global stability of gompertz model of three competing populations the model of three competitive populations with gompertz growth is studied the periodic solutions are ruled out by generalized dulac criteria on the basis of the analysis we obtain conditions that ensure the asymptotic behavior of the model is simple

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

on bendixson s criterion abstract for autonomous differential equations in r n criteria are developed which preclude the existence of invariant closed curves such as periodic or homoclinic trajectories the technique is based on the study of functionals on 2 surfaces results generalize to higher dimensions a criterion of bendixson for the nonexistence of nonconstant periodic solutions in the case n 2 as an example an application to the lorenz system in r 3 is given

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

central limit theorem for sequential monte carlo methods and its application to bayesian inference the term sequential monte carlo methods or equivalently particle filters refers to a general class of iterative algorithms that performs monte carlo approximations of a given sequence of distributions of interest t we establish in this paper a central limit theorem for the monte carlo estimates produced by these computational methods this result holds under minimal assumptions on the distributions t and applies in a general framework which encompasses most of the sequential monte carlo methods that have been considered in the literature including the resample move algorithm of gilks and berzuini j r stat soc ser b stat methodol 63 2001 127 146 and the residual resampling scheme the corresponding asymptotic variances provide a convenient measurement of the precision of a given particle filter we study in particular in some typical examples of bayesian applications whether and at which rate these asymptotic variances diverge in time in order to assess the long term reliability of the considered algorithm

a method for proving the non existence of limit cycles abstract a general criterion is established for showing the non existence of periodic solutions and closed phase polygons of differential equations several known criteria of this type are obtained as special cases an extension is obtained for functional differential equations and several applications are given for specific special cases including homogeneous systems and population dynamics equations

bounds on the mean power weighted nearest neighbour distance in this paper bounds on the mean power weighted nearest neighbour distance are derived previous work concentrates mainly on the infinite sample limit whereas our bounds hold for any sample size the results are expected to be of importance for example in statistical physics non parametric statistics and computational geometry where they are related to the structure of matter as well as properties of statistical estimators and random graphs

a law of large numbers for nearest neighbour statistics in practical data analysis methods based on proximity near neighbour relationships between sample points are important because these relations can be computed in time n log n as the number of points n associated with such methods are a class of random variables defined to be functions of a given point and its nearest neighbours in the sample if the sample points are independent and identically distributed the associated random variables will also be identically distributed but not independent despite this we show that random variables of this type satisfy a strong law of large numbers in the sense that their sample means converge to their expected values almost surely as the number of sample points n

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

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

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

a computationally efficient estimator for mutual information mutual information quantifies the determinism that exists in a relationship between random variables and thus plays an important role in exploratory data analysis we investigate a class of non parametric estimators for mutual information based on the nearest neighbour structure of observations in both the joint and marginal spaces unless both marginal spaces are one dimensional we demonstrate that a well known estimator of this type can be computationally expensive under certain conditions and propose a computationally efficient alternative that has a time complexity of order o n log n a s the number of observations n n

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

on the validity of zeeman s classification for three dimensional competitive differential equations with linearly determined nullclines abstract we study three dimensional competitive differential equations with linearly determined nullclines and prove that they always have 33 stable nullcline classes in total each class is given in terms of inequalities on the intrinsic growth rates and competitive coefficients and is independent of generating functions the common characteristics are that every trajectory converges to an equilibrium in classes 1 25 that hopf bifurcations do not occur within class 32 and that there is always a heteroclinic cycle in class 27 nontrivial dynamical behaviors such as the existence and multiplicity of limit cycles only may occur in classes 26 33 but these nontrivial dynamical behaviors depend on generating functions we show that hopf bifurcation can occur within each of classes 26 31 for continuous time leslie gower system and ricker system the same as lotka volterra system but it only occurs in classes 26 and 27 for continuous time atkinson allen system and gompertz system there is an apparent distinction between lotka volterra system and leslie gower system ricker system atkinson allen system and gompertz system with the identical growth rate lotka volterra system with the identical growth rate has no limit cycle but admits a center on the carrying simplex in classes 26 and 27 but leslie gower system ricker system atkinson allen system and gompertz system with the identical growth rate do possess limit cycles at last we provide examples to show that leslie gower system and ricker system can also admit two limit cycles this general classification greatly widens applications of zeeman s method and makes it possible to investigate the existence and multiplicity of limit cycles centers and stability of heteroclinic cycles for three dimensional competitive systems with linearly determined nullclines as done in planar systems

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

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

limit theorems for weighted samples with applications to sequential monte carlo methods in the last decade sequential monte carlo methods smc emerged as a key tool in computational statistics see e g sequential monte carlo methods in practice 2001 springer new york monte carlo strategies in scientific computing 2001 springer new york complex stochastic systems 2001 109 173 these algorithms approximate a sequence of distributions by a sequence of weighted empirical measures associated to a weighted population of particles which are generated recursively despite many theoretical advances see e g j roy statist soc ser b 63 2001 127 146 ann statist 33 2005 1983 2021 feynman kac formulae genealogical and interacting particle systems with applications 2004 springer ann statist 32 2004 2385 2411 the large sample theory of these approximations remains a question of central interest in this paper we establish a law of large numbers and a central limit theorem as the number of particles gets large we introduce the concepts of weighted sample consistency and asymptotic normality and derive conditions under which the transformations of the weighted sample used in the smc algorithm preserve these properties to illustrate our findings we analyze smc algorithms to approximate the filtering distribution in state space models we show how our techniques allow to relax restrictive technical conditions used in previously reported works and provide grounds to analyze more sophisticated sequential sampling strategies including branching resampling at randomly selected times and so on

estimation of nonlinear functionals of densities with confidence this paper introduces a class of k nearest neighbor k nn estimators called bipartite plug in bpi estimators for estimating integrals of nonlinear functions of a probability density such as shannon entropy and renyi entropy the density is assumed to be smooth have bounded support and be uniformly bounded from below on this set unlike previous k nn estimators of nonlinear density functionals the proposed estimator uses data splitting and boundary correction to achieve lower mean square error specifically we assume that t i i d samples xi rd from the density are split into two pieces of cardinality m and n respectively with m samples used for computing a k nn density estimate and the remaining n samples used for empirical estimation of the integral of the density functional by studying the statistical properties of k nn balls explicit rates for the bias and variance of the bpi estimator are derived in terms of the sample size the dimension of the samples and the underlying probability distribution based on these results it is possible to specify optimal choice of tuning parameters m t k for maximizing the rate of decrease of the mean square error the resultant optimized bpi estimator converges faster and achieves lower mean squared error than previous k nn entropy estimators in addition a central limit theorem is established for the bpi estimator that allows us to specify tight asymptotic confidence intervals

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

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

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

geometric approach for global asymptotic stability for three species competitive gompertz models abstract this paper deals with the three dimensional competitive models with gompertz growth in population dynamics by using the geometric criterion and time average property to gompertz models a new criterion on the global asymptotical stability of the models is established furthermore based on this criterion a partial affirmative answer to jiang niu zhu s open problems is given

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

the iterated auxiliary particle filter we present an offline iterated particle filter to facilitate statistical inference in general state space hidden markov models given a model and a sequence of observations the associated margina

a proof of the gamma test from a dataset of input output vectors the gamma test estimates the variance of the noise on an output modulo any smooth model with bounded partial derivatives we present a proof of the gamma test under fairly weak hypotheses

non parametric estimation of residual moments and covariance the aim of non parametric regression is to model the behaviour of a response vector y in terms of an explanatory vector x based only on a finite set of empirical observations this is usually perf

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

twisted particle filters we investigate sampling laws for particle algorithms and the influence of these laws on the efficiency of particle approximations of marginal likelihoods in hidden markov models among a broad class of candidates we characterize the essentially unique family of particle system transition kernels which is optimal with respect to an asymptotic in time variance growth rate criterion the sampling structure of the algorithm defined by these optimal transitions turns out to be only subtly different from standard algorithms and yet the fluctuation properties of the estimates it provides can be dramatically different the structure of the optimal transition suggests a new class of algorithms which we term twisted particle filters and which we validate with asymptotic analysis of a more traditional nature in the regime where the number of particles tends to infinity

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

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

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

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

a class of renyi information estimators for multidimensional densities a class of estimators of the renyi and tsallis entropies of an unknown distribution f in r m is presented these estimators are based on the k th nearest neighbor distances computed from a sample of n i i d vectors with distribution f we show that entropies of any order q including shannon s entropy can be estimated consistently with minimal assumptions on f moreover we show that it is straightforward to extend the nearest neighbor method to estimate the statistical distance between two distributions using one i i d sample from each

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

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

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

spacing distributions for point processes on a regular fractal the homogeneous poisson point process in rd denoted by pd is a basic model of stochastic geometry and modern statistical physics using ideas from fractal geometry geometrical statistics and random matrix theory we introduce the model of random points on a self similar fractal as a model of intermediate statistics in the sense that the interpoint spacing statistics of the model are intermediate between those of p1 and p2 when the fractal dimension is in between 1 and 2 and intermediate between those of p2 and p3 when the fractal dimension is in between 2 and 3 and so on we also introduce the idea of using a continuous family of such models to interpolate between p1 and p2 and thereby effectuate crossover transitions between p1 statistics and p2 statistics we first derive the kth nearest neighbor spacing distribution for the general model and then study the interpoint spacing statistics of several realizations of the model involving sierpinski fractals in r2 and r3 we also study a realization of a continuous interpolation between p1 and p2 in particular a continuous interpolation between a point process on a line and a point process on a plane filling curve using the continuous family of self similar koch curves in r2 in the latter study we specifically analyze the second nearest neighbor interpoint spacing statistics which undergo a crossover transition between semi poisson and ginibre statistics

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

asymptotic moments of near neighbour distance distributions let c be a compact convex body in r m and consider a set of points selected at random from c according to some well behaved sampling distribution we obtain an asymptotic expression for the positive moments of the k th near neighbour distance distribution as the number of points increases to infinity

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

linearn a new approach to nearest neighbour density estimator abstract despite their wide spread use nearest neighbour density estimators have two fundamental limitations o n 2 time complexity and o n space complexity both limitations constrain nearest neighbour density estimators to small data sets only recent progress using indexing schemes has improved to near linear time complexity only we propose a new approach called linearn for linear time nearest neighbour algorithm that yields the first nearest neighbour density estimator having o n time complexity and constant space complexity as far as we know this is achieved without using any indexing scheme because linearn uses a subsampling approach for which the subsample values are significantly less than the data size like existing density estimators our asymptotic analysis reveals that the new density estimator has a parameter to trade off between bias and variance we show that algorithms based on the new nearest neighbour density estimator can easily scale up to data sets with millions of instances in anomaly detection and clustering tasks

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

consistent estimation of linear regression models using matched data abstract economists often use matched samples especially when dealing with earnings data where a number of missing observations need to be imputed in this paper we demonstrate that the ordinary least squares estimator of the linear regression model using matched samples is inconsistent and has a non standard convergence rate to its probability limit if only a few variables are used to impute the missing data then it is possible to correct for the bias we propose two semiparametric bias corrected estimators and explore their asymptotic properties the estimators have an indirect inference interpretation and they attain the parametric convergence rate when the number of matching variables is no greater than four monte carlo simulations confirm that the bias correction works very well in such cases

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