Linear Gaussian Model Research Articles

Distributed Bayesian filtering using logarithmic opinion pool for dynamic sensor networks

The discrete-time Distributed Bayesian Filtering (DBF) algorithm is presented for the problem of tracking a target dynamic model using a time-varying network of heterogeneous sensing agents. In the DBF algorithm, the sensing agents combine their normalized likelihood functions in a distributed manner using the logarithmic opinion pool and the dynamic average consensus algorithm. We show that each agent’s estimated likelihood function globally exponentially converges to an error ball centered on the joint likelihood function of the centralized multi-sensor Bayesian filtering algorithm. We rigorously characterize the convergence, stability, and robustness properties of the DBF algorithm. Moreover, we provide an explicit bound on the time step size of the DBF algorithm that depends on the time-scale of the target dynamics, the desired convergence error bound, and the modeling and communication error bounds. Furthermore, the DBF algorithm for linear-Gaussian models is cast into a modified form of the Kalman information filter. The performance and robust properties of the DBF algorithm are validated using numerical simulations.

Particle Smoothing for Conditionally Linear Gaussian Models as Message Passing Over Factor Graphs

In this paper, the fixed-lag smoothing problem for conditionally linear Gaussian state-space models is investigated from a factor graph perspective. More specifically, after formulating Bayesian smoothing for an arbitrary state-space model as a forward–backward message passing over a factor graph, we focus on the above-mentioned class of models and derive two novel particle smoothers for it. Both the proposed techniques are based on the well-known two-filter smoothing approach and employ marginalized particle filtering in their forward pass. However, on the one hand, the first smoothing technique can only be employed to improve the accuracy of state estimates with respect to that achieved by forward filtering. On the other hand, the second method, that belongs to the class of Rao–Blackwellized particle smoothers, also provides a point mass approximation of the so-called joint smoothing distribution. Finally, our smoothing algorithms are compared, in terms of estimation accuracy and computational requirements, with a Rao–Blackwellized particle smoother recently proposed by Lindsten et al. (“Rao–Blackwellized particle smoothers for conditionally linear Gaussian models,” IEEE J. Sel. Topics Signal Process. , vol. 10, no. 2, pp. 353–365, 2016).

Cognitive-Behavioral Therapy for Insomnia to Reduce Chronic Migraine: A Sequential Bayesian Analysis.

Insomnia is frequently comorbid with chronic migraine, and small trials suggest that cognitive-behavioral treatment of insomnia (CBTi) may reduce migraine frequency. This study endeavored to provide a quantitative synthesis of existing CBTi trials for adults with chronic migraine using Bayesian statistical methods, given their utility in combining prior knowledge with sequentially gathered data. Completer analyses of 2 randomized trials comparing CBTi to a sham control intervention (Calhoun and Ford, 2007; Smitherman et al, 2016) were used to quantify the effects of a brief course of treatment on headache frequency. Change in headache frequency from baseline to the primary endpoint (6-8 weeks posttreatment) was regressed on group status using a Gaussian linear model with each study specified in the order of completion. To estimate the combined effect, posterior distributions from the Calhoun and Ford study were used as informative priors for conditioning on the Smitherman et al data. In a combined analysis of these prior studies, monthly headache frequency of the treatment group decreased by 6.2 days (95%CrI: -9.7 to -2.7) more than the control group, supporting an interpretation that there is a 97.5% chance that the treatment intervention is at least 2.7 days better than the control intervention. The analysis supports the hypothesis that at least for those who complete treatment, there is high probability that individuals who receive CBTi experience greater headache reduction than those who receive a control intervention equated for therapist time and out-of-session skills practice. Cognitive-behavioral interventions for comorbid insomnia hold promise for reducing headache frequency among those with chronic migraine. These findings add to a small but growing body of literature that migraineurs with comorbid conditions often respond well to behavioral interventions, and that targeting comorbidities may improve migraine itself.

Inversion copulas from nonlinear state space models with an application to inflation forecasting

We propose the construction of copulas through the inversion of nonlinear state space models. These copulas allow for new time series models that have the same serial dependence structure as a state space model, but with an arbitrary marginal distribution, and flexible density forecasts. We examine the time series properties of the copulas, outline serial dependence measures, and estimate the models using likelihood-based methods. Copulas constructed from three example state space models are considered: a stochastic volatility model with an unobserved component, a Markov switching autoregression, and a Gaussian linear unobserved component model. We show that all three inversion copulas with flexible margins improve the fit and density forecasts of quarterly U.S. broad inflation and electricity inflation.

A General Class of Score-Driven Smoothers

We propose a methodology for filtering, smoothing and assessing parameter and filtering uncertainty in misspecified score-driven models. Our technique is based on a general representation of the well-known Kalman filter and smoother recursions for linear Gaussian models in terms of the score of the conditional log-likelihood. We prove that, when data are generated by a nonlinear non-Gaussian state-space model, the proposed methodology results from a first-order expansion of the true observation density around the optimal filter. The error made by such approximation is assessed analytically. As shown in extensive Monte Carlo analyses, our methodology performs very similarly to exact simulation-based methods, while remaining computationally extremely simple. We illustrate empirically the advantages in employing score-driven models as misspecified filters rather than purely predictive processes.

Optimal projection of observations in a Bayesian setting

Optimal dimensionality reduction methods are proposed for the Bayesian inference of a Gaussian linear model with additive noise in presence of overabundant data. Three different optimal projections of the observations are proposed based on information theory: the projection that minimizes the Kullback–Leibler divergence between the posterior distributions of the original and the projected models, the one that minimizes the expected Kullback–Leibler divergence between the same distributions, and the one that maximizes the mutual information between the parameter of interest and the projected observations. The first two optimization problems are formulated as the determination of an optimal subspace and therefore the solution is computed using Riemannian optimization algorithms on the Grassmann manifold. Regarding the maximization of the mutual information, it is shown that there exists an optimal subspace that minimizes the entropy of the posterior distribution of the reduced model; a basis of the subspace can be computed as the solution to a generalized eigenvalue problem; an a priori error estimate on the mutual information is available for this particular solution; and that the dimensionality of the subspace to exactly conserve the mutual information between the input and the output of the models is less than the number of parameters to be inferred. Numerical applications to linear and nonlinear models are used to assess the efficiency of the proposed approaches, and to highlight their advantages compared to standard approaches based on the principal component analysis of the observations.

Simulation Study of cDNA Dataset to Investigate Possible Association of Differentially Expressed Genes of Human THP1-Monocytic Cells in Cancer Progression Affected by Bacterial Shiga Toxins.

Shiga toxin (Stxs) is a family of structurally and functionally related bacterial cytotoxins produced by Shigella dysenteriae serotype 1 and shigatoxigenic group of Escherichia coli that cause shigellosis and hemorrhagic colitis, respectively. Until recently, it has been thought that Stxs only inhibits the protein synthesis and induces expression to a limited number of genes in host cells, but recent data showed that Stxs can trigger several signaling pathways in mammalian cells and activate cell cycle and apoptosis. To explore the changes in gene expression induced by Stxs that have been shown in other systems to correlate with cancer progression, we performed the simulated analysis of cDNA dataset and found differentially expressed genes (DEGs) of human THP1-monocytic cells treated with Stxs. In this study, the entire data (treated and untreated replicates) was analyzed by statistical algorithms implemented in Bioconductor packages. The output data was validated by the k-fold cross technique using generalized linear Gaussian models. A total of 50 DEGs were identified. 7 genes including TSLP, IL6, GBP1, CD274, TNFSF13B, OASL, and PNPLA3 were considerably (<0.00005) related to cancer proliferation. The functional enrichment analysis showed 6 down-regulated and 1 up-regulated genes. Among these DEGs, IL6 was associated with several cancers, especially with leukemia, lymphoma, lungs, liver and breast cancers. The predicted regulatory motifs of these genes include conserved RELA, STATI, IRFI, NF-kappaB, PEND, HLF, REL, CEBPA, DI_2, and NFKB1 transcription factor binding sites (TFBS) involved in the complex biological functions. Thus, our findings suggest that Stxs has the potential as a valuable tool for better understanding of treatment strategies for several cancers.

A proposition of generalized stochastic Milevsky–Promislov mortality models

The aim of this article is to propose a new approach to the estimation of the mortality rates based on two extended Milevsky and Promislov models: the first one with colored excitations modeled by Gaussian linear filters and the second one with excitations modeled by a continuous non-Gaussian process. The exact analytical formulas for theoretical mortality rates based on Gaussian linear scalar filter models have been derived. The theoretical values obtained in both cases were compared with theoretical mortality rates based on a classical Lee–Carter model, and verified on the basis of empirical Polish mortality data. The obtained results confirm the usefulness of the switched model based on the continuous non-Gaussian process for modeling mortality rates.

Power of the spacing test for least-angle regression

Recent advances in Post-Selection Inference have shown that conditional testing is relevant and tractable in high-dimensions. In the Gaussian linear model, further works have derived unconditional test statistics such as the Kac–Rice Pivot for general penalized problems. In order to test the global null, a prominent offspring of this breakthrough is the Spacing test that accounts the relative separation between the first two knots of the celebrated least-angle regression (LARS) algorithm. However, no results have been shown regarding the distribution of these test statistics under the alternative. For the first time, this paper addresses this important issue for the Spacing test and shows that it is unconditionally unbiased. Furthermore, we provide the first extension of the Spacing test to the frame of unknown noise variance. More precisely, we investigate the power of the Spacing test for LARS and prove that it is unbiased: its power is always greater or equal to the significance level $\alpha$. In particular, we describe the power of this test under various scenarii: we prove that its rejection region is optimal when the predictors are orthogonal; as the level $\alpha$ goes to zero, we show that the probability of getting a true positive is much greater than $\alpha$; and we give a detailed description of its power in the case of two predictors. Moreover, we numerically investigate a comparison between the Spacing test for LARS, the Pearson’s chi-squared test (goodness of fit) and a numerical testing procedure based on the maximal correlation. When the noise variance is unknown, our analysis unleashes a new test statistic that can be computed in cubic time in the population size and which we refer to as the $t$-Spacing test for LARS. The $t$-Spacing test involves the first two knots of the LARS algorithm and we give its distribution under the null hypothesis. Interestingly, numerical experiments witness that the $t$-Spacing test for LARS enjoys the same aforementioned properties as the Spacing test.

A Novel Adaptive Kalman Filter With Inaccurate Process and Measurement Noise Covariance Matrices

In this paper, a novel variational Bayesian (VB)-based adaptive Kalman filter (VBAKF) for linear Gaussian state-space models with inaccurate process and measurement noise covariance matrices is proposed. By choosing inverse Wishart priors, the state together with the predicted error and measurement noise covariance matrices are inferred based on the VB approach. Simulation results for a target tracking example illustrate that the proposed VBAKF has better robustness to resist the uncertainties of process and measurement noise covariance matrices than existing state-of-the-art filters.

Weighted-average least squares estimation of generalized linear models

The weighted-average least squares (WALS) approach, introduced by Magnus et al. (2010) in the context of Gaussian linear models, has been shown to enjoy important advantages over other strictly Bayesian and strictly frequentist model-averaging estimators when accounting for problems of uncertainty in the choice of the regressors. In this paper we extend the WALS approach to deal with uncertainty about the specification of the linear predictor in the wider class of generalized linear models (GLMs). We study the large-sample properties of the WALS estimator for GLMs under a local misspecification framework, and the finite-sample properties of this estimator by a Monte Carlo experiment the design of which is based on a real empirical analysis of attrition in the first two waves of the Survey of Health, Aging and Retirement in Europe (SHARE).

Compressed Sensing With a Gaussian Scale Mixture Model for Limited View Photoacoustic Computed Tomography In Vivo.

Photoacoustic computed tomography using an ultrasonic array is an attractive noninvasive imaging modality for many biomedical applications. However, the potentially long data acquisition time of array-based photoacoustic computed tomography—usually due to the required time-multiplexing for multiple laser pulses—decreases its applicability for rapid disease diagnoses and the successive monitoring of physiological functions. Compressed sensing is used to improve the imaging speed of photoacoustic computed tomography by decreasing the amount of acquired data; however, the imaging quality can be limited when fewer measurements are used, as traditional compressed sensing considers only the sparsity of the signals in the imaging process. In this work, an advanced compressed sensing reconstruction framework with a Wiener linear estimation-based Gaussian scale mixture model was developed for limited view photoacoustic computed tomography. In this method, the structure dependencies of signals in the wavelet domain were incorporated into the imaging framework through the Gaussian scale mixture model, and an operator based on the Wiener linear estimation was designed to filter the reconstruction artifacts. Phantom and human forearm imaging were performed to verify the developed method. The results demonstrated that compressed sensing with a Wiener linear estimation-based Gaussian scale mixture model more effectively suppressed the reconstruction artifacts of sparse-sampling photoacoustic computed tomography and recovered photoacoustic images with a higher contrast-to-noise ratio and edge resolution than the traditional compressed sensing method. This work may promote the development of low-cost photoacoustic computed tomography techniques with rapid data acquisition and enhance the performance of photoacoustic computed tomography in various biomedical studies.

Application of a Linear Gaussian State Space Model and the Kalman Filter in Estimating Expectations of the Natural Logarithmic Monthly Nav Returns of the Open – End Funds of Major Investment Banks.

In this article, we have tested a linear Gaussian state space model and the Kalman filter in testing ARMA(2,4) model of the natural logarithmic monthly market returns of the of the open – end funds of major investment banks such as: Merrill Lynch small cap value A, Fidelity equity income I, Goldman Sachs capital growth A, JPMorgan capital growth A, Invesco value equity investment, and Credit Suisse blue chip A. The purpose of this article is to estimate expectations that arises from the interaction of arbitrageurs and noise traders. The software that we have used is EViews 6. The state space model is composed from the observation and the state equation. It is analyzed by using the Kalman recursive algorithm filter to calculate finite sample forecasts for Gaussian ARMA models. We have found that the natural logarithmic monthly NAV returns of all open-end funds are a stationary series. The natural logarithmic monthly NAV returns for all open-end funds have no serial correlation and are not normally distributed. We have found that the AR coefficients as shown in terms of C(7) and C(8) are not statistically significant at the 5% significance level for Merrill Lynch small cap value A, Fidelity equity income I. The AR coefficient, C(7) is statistically significant and the C(8) coefficient is not statistically significant for Invesco value equity investment, Credit Suisse blue chip A, JPMorgan capital growth A, and Goldman Sachs capital growth A. The MA coefficient C(2) of the Goldman Sachs capital growth A, and Credit Suisse blue chip A, is statistically significant and C(3), C(4), and C(5) are not statistically significant at the 5% significance level. The MA coefficients as displayed by C(2), C(3), C(4), and C(5) are not statistically significant at the 5% significance level for the remaining open-end funds, namely, Merrill Lynch small cap value A, Fidelity equity income I, JPMorgan capital growth A, and Invesco value equity investment. The variance of the error is denoted by C(6) and it is statistically significant for all open-end funds as the p-value is 0.0000. The Final one – step ahead values of the state vector, SV1, SV2, SV3,SV4, SV5 are not statistically significant for all open-end funds except Merril Lynch at the 5% significance level. We did not found unanticipated changes in the NAV prices of the open-end funds. The whole dataset is from 31/01/1990 to 31/12/2001. The total observations are 144 and the logarithmic monthly NAV returns observations are 143. The data was obtained from Thomson Financial Investment View database.

Learning Robot Dynamics from Raw Image Time Series using Kalman Variational Auto-Encoders

Learning dynamical models from high dimensional time series data is an crucial research topic for a variety of applications. Kalman Variational Auto-Encoders (KVAE) is one of the recent methods, which is composed of VAE and Linear Gaussian State Space Models (LGSSM). In this paper, the predictive performance of KVAE is investigated with control inputs through a 2DOF robot arm reaching task in simulations.

Real-time pricing for LQG power networks with independent types: A dynamic mechanism design approach

We investigate dynamic integration mechanisms for a power network system using a technique from economic theory. We represent a power network consisting of agents who are the generators and consumers and one public commission, called the utility, as a dynamic game. The game has a prescribed dynamic mechanism and each agent exercises private control to minimize the costs according to a personal cost functional, while the utility chooses prices to minimize the costs according to a public cost functional and manages information transmission. The model of this paper is a generic linear Gaussian power network model in which each agent has a type parameter representing private information. In this setting, inspired by the pivot function from mechanism design theory in economics, we design dynamic mechanisms that integrate the strategic determination of private controls by rational agents into the optimal public controls with real-time pricing and monetary transfer costs. Two dynamic integration mechanisms, which together achieve all of social welfare maximization, incentive compatibility, and individual rationality, are proposed based on the cost functional and the Hamiltonian. The effectiveness of the proposed mechanisms are assessed through simulations. Specifically, we have shown that an agent’s fictitious report produces a loss for the agent’s benefit in the both cases of the cost functional and the Hamiltonian.

On the Efficiency of SNR Estimation via Birnbaum's Method

The problem of signal-to-noise ratio (SNR) estimation for a linear Gaussian observation model when independent sequences of noisy signal and pure noise measurements are available is considered from the perspective of Birnbaum's sequential sampling method, which transforms the observed signal and noise sequences into a single sequence of Bernoulli random variables. The minimum-variance unbiased estimator for the SNR based on the transformed binary sequence is derived and shown to achieve the corresponding Cramer–Rao lower bound. Some remarks on parameter selection for the transformation are provided and its efficiency is analyzed in relation to that of the standard approach acting on the raw measurements. The proposed method may draw attention due to its simplicity of application in terms of data storage, computation, and bandwidth requirements.

Estimation of Frequency Offset for Time Synchronization With Immediate Clock Adjustment in Multihop Wireless Sensor Networks

The clock synchronization problem for wireless sensor networks (WSNs) is inherently related to parameter estimation. Nowadays, extensive studies on time synchronization have been conducted by adopting statistical signal processing methods. However, most estimation schemes do not readjust clock offset during the process of synchronization parameter estimation, and it would lead to unsatisfactory clock accuracy during synchronization. Thus, the applications of these methods are greatly limited in WSNs. This paper analyzes time synchronization of sensor nodes with immediate clock adjustment at every cycle under multihop scenario, and presents an estimator of clock skew under the Gaussian linear delay model and the corresponding algorithms for finding the estimator in detail. Simulation results verify that the proposed estimator is efficient.

Unsupervised detection of ruptures in spatial relationships in video sequences based on log-likelihood ratio

In this work, we propose a new approach to automatically detect ruptures in spatial relationships in video sequences, based on low-level primitives, in unsupervised manner. The spatial relationships between two objects of interest are modeled using angle and distance histograms as examples. The evolution of the spatial relationships during time is estimated from the distances between two successive angle or distance histograms and then considered as a temporal signal. The evolution of a spatial relationship is modeled by a linear Gaussian model. Then, two hypotheses “without change” and “with change” are considered, and a log-likelihood ratio is computed. The distribution of the log-likelihood ratio, given that $$H_0$$ is true, is estimated and used to compute the p value. The comparison of this p value to a significance level $$\alpha $$ , expressing the probability of false alarms, allows us to detect significant ruptures in spatial relationships during time. In addition, this approach is generalized to detect multiple object events such as merging, splitting, and other events that contain ruptures in their spatial relationships evolution. This work shows that the description of spatial relationships across time is a promising step toward event detection.

Forecasting energy futures volatility based on the unbiased extreme value volatility estimator

This paper uses the opening, high, low, and closing prices of five energy futures to estimate and model volatility based on the unbiased extreme value volatility estimator (the Add RS estimator). The statistical and distributional properties of the logarithm of the Add RS estimator support the use of the appropriate order linear long-memory Gaussian model (ARFIMA-Add RS model) to model the Add RS estimator. The out-of-sample evaluation analysis indicates that the volatility forecasts based on the ARFIMA-Add RS model provide superior forecasts of realised volatility of energy futures in relation to the alternative models from the GARCH family. This suggests that the ARFIMA-Add RS model can be a viable candidate for generating more accurate forecasts of realised volatility for energy futures. The study has important implications for governments, policy makers, oil importers, and oil traders.

Z-scores-based methods and their application to biological monitoring: an example in professional soccer players.

The clinical and biological follow-up of individuals, such as the biological passport for athletes, is typically based on the individual and longitudinal monitoring of hematological or urine markers. These follow-ups aim to identify abnormal behavior by comparing the individual's biological samples to an established baseline. These comparisons may be done via different ways, but each of them requires an appropriate extra population to compute the significance levels, which is a non-trivial issue. Moreover, it is not necessarily relevant to compare the measures of a biomarker of a professional athlete to that of a reference population (even restricted to other athletes), and a reasonable alternative is to detect the abnormal values by considering only the other measurements of the same athlete. Here we propose a simple adaptive statistic based on maxima of Z-scores that does not rely on the use of an extra population. We show that, in the Gaussian framework, it is a practical and relevant method for detecting abnormal values in a series of observations from the same individual. The distribution of this statistic does not depend on the individual parameters under the null hypothesis, and its quantiles can be computed using Monte Carlo simulations. The proposed method is tested on the 3-year follow-up of ferritin, serum iron, erythrocytes, hemoglobin, and hematocrit markers in 2577 elite male soccer players. For instance, if we consider the abnormal values for the hematocrit at a 5% level, we found that 5.57% of the selected cohort had at least one abnormal value (which is not significantly different from the expected false-discovery rate). The approach is a starting point for more elaborate models that would produce a refined individual baseline. The method can be extended to the Gaussian linear model, in order to include additional variables such as the age or exposure to altitude. The method could also be applied to other domains, such as the clinical patient follow-up in monitoring abnormal values of biological markers.