Block sampler and posterior mode estimation for asymmetric stochastic volatility models

A new efficient simulation smoother and disturbance smoother are introduced for asymmetric stochastic volatility models where there exists a correlation between today's return and tomorrow's volatility. The state vector is divided into several blocks where each block consists of many state variables. For each block, corresponding disturbances are sampled simultaneously from their conditional posterior distribution. The algorithm is based on the multivariate normal approximation of the conditional posterior density and exploits a conventional simulation smoother for a linear and Gaussian state-space model. The performance of our method is illustrated using two examples: (1) simple asymmetric stochastic volatility model and (2) asymmetric stochastic volatility model with state-dependent variances. The popular single move sampler which samples a state variable at a time is also conducted for comparison in the first example. It is shown that our proposed sampler produces considerable improvement in the mixing property of the Markov chain Monte Carlo chain.     

Efficient Bayesian estimation of multivariate state space models

A Bayesian Markov chain Monte Carlo methodology is developed for the estimation of multivariate linear Gaussian state space models. In particular, an efficient simulation smoothing algorithm is proposed that makes use of the univariate representation of the state space model. Substantial gains over existing algorithms in computational efficiency are achieved using the new simulation smoother for the analysis of high dimensional multivariate time series.The methodology is used to analyse a multivariate time series dataset of the Normalised Difference Vegetation Index (NDVI), which is a proxy for the level of live vegetation, for a particular grazing property located in Queensland, Australia.     

VISIM: Sequential simulation for linear inverse problems

Linear inverse Gaussian problems are traditionally solved using least squares-based inversion. The center of the posterior Gaussian probability distribution is often chosen as the solution to such problems, while the solution is in fact the posterior Gaussian probability distribution itself. We present an algorithm, based on direct sequential simulation, which can be used to efficiently draw samples of the posterior probability distribution for linear inverse problems. There is no Gaussian restriction on the distribution in the model parameter space, as inherent in traditional least squares-based algorithms.As data for linear inverse problems can be seen as weighed linear averages over some volume, block kriging can be used to perform both estimation (i.e. finding the center of the posterior Gaussian pdf) and simulation (drawing samples of the posterior Gaussian pdf). We present the kriging system which we use to implement a flexible GSLIB-based algorithm for solving linear inverse problems.We show how we implement such a simulation program conditioned to linear average data. The program is called VISIM as an acronym for Volume average Integration SIMulation. An effort has been made to make the program efficient, even for larger scale problems, and the computational efficiency and accuracy of the code is investigated.Using a synthetic cross-borehole tomography case study, we show how the program can be used to generate realizations of the a posteriori distributions (i.e. solutions) from a linear tomography problem. Both Gaussian and non-Gaussian a priori model parameter distributions are considered.     

Approximate Program Smoothing Using Mean‐Variance Statistics,with Application to Procedural Shader Bandlimiting

We introduce a general method to approximate the convolution of a program with a Gaussian kernel. This results in the program being smoothed. Our compiler framework models intermediate values in the program as random variables, by using mean and variance statistics. We decompose the input program into atomic parts and relate the statistics of the different parts of the smoothed program. We give several approximate smoothing rules that can be used for the parts of the program. These include an improved variant of Dorn et al. [ DBLW15 ], a novel adaptive Gaussian approximation, Monte Carlo sampling, and compactly supported kernels. Our adaptive Gaussian approximation handles multivariate Gaussian distributed inputs, gives exact results for a larger class of programs than previous work, and is accurate to the second order in the standard deviation of the kernel for programs with certain analytic properties. Because each expression in the program can have multiple approximation choices, we use a genetic search to automatically select the best approximations. We apply this framework to the problem of automatically bandlimiting procedural shader programs. We evaluate our method on a variety of geometries and complex shaders, including shaders with parallax mapping, animation, and spatially varying statistics. The resulting smoothed shader programs outperform previous approaches both numerically and aesthetically.     

Order-reduction abstractions for safety verification of high-dimensional linear systems

Order-reduction is a standard automated approximation technique for computer-aided design, analysis, and simulation of many classes of systems, from circuits to buildings. To be used as a sound abstraction for formal verification, a measure of the similarity of behavior must be formalized and computed, which we develop in a computational way for a class of asymptotic stable linear systems as the main contributions of this paper. We have implemented the order-reduction as a sound abstraction process through a source-to-source model transformation in the HyST tool and use SpaceEx to compute sets of reachable states to verify properties of the full-order system through analysis of the reduced-order system. Our experimental results suggest systems with thousand of state variables can be reduced to systems with tens of state variables such that the order-reduction overapproximation error is small enough to prove or disprove safety properties of interest using current reachability analysis tools. Our results illustrate this approach is effective in tackling the state-space explosion problem for verification of high-dimensional linear systems.     

Application of interval predictor model into robust model predictive control

Here we apply interval prediction model into robust model predictive control (MPC) strategy. After introducing the family of models and some basic information, we present the computational results for the construction of interval predictor model, whose regression parameters are included in a sphere parameter set. Given a size measure to scale the average amplitude of the predictor interval, one optimal model that minimises a size measure is efficiently computed by solving a linear programming problem. We apply the active set approach to solve the linear programming problem and based on these optimisation variables, the predictor interval of the considered model with sphere parameter set can be constructed. As for a fixed non-negative number from the size measure, we propose a better choice by using the optimality conditions. In order to apply interval prediction model into robust MPC, two strategies are proposed to analyse a min-max optimisation problem. After input and output variables are regarded as decision variables, a standard quadratic optimisation is obtained and its dual form is derived, then Gauss–Seidel algorithm is proposed to solve the dual problem and convergence of Gauss–Seidel algorithm is provided too. Finally two simulation examples confirm the theoretical results.     

A cell technique for computing the failure probabilities of structural systems

Several methods for computing structural system reliability are reviewed. A discretization or cell technique for determining the failure probabilites of structural systems is proposed. The Gaussian numerical integration method is introduced to improve its computational accuracy. The method can apply to Gaussian or non-Gaussian variables with linear or nonlinear safety margin equations. The method is easy to realize and requires no iteration or partial differentiation of the safety margin equations. The theory and examples show that the computer run-time of this method is very low.     

Discrete time LQG controls with control dependent noise

This paper presents some studies on partially observed linear quadratic Gaussian (LQG) models where the stochastic disturbances depend on both the states and the controls, and the measurements are bilinear in the noise and the states/controls. While the Separation Theorem of standard LQG design does not apply, suboptimal linear state estimate feedback controllers are derived based on certain linearizations. The controllers are useful for nonlinear stochastic systems where the linearized models include terms bilinear in the noise and states/controls and are significantly more accurate than if the bilinear terms are set to zero. The controllers are calculated by solving a generalized discrete time Riccati equation, which in turn has properties relating to well posedness of the associated LQG problem.     

Computation of transfer-function matrices of generalized state-space models

A reliable computational algorithm is proposed for the evaluation of the transfer-function matrices of linear multivariable systems described by generalized state-Space models. The algorithm is based on a new, efficient and numerically stable procedure for computing irreducible state-space realizations of generalized state-space models. For each input-output channel, the proposed algorithm computes an irreducible realization using this procedure. Then, the parameters of the corresponding transfer function (gain, poles, zeros) are determined from the resulting irreducible model.     

Mechanism-based emulation of dynamic simulation models: Concept and application in hydrology

Many model-based investigation techniques, such as sensitivity analysis, optimization, and statistical inference, require a large number of model evaluations to be performed at different input and/or parameter values. This limits the application of these techniques to models that can be implemented in computationally efficient computer codes. Emulators, by providing efficient interpolation between outputs of deterministic simulation models, can considerably extend the field of applicability of such computationally demanding techniques. So far, the dominant techniques for developing emulators have been priors in the form of Gaussian stochastic processes (GASP) that were conditioned with a design data set of inputs and corresponding model outputs. In the context of dynamic models, this approach has two essential disadvantages: (i) these emulators do not consider our knowledge of the structure of the model, and (ii) they run into numerical difficulties if there are a large number of closely spaced input points as is often the case in the time dimension of dynamic models. To address both of these problems, a new concept of developing emulators for dynamic models is proposed. This concept is based on a prior that combines a simplified linear state space model of the temporal evolution of the dynamic model with Gaussian stochastic processes for the innovation terms as functions of model parameters and/or inputs. These innovation terms are intended to correct the error of the linear model at each output step. Conditioning this prior to the design data set is done by Kalman smoothing. This leads to an efficient emulator that, due to the consideration of our knowledge about dominant mechanisms built into the simulation model, can be expected to outperform purely statistical emulators at least in cases in which the design data set is small. The feasibility and potential difficulties of the proposed approach are demonstrated by the application to a simple hydrological model.     

Simulation and visualization of the Saint-Venant system using GPUs

We consider three high-resolution schemes for computing shallow-water waves as described by the Saint-Venant system and discuss how to develop highly efficient implementations using graphical processing units (GPUs). The schemes are well-balanced for lake-at-rest problems, handle dry states, and support linear friction models. The first two schemes handle dry states by switching variables in the reconstruction step, so that bilinear reconstructions are computed using physical variables for small water depths and conserved variables elsewhere. In the third scheme, reconstructed slopes are modified in cells containing dry zones to ensure non-negative values at integration points. We discuss how single and double-precision arithmetics affect accuracy and efficiency, scalability and resource utilization for our implementations, and demonstrate that all three schemes map very well to current GPU hardware. We have also implemented direct and close-to-photo-realistic visualization of simulation results on the GPU, giving visual simulations with interactive speeds for reasonably-sized grids.     

祛除图像斑点的曲面细节动态转移技术

针对曲面细节转移在祛除图像斑点应用时,需要依赖用户对斑点几何细节模型的视觉观察确定Gaussian平滑参数σ的大小,对用户每次改变σ的取值都需要实施将Gaussian平滑应用到整个图像的耗时操作,提出了一种曲面细节动态转移的技术,它能够根据斑点的大小自动确定σ的大小,且仅需要将Gaussian平滑应用到与斑点相对应的小区域,使祛除图像斑点智能化,极大地提高了运算效率。     

Combining particle MCMC with Rao-Blackwellized Monte Carlo data association for parameter estimation in multiple target tracking

We consider state and parameter estimation in multiple target tracking problems with data association uncertainties and unknown number of targets. We show how the problem can be recast into a conditionally linear Gaussian state-space model with unknown parameters and present an algorithm for computationally efficient inference on the resulting model. The proposed algorithm is based on combining the Rao-Blackwellized Monte Carlo data association algorithm with particle Markov chain Monte Carlo algorithms to jointly estimate both parameters and data associations. Both particle marginal Metropolis–Hastings and particle Gibbs variants of particle MCMC are considered. We demonstrate the performance of the method both using simulated data and in a real-data case study of using multiple target tracking to estimate the brown bear population in Finland.     

Speech Recognition Using Linear Dynamic Models

The majority of automatic speech recognition systems rely on hidden Markov models, in which Gaussian mixtures model the output distributions associated with sub-phone states. This approach, whilst successful, models consecutive feature vectors (augmented to include derivative information) as statistically independent. Furthermore, spatial correlations present in speech parameters are frequently ignored through the use of diagonal covariance matrices. This paper continues the work of Digalakis and others who proposed instead a first-order linear state-space model which has the capacity to model underlying dynamics, and furthermore give a model of spatial correlations. This paper examines the assumptions made in applying such a model and shows that the addition of a hidden dynamic state leads to increases in accuracy over otherwise equivalent static models. We also propose a time-asynchronous decoding strategy suited to recognition with segment models. We describe implementation of decoding for linear dynamic models and present TIMIT phone recognition results     

Approximate Bayesian inference in spatial GLMM with skew normal latent variables

Spatial generalized linear mixed models are common in applied statistics. Most users are satisfied using a Gaussian distribution for the spatial latent variables in this model, but it is unclear whether the Gaussian assumption holds. Wrong Gaussian assumptions cause bias in the parameter estimates and affect the accuracy of spatial predictions. Thus, there is a need for more flexible priors for the latent variables, and to perform efficient inference and spatial prediction in the resulting models. In this paper we use a skew normal prior distribution for the spatial latent variables. We propose new approximate Bayesian methods for the inference and spatial prediction in this model. A key ingredient in our approximations is using the closed skew normal distribution to approximate the full conditional for the latent variables. Our approximate inference and spatial prediction methods are fast and deterministic, using no sampling based strategies. The results indicate that the skew normal prior model can give better predictions than the normal model, while avoiding overfitting.     

A state-space approach to optimum postfiltering of sampled data

In this paper, we apply state-space techniques to the problem of reconstructing a random continuous-time waveform from its discrete-time samples. The optimal zero-lag filter that accomplishes this is well known, but to our knowledge the smoothing problem has not been previously considered in this context. We develop smoothing algorithms in the mixed-time framework appropriate to the interpolation problem, and then compare our results with those obtained previously in discrete time. Our results are related to those previously obtained in a simple and intuitive way, and the required computations are straightforward modifications of those described previously for purely discrete and purely continuous time.     

Continuous speech recognition using linear dynamic models

Hidden Markov models (HMMs) with Gaussian mixture distributions rely on an assumption that speech features are temporally uncorrelated, and often assume a diagonal covariance matrix where correlations between feature vectors for adjacent frames are ignored. A Linear Dynamic Model (LDM) is a Markovian state-space model that also relies on hidden state modeling, but explicitly models the evolution of these hidden states using an autoregressive process. An LDM is capable of modeling higher order statistics and can exploit correlations of features in an efficient and parsimonious manner. In this paper, we present a hybrid LDM/HMM decoder architecture that postprocesses segmentations derived from the first pass of an HMM-based recognition. This smoothed trajectory model is complementary to existing HMM systems. An Expectation-Maximization (EM) approach for parameter estimation is presented. We demonstrate a 13 % relative WER reduction on the Aurora-4 clean evaluation set, and a 13 % relative WER reduction on the babble noise condition.     

Probabilistic approximation of runtime quantitative verification in self-adaptive systems

Cyber-physical systems (CPS) are expected to continuously monitor the physical components to autonomously calculate appropriate runtime reactions to deal with the uncertain environmental conditions. Self-adaptation, as a promising concept to fulfill a set of provable rules, majorly needs runtime quantitative verification (RQV). Taking a few probabilistic variables into account to represent the uncertainties, the system configuration will be extremely large. Thus, efficient approaches are needed to reduce the model state-space, preferably with certain bounds on the approximation error. In this paper, we propose an approximation framework to efficiently approximate the entire model of a self-adaptive system. We split up the large model into strongly-connected components (SCCs), apply the approximation algorithm separately on each SCC, and integrate the result of each part using a centralized algorithm. Due to a number of changes in probabilistic variables, it is not possible to use static models. Addressing this issue, we have deployed parametric Markov decision process. In order to apply approximation on the model, the notion of ε-approximate probabilistic bisimulation is utilized that introduces the approximation level ε. We show that our approximation framework offers a certain error bound on each level of approximation. Then, we denote that the approximation framework is appropriate to be applied in decision-making process of self-adaptive systems where the models are relatively large. The results reveal that we can achieve up to 50% size reduction in the approximate model while maintaining the accuracy about 95%. In addition, we discuss about the trade-off between efficiency and accuracy of our approximation framework.     

Modeling and estimation of discrete-time Gaussian reciprocalprocesses

Discrete-time Gaussian reciprocal processes are characterized in terms of a second-order two-point boundary-value nearest-neighbor model driven by a locally correlated noise whose correlation is specified by the model dynamics. This second-order model is the analog for reciprocal processes of the standard first-order state-space models for Markov processes. The model is used to obtain a solution to the smoothing problem for reciprocal processes. The resulting smoother obeys second-order equations whose structure is similar to that of the Kalman filter for Gauss-Markov processes. It is shown that the smoothing error is itself a reciprocal process