampling which allows us to compare partially simulated samples at different stages to terminate unpromising partial samples and to multiply promising samples early on to illustrate the idea we first apply the new method to approximate the solution of a dirichlet problem and the likelihood function of a non markovian process then we focus on its application in population genetics all our examples show that the new resampling method can significantly improve the computational efficiency of existing sequential importance sampling methods

likelihood analysis of non gaussian measurement time series summary in this paper we provide methods for estimating non gaussian time series models these techniques rely on markov chain monte carlo to carry out simulation smoothing and bayesian posterior analysis of parameters and on importance sampling to estimate the likelihood function for classical inference the time series structure of the models is used to ensure that our simulation algorithms are efficient

particle efficient importance sampling abstract the efficient importance sampling eis method is a general principle for the numerical evaluation of high dimensional integrals that uses the sequential structure of target integrands to build variance minimising importance samplers despite a number of successful applications in high dimensions it is well known that importance sampling strategies are subject to an exponential growth in variance as the dimension of the integration increases we solve this problem by recognising that the eis framework has an offline sequential monte carlo interpretation the particle eis method is based on non standard resampling weights that take into account the construction of the importance sampler as a sequential approximation to the state smoothing density we apply the method for a range of univariate and bivariate stochastic volatility specifications we also develop a new application of the eis approach to state space models with student s t state innovations our results show that the particle eis method strongly outperforms both the standard eis method and particle filters for likelihood evaluation in high dimensions we illustrate the efficiency of the method for bayesian inference using the particle marginal metropolis hastings and importance sampling squared algorithms

a sequential particle filter method for static models summary particle filter methods are complex inference procedures which combine importance sampling and monte carlo schemes in order to explore consistently a sequence of multiple distributions of interest we show that such methods can also offer an efficient estimation

particle filters for state space models with the presence of unknown static parameters particle filters for dynamic state space models handling unknown static parameters are discussed the approach is based on marginalizing the static parameters out of the posterior distribution such that only the state vector needs to be considered such a marginalization can always be applied however real time applications are only possible when the distribution of the unknown parameters given both observations and the hidden state vector depends on some low dimensional sufficient statistics such sufficient statistics are present in many of the commonly used state space models marginalizing the static parameters avoids the problem of impoverishment which typically occurs when static parameters are included as part of the state vector the filters are tested on several different models with promising results

the connection between bayesian estimation of a gaussian random field and rkhs reconstruction of a function from noisy data is key in machine learning and is often formulated as a regularized optimization problem over an infinite dimensional reproducing kernel hilbert space rkhs the solution suitably balances adherence to the observed data and the corresponding rkhs norm when the data fit is measured using a quadratic loss this estimator has a known statistical interpretation given the noisy measurements the rkhs estimate represents the posterior mean minimum variance estimate of a gaussian random field with covariance proportional to the kernel associated with the rkhs in this brief we provide a statistical interpretation when more general losses are used such as absolute value vapnik or huber specifically for any finite set of sampling locations that includes where the data were collected the maximum a posteriori estimate for the signal samples is given by the rkhs estimate evaluated at the sampling locations this connection establishes a firm statistical foundation for several stochastic approaches used to estimate unknown regularization parameters to illustrate this we develop a numerical scheme that implements a bayesian estimator with an absolute value loss this estimator is used to learn a function from measurements contaminated by outliers

on line inference for multiple changepoint problems we propose an on line algorithm for exact filtering of multiple changepoint problems this algorithm enables simulation from the true joint posterior distribution of the number and position of the changepoints for a class of changepoint models the computational cost of this exact algorithm is quadratic in the number of observations we further show how resampling ideas from particle filters can be used to reduce the computational cost to linear in the number of observations at the expense of introducing small errors and propose two new optimum resampling algorithms for this problem one a version of rejection control allows the particle filter to automatically choose the number of particles required at each time step the new resampling algorithms substantially out perform standard resampling algorithms on examples we consider and we demonstrate how the resulting particle filter is practicable for segmentation of human gc content

expectation propagation for likelihood free inference many models of interest in the natural and social sciences have no closed form likelihood function which means that they cannot be treated using the usual techniques of statistical inference in the case where such models can be efficiently simulated bayesian inference is still possible thanks to the approximate bayesian computation abc algorithm although many refinements have been suggested abc inference is still far from routine abc is often excruciatingly slow due to very low acceptance rates in addition abc requires introducing a vector of summary statistics s y the choice of which is relatively arbitrary and often require some trial and error making the whole process laborious for the user we introduce in this work the ep abc algorithm which is an adaptation to the likelihood free context of the variational approximation algorithm known as expectation propagation the main advantage of ep abc is that it is faster by a few orders of magnitude than standard algorithms while producing

discussion to approximate bayesian inference for latent gaussian models by using integrated nested laplace approximations by havard rue sara martino and nicolas chopin

on gibbs sampling for state space models summary we show how to use the gibbs sampler to carry out bayesian inference on a linear state space model with errors that are a mixture of normals and coefficients that can switch over time our approach simultaneously generates the whole of the state vector given the mixture and coefficient indicator variables and simultaneously generates all the indicator variables conditional on the state vectors the states are generated efficiently using the kalman filter we illustrate our approach by several examples and empirically compare its performance to another gibbs sampler where the states are generated one at a time the empirical results suggest that our approach is both practical to implement and dominates the gibbs sampler that generates the states one at a time

particle markov chain monte carlo methods summary markov chain monte carlo and sequential monte carlo methods have emerged as the two main tools to sample from high dimensional probability distributions although asymptotic convergence of markov chain monte carlo algorithms is ensured under weak assumptions the performance of these algorithms is unreliable when the proposal distributions that are used to explore the space are poorly chosen and or if highly correlated variables are updated independently we show here how it is possible to build efficient high dimensional proposal distributions by using sequential monte carlo methods this allows us not only to improve over standard markov chain monte carlo schemes but also to make bayesian inference feasible for a large class of statistical models where this was not previously so we demonstrate these algorithms on a non linear state space model and a levy driven stochastic volatility model

dimension independent likelihood informed mcmc many bayesian inference problems require exploring the posterior distribution of high dimensional parameters that represent the discretization of an underlying function this work introduces a family of markov chain monte carlo mcmc samplers that can adapt to the particular structure of a posterior distribution over functions two distinct lines of research intersect in the methods developed here first we introduce a general class of operator weighted proposal distributions that are well defined on function space such that the performance of the resulting mcmc samplers is independent of the discretization of the function second by exploiting local hessian information and any associated low dimensional structure in the change from prior to posterior distributions we develop an inhomogeneous discretization scheme for the langevin stochastic differential equation that yields operator weighted proposals adapted to the non gaussian structure of the posterior the resulting dimension independent and likelihood informed dili mcmc samplers may be useful for a large class of high dimensional problems where the target probability measure has a density with respect to a gaussian reference measure two nonlinear inverse problems are used to demonstrate the efficiency of these dili samplers an elliptic pde coefficient inverse problem and path reconstruction in a conditioned diffusion

monte carlo smoothing for nonlinear time series we develop methods for performing smoothing computations in general state space models the methods rely on a particle representation of the filtering distributions and their evolution through time using sequential importance sampling and resampling ideas in particular novel techniques are presented for generation of sample realizations of historical state sequences this is carried out in a forward filtering backward smoothing procedure that can be viewed as the nonlinear non gaussian counterpart of standard kalman filter based simulation smoothers in the linear gaussian case convergence in the mean squared error sense of the smoothed trajectories is proved showing the validity of our proposed method the methods are tested in a substantial application for the processing of speech signals represented by a time varying autoregression and parameterized in terms of time varying partial correlation coefficients comparing the results of our algorithm with those from a simple smoother based on the filte

bayesian model comparison with the hyvarinen score computation and consistency the bayes factor is a widely used criterion in model comparison and its logarithm is a difference of out of sample predictive scores under the logarithmic scoring rule however when some of the ca

approximate smoothing and parameter estimation in high dimensional state space models we present approximate algorithms for performing smoothing in a class of high dimensional state space models via sequential monte carlo methods particle filters in high dimensions a prohibitively large number of monte carlo samples particles growing exponentially in the dimension of the state space are usually required to obtain a useful smoother employing blocking approximations we exploit the spatial ergodicity properties of the model to circumvent this curse of dimensionality we thus obtain approximate smoothers that can be computed recursively in time and parallel in space first we show that the bias of our blocked smoother is bounded uniformly in the time horizon and in the model dimension we then approximate the blocked smoother with particles and derive the asymptotic variance of idealized versions of our blocked particle smoother to show that variance is no longer adversely effected by the dimension of the model finally we employ our method to successfully perform maximum likelihood estimation via stochastic gradient ascent and stochastic expectation maximization algorithms in a 100 dimensional state space model

sequential imputations and bayesian missing data problems abstract for missing data problems tanner and wong have described a data augmentation procedure that approximates the actual posterior distribution of the parameter vector by a mixture of complete data posteriors their method of constructing the complete data sets is closely related to the gibbs sampler both required iterations and similar to the em algorithm convergence can be slow we introduce in this article an alternative procedure that involves imputing the missing data sequentially and computing appropriate importance sampling weights in many applications this new procedure works very well without the need for iterations sensitivity analysis influence analysis and updating with new data can be performed cheaply bayesian prediction and model selection can also be incorporated examples taken from a wide range of applications are used for illustration

cubature versus fekete gauss nodes for spectral element methods on simplicial meshes in a recent jcp paper by y liu et al vol 336 p 458 2017 a higher order triangular spectral element method t sem is proposed to address seismic wave field modeling the main interest of this t sem is that the mass matrix is diagonal so that an explicit time marching becomes very cheap this property results from the fact that similarly to the usual sem the basis functions are lagrange polynomials based on a set of points that shows both nice interpolation and quadrature properties in the quadrangle i e for the qsem the set of points is simply obtained by tensorial product of gauss lobatto legendre gll points in the triangle finding such an appropriate set of points is however not trivial thus the recent jcp work follows anterior works that started in 2000 s and now provides cubature nodes and weights up to n 9 where n is the total degree of the polynomial approximation here we wish to evaluate the accuracy of this cubature nodes t sem with respect to the fekete gauss one that makes use of two sets of points namely the fekete points and the gauss points of the triangle for interpolation and quadrature respectively because the fekete gauss t sem is in the spirit of any nodal hp finite element methods one may expect that the conclusions of this note will remain relevant if using other sets of carefully defined interpolation points

predicting population extinction from early observations of the lotka volterra system abstract population extinction is one of the central themes in population biology we propose a statistical algorithm for long term prediction of an extinction event in the paradigmatic predator prey model the algorithm is based on noisy and sporadic observations of the lotka volterra lv system at the early stages of its evolution when the system is still very far from extinction there are two stages in the algorithm first the unknown parameters reaction rates of the lv system are estimated using the approximate bayesian computation method then an analytical expression for the time scale of extinction which involves the estimated parameters is applied to compute the probability density function of extinction time the proposed algorithm is validated by numerical simulations for the case of a stochastic lv system specified by the birth death rate equations the algorithm can be seen as an initial step in the quest for long term prediction of rare catastrophic events in complex stochastic dynamic systems epidemics host parasite dynamics enzyme kinetics dynamic trading etc

on line inference for hidden markov models via particle filters we consider the on line bayesian analysis of data by using a hidden markov model where inference is tractable conditional on the history of the state of the hidden component a new particle filter algorithm is introduced and shown to produce promising results when analysing data of this type the algorithm is similar to the mixture kalman filter but uses a different resampling algorithm we prove that this resampling algorithm is computationally efficient and optimal among unbiased resampling algorithms in terms of minimizing a squared error loss function in a practical example that of estimating break points from well log data our new particle filter outperforms two other particle filters one of which is the mixture kalman filter by between one and two orders of magnitude

an efficient markov chain monte carlo method for distributions with intractable normalising constants maximum likelihood parameter estimation and sampling from bayesian posterior distributions are problematic when the probability density for the parameter of interest involves an intractable normalising constant which is also a function of that parameter in this paper an auxiliary variable method is presented which requires only that independent samples can be drawn from the unnormalised density at any particular parameter value the proposal distribution is constructed so that the normalising constant cancels from the metropolis hastings ratio the method is illustrated by producing posterior samples for parameters of the ising model given a particular lattice realisation

sequential monte carlo samplers summary we propose a methodology to sample sequentially from a sequence of probability distributions that are defined on a common space each distribution being known up to a normalizing constant these probability distributions are approximated by a cloud of weighted random samples which are propagated over time by using sequential monte carlo methods this methodology allows us to derive simple algorithms to make parallel markov chain monte carlo algorithms interact to perform global optimization and sequential bayesian estimation and to compute ratios of normalizing constants we illustrate these algorithms for various integration tasks arising in the context of bayesian inference

bayesian phylogenetic inference using a combinatorial sequential monte carlo method the application of bayesian methods to large scale phylogenetics problems is increasingly limited by computational issues motivating the development of methods that can complement existing markov chain monte carlo mcmc schemes sequential monte carlo smc methods are approximate inference algorithms that have become very popular for time series models such methods have been recently developed to address phylogenetic inference problems but currently available techniques are only applicable to a restricted class of phylogenetic tree models compared to mcmc in this article we propose an original combinatorial smc csmc method to approximate posterior phylogenetic tree distributions which is applicable to a general class of models and can be easily combined with mcmc to infer evolutionary parameters our method only relies on the existence of a flexible partially ordered set structure and is more generally applicable to sampling problems on combinatorial spaces we demonstrate that the proposed csmc

estimating the granularity coefficient of a potts markov random field within a markov chain monte carlo algorithm this paper addresses the problem of estimating the potts parameter jointly with the unknown parameters of a bayesian model within a markov chain monte carlo mcmc algorithm standard mcmc methods cannot be applied to this problem because performing inference on requires computing the intractable normalizing constant of the potts model in the proposed mcmc method the estimation of is conducted using a likelihood free metropolis hastings algorithm experimental results obtained for synthetic data show that estimating jointly with the other unknown parameters leads to estimation results that are as good as those obtained with the actual value of on the other hand choosing an incorrect value of can degrade estimation performance significantly to illustrate the interest of this method the proposed algorithm is successfully applied to real bidimensional sar and tridimensional ultrasound images

rates of convergence of the hastings and metropolis algorithms we apply recent results in markov chain theory to hastings and metropolis algorithms with either independent or symmetric candidate distributions and provide necessary and sufficient conditions for the algorithms to converge at a geometric rate to a prescribed distribution pi in the independence case in mathbb r k these indicate that geometric convergence essentially occurs if and only if the candidate density is bounded below by a multiple of pi in the symmetric case in mathbb r only we show geometric convergence essentially occurs if and only if pi has geometric tails we also evaluate recently developed computable bounds on the rates of convergence in this context examples show that these theoretical bounds can be inherently extremely conservative although when the chain is stochastically monotone the bounds may well be effective

the multiple try method and local optimization in metropolis sampling abstract this article describes a new metropolis like transition rule the multiple try metropolis for markov chain monte carlo mcmc simulations by using this transition rule together with adaptive direction sampling we propose a novel method for incorporating local optimization steps into a mcmc sampler in continuous state space numerical studies show that the new method performs significantly better than the traditional metropolis hastings m h sampler with minor tailoring in using the rule the multiple try method can also be exploited to achieve the effect of a griddy gibbs sampler without having to bear with griddy approximations and the effect of a hit and run algorithm without having to figure out the required conditional distribution in a random direction

recursive monte carlo filters algorithms and theoretical analysis recursive monte carlo filters also called particle filters are a powerful tool to perform the computations in general state space models we discuss and compare the accept reject version with the more common sampling importance resampling version of the algorithm in particular we show how auxiliary variable methods and stratification can be used in the accept reject version and we compare dierent resampling techniques in a second part we show laws of large numbers and a central limit theorem for these monte carlo filters by simple induction arguments that need only weak conditions we also show that under stronger conditions the required sample size is independent of the length of the observed series ams 2000 subject classifications primary 62m09 secondary 60g35 60j22 65c05

filtering via simulation auxiliary particle filters this article analyses the recently suggested particle approach to filtering time series we suggest that the algorithm is not robust to outliers for two reasons the design of the simulators and the use of the discrete support to represent the sequentially updating prior distribution here we tackle the first of these problems

adaptive approximate bayesian computation sequential techniques can be adapted to the abc algorithm to enhance its efficiency for instance when sisson et al 2007 introduced the abc prc algorithm the goal was to improve upon existing abc mcmc algorithms marjoram et al 2003 while the abc prc method is based upon the theoretical developments of del moral et al 2006 the application to the setting of approximate bayesian computation induces a bias in the approximation to the posterior distribution of interest as we demonstrate in this paper via both theoretical reasoning and experimental results it is however possible to devise an alternative version based on genuine importance sampling arguments that we call abc pmc in connection with the population monte carlo method introduced in cappe et al 2004 furthermore the abc pmc algorithm is simpler than the abc prc algorithm in that it does not require any backward transition kernel and proposes an automatic scaling of the forward kernel in this paper we demonstrate the applicability of abc pmc and compare its performances with abc prc

marginal likelihood from the gibbs output abstract in the context of bayes estimation via gibbs sampling with or without data augmentation a simple approach is developed for computing the marginal density of the sample data marginal likelihood given parameter draws from the posterior distribution consequently bayes factors for model comparisons can be routinely computed as a by product of the simulation hitherto this calculation has proved extremely challenging our approach exploits the fact that the marginal density can be expressed as the prior times the likelihood function over the posterior density this simple identity holds for any parameter value an estimate of the posterior density is shown to be available if all complete conditional densities used in the gibbs sampler have closed form expressions to improve accuracy the posterior density is estimated at a high density point and the numerical standard error of resulting estimate is derived the ideas are applied to probit regression and finite mixture models

following a moving target monte carlo inference for dynamic bayesian models markov chain monte carlo mcmc sampling is a numerically intensive simulation technique which has greatly improved the practicality of bayesian inference and prediction however mcmc sampling is too slow to be of practical use in problems involving a large number of posterior target distributions as in dynamic modelling and predictive model selection alternative simulation techniques for tracking moving target distributions known as particle filters which combine importance sampling importance resampling and mcmc sampling tend to suffer from a progressive degeneration as the target sequence evolves we propose a new technique based on these same simulation methodologies which does not suffer from this progressive degeneration

approximate bayesian inference for latent gaussian models by using integrated nested laplace approximations summary structured additive regression models are perhaps the most commonly used class of models in statistical applications it includes among others generalized linear models generalized additive models smoothing spline models state space models semiparametric regression spatial and spatiotemporal models log gaussian cox processes and geostatistical and geoadditive models we consider approximate bayesian inference in a popular subset of structured additive regression models latent gaussian models where the latent field is gaussian controlled by a few hyperparameters and with non gaussian response variables the posterior marginals are not available in closed form owing to the non gaussian response variables for such models markov chain monte carlo methods can be implemented but they are not without problems in terms of both convergence and computational time in some practical applications the extent of these problems is such that markov chain monte carlo sampling is simply not an appropriate tool for routine analysis we show that by using an integrated nested laplace approximation and its simplified version we can directly compute very accurate approximations to the posterior marginals the main benefit of these approximations is computational where markov chain monte carlo algorithms need hours or days to run our approximations provide more precise estimates in seconds or minutes another advantage with our approach is its generality which makes it possible to perform bayesian analysis in an automatic streamlined way and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged

the calculation of posterior distributions by data augmentation comment a noniterative sampling importance resampling alternative to the data augmentation algorithm for creating a few imputations when fractions of missing information are modest the sir algorithm

non gaussian ornstein uhlenbeck based models and some of their uses in financial economics non gaussian processes of ornstein uhlenbeck ou type offer the possibility of capturing important distributional deviations from gaussianity and for flexible modelling of dependence structures this paper develops this potential drawing on and extending powerful results from probability theory for applications in statistical analysis their power is illustrated by a sustained application of ou processes within the context of finance and econometrics we construct continuous time stochastic volatility models for financial assets where the volatility processes are superpositions of positive ou processes and we study these models in relation to financial data and theory

adapting the number of particles in sequential monte carlo methods through an online scheme for convergence assessment particle filters are broadly used to approximate posterior distributions of hidden states in state space models by means of sets of weighted particles while the convergence of the filter is guaranteed when the number of particles tends to infinity the quality of the approximation is usually unknown but strongly dependent on the number of particles in this paper we propose a novel method for assessing the convergence of particle filters in an online manner as well as a simple scheme for the online adaptation of the number of particles based on the convergence assessment the method is based on a sequential comparison between the actual observations and their predictive probability distributions approximated by the filter we provide a rigorous theoretical analysis of the proposed methodology and as an example of its practical use we present simulations of a simple algorithm for the dynamic and online adaptation of the number of particles during the operation of a particle filter on a stochastic version of the lorenz 63 system

inference and model choice for sequentially ordered hidden markov models summary the system equation of a hidden markov model is rewritten to label the components by order of appearance and to make explicit the random behaviour of the number of components mt we argue that this reformulation is often a good way to achieve identifiability as it facilitates the interpretation of the posterior density and the estimation of the number of components that have appeared in a given sample we develop a sequential monte carlo algorithm for estimating the reformulated model which relies on particle filtering and gibbs sampling our algorithm has a computational cost that is similar to that of a markov chain monte carlo sampler and is much less likely to be affected by label switching i e the possibility of becoming trapped in a local mode of the posterior density the extension to transdimensional priors is also considered the approach is illustrated by two real data examples

the estimation of time invariant parameters of noisy nonlinear oscillatory systems the inverse problem of estimating time invariant static parameters of a nonlinear system exhibiting noisy oscillation is considered in this paper firstly a markov chain monte carlo mcmc simulation is used for the time invariant parameter estimation which exploits a non gaussian filter namely the ensemble kalman filter enkf for state estimation required to compute the likelihood function secondly a recently proposed particle filter pf that uses the enkf for its proposal density for the state estimation has been adapted for combined state and parameter estimation numerical illustrations highlight the strengths and limitations of the mcmc enkf and pf algorithms for time invariant parameter estimation for low measurement noise and dense measurement data the performances of the mcmc enkf and pf algorithms are comparable for high measurement noise and sparse observational data the enkf fails to provide accurate parameter estimates hence the adapted pf algorithm becomes necessary in order to obtain parameter estimates comparable in accuracy to the mcmc simulation with enkf it highlights the fact that the augmented state space model for the combined state and parameter estimation contains stronger nonlinearity than the original state space model hence the enkf effectively handles the state estimation of the original state space model but it fails for the combined state and parameter estimation using the augmented system the effectiveness of the enkf for the state estimation is therefore leveraged in the mcmc simulation for the time invariant parameter estimation in order to obtain accurate parameter estimates using the augmented system the adapted pf becomes necessary to match the parameter estimates obtained using the mcmc simulation complemented by enkf for likelihood function computation

approximations of the optimal importance density using gaussian particle flow importance sampling abstractrecently developed particle flow algorithms provide an alternative to importance sampling for drawing particles from a posterior distribution and a number of particle filters based on this principle have been proposed samples are drawn from the prior and then moved according to some dynamics over an interval of pseudo time such that their final values are distributed according to the desired posterior in practice implementing a particle flow sampler requires multiple layers of approximation with the result that the final samples do not in general have the correct posterior distribution in this article we consider using an approximate gaussian flow for sampling with a class of nonlinear gaussian models we use the particle flow within an importance sampler correcting for the discrepancy between the target and actual densities with importance weights we present a suitable numerical integration procedure for use with this flow and an accompanying step size control algorithm in a filtering co

bayesian inference for non gaussian ornstein uhlenbeck stochastic volatility processes we develop markov chain monte carlo methodology for bayesian inference for non gaussian ornstein uhlenbeck stochastic volatility processes the approach introduced involves expressing the unobserved stochastic volatility process in terms of a suitable marked poisson process we introduce two specific classes of metropolis hastings algorithms which correspond to different ways of jointly parameterizing the marked point process and the model parameters the performance of the methods is investigated for different types of simulated data the approach is extended to consider the case where the volatility process is expressed as a superposition of ornstein uhlenbeck processes we apply our methodology to the us dollar deutschmark exchange rate