Sequential importance sampling for structural reliability analysis

In 2005, Chen et al. introduced a sequential importance sampling (SIS) procedure to analyze zero-one two-way tables with given fixed marginal sums (row and column sums) via the conditional Poisson (CP) distribution. They showed that compared with Monte Carlo Markov chain (MCMC)-based approaches, their importance sampling method is more efficient in terms of running time and also provides an easy and accurate estimate of the total number of contingency tables with fixed marginal sums. In this paper, we extend their result to zero-one multi-way ( $$d$$ -way, $$d \ge 2$$ ) contingency tables under the no $$d$$ -way interaction model, i.e., with fixed $$d-1$$ marginal sums. Also, we show by simulations that the SIS procedure with CP distribution to estimate the number of zero-one three-way tables under the no three-way interaction model given marginal sums works very well even with some rejections. We also applied our method to Samson’s monks data set.

Publication in the conference proceedings of EUSIPCO, Toulouse, France, 2002

Applications of graphical models often require the use of approximate inference, such as sequential importance sampling (SIS), for estimation of the model distribution given partial evidence, i.e., the target distribution. However, when SIS proposal and target distributions are dissimilar, such procedures lead to biased estimates or require a prohibitive number of samples. We introduce ReBaSIS, a method that better approximates the target distribution by sampling variable by variable from existing importance samplers and accepting or rejecting each proposed assignment in the sequence: a choice made based on anticipating upcoming evidence. We relate the per-variable proposal and model distributions by expected weight ratios of sequence completions and show that we can learn accurate models of optimal acceptance probabilities from local samples. In a continuous-time domain, our method improves upon previous importance samplers by transforming an SIS problem into a machine learning one.

We propose a sequential Monte Carlo (SMC) method to efficiently and accurately compute cut-Bayesian posterior quantities of interest, variations of standard Bayesian approaches constructed primarily to account for model misspecification. We prove finite sample concentration bounds for estimators derived from the proposed method along with a linear tempering extension and apply these results to a realistic setting where a computer model is misspecified. We then illustrate the SMC method for inference in a modular chemical reactor example that includes submodels for reaction kinetics, turbulence, mass transfer, and diffusion. The samples obtained are commensurate with a direct-sampling approach that consists of running multiple Markov chains, with computational efficiency gains using the SMC method. Overall, the SMC method presented yields a novel, rigorous approach to computing with cut-Bayesian posterior distributions.

Based on the concept of sequential importance sampling (SIS) and the use of Bayesian theory, particle filter is particularly useful in dealing with nonlinear and non-Gaussian problems. In this paper, a new particle filter is proposed that uses a divided difference filter to generate the importance proposal distribution is proposed. The proposal distribution integrates the latest measurements into system state transition density so it can match the posterior density well. The simulation results show that the new particle filter performs superior to the generic particle filter and other particle filters such as the extended Kalman particle filter and the unscented particle filter.

For state estimation problem, particle filter is generally used to construct the posterior probability density function by a set of particles, which is regarded as a solution to state estimation. Many techniques have been developed to improve performance of particle filter, at the cost of largely increased computational burden for each particle. In this paper, we propose a post-resampling based particle filter. The modified particle filter is capable of accurately representing the posterior probability density function through properly sampling particles. We applied the proposed particle filter to the classic bearings-only tracking problem. Simulation results showed that our modified particle filter had superior performance and reasonably computational cost, compared with the general approaches. It may provide a promising alternative to the existent particle filters.

The reliability polynomial of a graph gives the probability that a graph is connected as a function of the probability that each edge is connected. The coefficients of the reliability polynomial count the number of connected subgraphs of various sizes. Algorithms based on sequential importance sampling (SIS) have been proposed to estimate a graph's reliability polynomial. We develop a new bottom-up SIS algorithm for estimating the reliability polynomial by choosing a spanning tree and adding edges. This algorithm improves on existing bottom-up algorithms in that it has lower complexity ≈ O(E2) as opposed to O(EV3), and it uses importance sampling to reduce variance.

This paper proposes a novel method for joint estimation of carrier phase, Doppler shift, Doppler rate, and data detection using particle filter (PF). Using sequential importance sampling (SIS) the proposed algorithm estimates the posterior joint probability of unknown parameters and transmitted data symbols in a recursive fashion. We also propose a method for fine tuning of particles for quick convergence. The Monte Carlo simulations confirm the validity of the proposed algorithm. We show numerically that the bit error rate (BER) performance of the proposed particle filter with the fine tuning method is within 0.5-1 dB of the ideal scenario (no error in parameter estimation) with only 100 particles. Simulations with fine tuning of particles depict significant gains in signal-to-noise ratio (SNR) for root-mean-square error (RMSE) of Doppler shift and Doppler rate (compared to cases without fine tuning of particles).

Damage detection of civil infrastructure has gained significant momentum in the last decade due to aging and being more prone to failure of infrastructure. New advances in sensing technology have made it possible to detect damage in giant infrastructure more effectively. As the size of structure increases, the number of installed sensors on the structure increases significantly. This increase in the number of sensors makes it more challenging to collect and interpret the data. Therefore, utilizing the minimum number of sensors at any time of detection while maintaining an effective monitoring system is of great interest. In this paper, we will develop an innovative on/off sensors methodology using the sequential importance sampling technique to choose the sensors to be turned on at any given time while tracking the potential damage. This method will be used on a cable stayed bridge over Mississippi River called Luling Bridge. The finite element (FE) model of the bridge is developed to introduce the damage at different girder locations in the bridge. This model will be used to show the effectiveness of the proposed sequential importance sampling method in providing effective monitoring with minimal number of turned activated sensors at any given time.

Online Estimation of DSGE Models

We study efficient importance sampling techniques for particle filtering (PF) when either (a) the observation likelihood (OL) is frequently multimodal or heavy-tailed, or (b) the state space dimension is large or both. When the OL is multimodal, but the state transition pdf (STP) is narrow enough, the optimal importance density is usually unimodal. Under this assumption, many techniques have been proposed. But when the STP is broad, this assumption does not hold. We study how existing techniques can be generalized to situations where the optimal importance density is multimodal, but is unimodal conditioned on a part of the state vector. Sufficient conditions to test for the unimodality of this conditional posterior are derived. Our result is directly extendable to testing for unimodality of any posterior. The number of particles N to accurately track using a PF increases with state space dimension, thus making any regular PF impractical for large dimensional tracking problems. But in most such problems, most of the state change occurs in only a few dimensions, while the change in the rest of the dimensions is small. Using this property, we propose to replace importance sampling from a large part of the state space (whose conditional posterior is narrow enough) by just tracking the mode of the conditional posterior. This introduces some extra error, but it also greatly reduces the importance sampling dimension. The net effect is much smaller error for a given N, especially when the available N is small. An important class of large dimensional problems with multimodal OL is tracking spatially varying physical quantities such as temperature or pressure in a large area using a network of sensors which may be nonlinear and/or may have nonnegligible failure probabilities. Improved performance of our proposed algorithms over existing PFs is demonstrated for this problem.

Particle filters are simulation-based algorithms for computational inference in dynamical systems that have become very popular over the years in many areas of science and engineering. They are derived from Bayes' theorem and the technique of importance sampling (IS), which entails the approximation of probability measures by way of weighted random samples in the space of interest. As a consequence, particle filters suffer from problems related to the degeneracy of these weights, a limitation shared with other IS-based methods. In practice, the weight degeneracy implies that in some scenarios (typically when the dimension of the state space is high or when the likelihood function of the system is sharp) classical particle filters become numerically unstable and fail to converge. In this paper we investigate the application of a recently proposed technique, termed nonlinear importance sampling (NIS), to the design of particle filters. We show how the standard particle filter can be easily modified to incorporate transformed weights computed according to the NIS scheme, then provide a concise proof of convergence of the resulting algorithm, and finally present computer simulation results to illustrate the potential improvement in performance that can be attained.

Demodulation of data transmitted over time-varying channels with a free running hidden Markov state, like the phase noise channel or the fading channel, requires that the receiver tracks the hidden channel state. The tracking technique adopted in the paper is based on non-data-aided sequential importance sampling, also known as particle filtering.The paper proposes a new particle filtering framework for data communication receivers based on an importance distribution such that each individual particle becomes a decision-directed Kalman filter relying upon its local symbol-by-symbol hard decisions. In this framework, different particles are left free to take different sequences of decisions. This leaves to the receiver the possibility of exploring different sequences of transmitted modulation symbols. The weight of the particle will be high for those particles that took in the past the correct sequence of decisions, while will be low for those particles that took wrong decisions. In the resampling procedure, particles with high weight will survive, while particles with low weight will be terminated, leaving space to the birth of new particles resampled from the surviving ones.The crucial point in importance sampling is the choice of the importance distribution and the main novelty of the paper is the proposal of an importance distribution such that the particles of the particle filter become decision-directed Kalman filters. One important benefit brought by our proposed method is that, being non-data-aided, it does not need pilot symbols, thus allowing to preserve the transmission rate. A significant application example, presented and developed in the paper, is constituted by MIMO systems affected by phase noise, where the channel state vector consists of many parameters.

This paper discusses new directions of research to detect and diagnose Gaussian and non-Gaussian faults a new nonlinear observer (NOFS) based on Fuzzy and Sequential Important Sampling (FSIS) filter for each unknown states of the plant depending on the diagnosed. The idea based on expanding the size of freedom for the dynamic states of the observers. Therefore, NOFS has been designed and implemented to be robust nonlinear observer against the colored noise and non-Gaussian noise.

Sequential importance sampling offers an alternative way to approximately evaluate the permanent. It is a stochastic algorithm which seems to work in practice but has eluded analysis. This paper offers examples where the analysis can be carried out and the first general bounds for the sample size required. This uses a novel importance sampling proof of Bregman’s inequality due to Lovasz.