Analysis Of State-space Models Research Articles

Sequential Monte Carlo Methods in the nimble and nimbleSMC R Packages

nimble is an R package for constructing algorithms and conducting inference on hierarchical models. The nimble package provides a unique combination of flexible model specification and the ability to program model-generic algorithms. Specifically, the package allows users to code models in the BUGS language, and it allows users to write algorithms that can be applied to any appropriate model. In this paper, we introduce the nimbleSMC R package. nimbleSMC contains algorithms for state-space model analysis using sequential Monte Carlo (SMC) techniques that are built using nimble. We first provide an overview of state-space models and commonly-used SMC algorithms. We then describe how to build a state-space model in nimble and conduct inference using existing SMC algorithms within nimbleSMC. SMC algorithms within nimbleSMC currently include the bootstrap filter, auxiliary particle filter, ensemble Kalman filter, IF2 method of iterated filtering, and a particle Markov chain Monte Carlo (MCMC) sampler. These algorithms can be run in R or compiled into C++ for more efficient execution. Examples of applying SMC algorithms to linear autoregressive models and a stochastic volatility model are provided. Finally, we give an overview of how model-generic algorithms are coded within nimble by providing code for a simple SMC algorithm. This illustrates how users can easily extend nimble's SMC methods in high-level code.

Estimating the spatial relationships between soil hydraulic properties and soil physical properties in the critical zone (0–100 m) on the Loess Plateau, China: A state-space modeling approach

Soil hydraulic properties (SHP) such as the soil water retention curve and soil saturated hydraulic conductivity (Ks) of the deep profile in the Earth's critical zone (CZ) are important factors for investigating the water cycle process in the CZ. However, details are lacking about the SHP for the deep profile as well as their relationships with other soil properties. In the present study, SHP were obtained for a 100-m profile by soil core drilling, where the objectives were to understand the spatial distributions of SHP and to quantify the relationships between SHP and soil properties based on state-space model analysis and linear regression analysis. The results showed that SHP were not significantly related to the silt content and there was no cross-correlation between SHP and the soil organic carbon content. The soil physical properties (bulk density, sand content, and clay content) could account for most of the total variation in SHP. Compared with linear regression analysis, state-space modeling described the spatial relationship between SHP and soil physical properties much better. This study provides information about the SHP in deep profiles, thereby provide important parameters for investigating the water cycling process in the CZ and for developing pedotransfer functions.

Transient Analysis of Electric Arc Burning at Insulated Rail Joints in High-Speed Railway Stations Based on State-Space Modeling

This paper aims to study the arc burning phenomenon of insulated rail joints in high-speed railway stations. First, combined with the actual situation of station and the grounding mode of electric multiple units, the potential difference between the two ends of insulated rail joint is calculated before the wheel’s arriving at the cutoff point. Then, transient analysis is carried out for the ordinary wheel and the discharge wheel, respectively. Each transient process is divided into three parts: the wheel reaches the cutoff point, bridges the cutoff point, and generates an arc. The equivalent state-space model is established for each part of transient process. The corresponding voltage and current waveforms are calculated by the state-space model analysis using MATLAB software. Through substituting a theoretical arc model that combines the Cassie and Mayr models into the state equation, the waveforms of arc voltage and arc current for the ordinary wheel and the discharge wheel are achieved, respectively. As a result, the transient analyses are in line with field observation records. The calculated arc waveforms appear to be in good agreement with the ones recorded by experiment.

Performance Analysis of PI and Fuzzy Control for Modified LCC Resonant Converter Incorporating Boost Converter

In this paper, the modified LCC type of series-parallel Resonant Converter (RC) was designed and state-space modeling analysis was implemented. In this proposed converter, one leg of full bridge diode rectifier is replaced with Synchronous Rectifier (SR) switches. The proposed LCC converter is controlled using frequency modulation in the nominal state. During hold-up time, the SRswitches control is changed from in-phase to phase-shifted gate signal to obtain high DC voltage conversion ratio. Furthermore, the closed loop PI and fuzzy provide control on the output side without decreasing the switching frequency. The parameter such as conduction loss on primary and secondary side, switching loss, core and copper also reduced. Simultaneously, the efficiency is increased about 94.79 is realized by this scheme. The proposed converter with an input of 40 V is built to produce an output of 235 V with the help of ZVS boost converter [1] even under line and load disturbances. As a comparison, the closed loop fuzzy controller performance is feasible and less sensitive than PI controller.

Posterior Analysis of State Space Model with Spherical Symmetricity

The present work investigates state space model with nonnormal disturbances when the deviation from normality has been observed only with respect to kurtosis and the distribution of disturbances continues to follow a symmetric family of distributions. Spherically symmetric distribution is used to approximate behavior of symmetric nonnormal disturbances for discrete time series. The conditional posterior densities of the involved parameters are derived, which are further utilized in Gibbs sampler scheme for estimating the marginal posterior densities. The state space model with disturbances following multivariate-tdistribution, which is a particular case of spherically symmetric distribution, is discussed.

SSMMATLAB: A Set ofMATLABPrograms for the Statistical Analysis of State Space Models

This article discusses and describes SSMMATLAB, a set of programs written by the author in MATLAB for the statistical analysis of state space models. The state space model considered is very general. It may have univariate or multivariate observations, time-varying system matrices, exogenous inputs, regression effects, incompletely specified initial conditions, such as those that arise with cointegrated VARMA models, and missing values. There are functions to put frequently used models, such as multiplicative VARMA models, VARMAX models in echelon form, cointegrated VARMA models, and univariate structural or ARIMA model-based unobserved components models, into state space form. There are also functions to implement the Hillmer-Tiao canonical decomposition and the smooth trend and cycle estimation proposed by Gómez (2001). Once the model is in state space form, other functions can be used for likelihood evaluation, model estimation, forecasting and smoothing. A set of examples is presented in the SSMMATLAB manual to illustrate the use of these functions.

Generator Outage Identification by Use of Electromechanical State-Space Model Analysis

In this paper, a theory is developed that relates the natural response of an electric power system to sudden outages of transmission elements. The key development is in determining, via state-space analysis, the anticipated spectral content of either frequency or phase angle measurements as observed immediately following the sudden outage. This theoretical development mainly focuses on frequency measurements and the elements subjected to sudden outages are generators. For any sudden generator outage, the power system exhibits a very specific natural response in terms of its kinetic and potential energies. Kinetic energy in the system is directly related to each specific generator's rotational speed. It is shown that the effect can be seen directly in bus frequency measurements. Each remaining generator on the system has its own unique response to the sudden outage which contributes to the overall system natural response. This overall response is generally composed of oscillatory components which have specific frequencies. These oscillations, as measured by frequency meters, can be used to identify sudden element outages via their spectral content.

SMC2: An Efficient Algorithm for Sequential Analysis of State Space Models

SummaryWe consider the generic problem of performing sequential Bayesian inference in a state space model with observation process y, state process x and fixed parameter θ. An idealized approach would be to apply the iterated batch importance sampling algorithm of Chopin. This is a sequential Monte Carlo algorithm in the θ-dimension, that samples values of θ, reweights iteratively these values by using the likelihood increments pyt∣y1:t−1,θ and rejuvenates the θ-particles through a resampling step and a Markov chain Monte Carlo update step. In state space models these likelihood increments are intractable in most cases, but they may be unbiasedly estimated by a particle filter in the x-dimension, for any fixed θ. This motivates the SMC2 algorithm that is proposed in the paper: a sequential Monte Carlo algorithm, defined in the θ-dimension, which propagates and resamples many particle filters in the x-dimension. The filters in the x-dimension are an example of the random weight particle filter. In contrast, the particle Markov chain Monte Carlo framework that has been developed by Andrieu and colleagues allows us to design appropriate Markov chain Monte Carlo rejuvenation steps. Thus, the θ-particles target the correct posterior distribution at each iteration t, despite the intractability of the likelihood increments. We explore the applicability of our algorithm in both sequential and non-sequential applications and consider various degrees of freedom, as for example increasing dynamically the number of x-particles. We contrast our approach with various competing methods, both conceptually and empirically through a detailed simulation study, and based on particularly challenging examples.

State Space Models inR

We give an overview of some of the software tools available in R, either as built- in functions or contributed packages, for the analysis of state space models. Several illustrative examples are included, covering constant and time-varying models for both univariate and multivariate time series. Maximum likelihood and Bayesian methods to obtain parameter estimates are considered.

Model for Estimation of Traffic Pollutant Levels in Northern Communities

Using models to estimate the contribution of traffic to air pollution levels from known traffic data typically requires the knowledge of model parameters such as emission factors and meteorological conditions. This paper presents a state-space model analysis method that does not require the knowledge of model parameters; these parameters are identified from measured traffic and ambient air quality data. This method was used to analyze carbon monoxide (CO) in downtown Fairbanks, AK, which is the community of focus for this paper. It was found that traffic contributed, on average, 53% to the total CO levels over the last six winters. The correlation coefficient between the measured and model-predicted daily profiles of the CO concentration was 0.98, and the results were in good agreement with earlier findings obtained via a thorough CO emission inventory. This justified the usability of the method and it was further used to analyze fine particulate matter (PM2.5) in downtown Fairbanks. It was found that traffic contributed, on average, approximately 30% to the total PM2.5 levels over the last six winters. The correlation coefficient between the measured and model-predicted daily profiles of the PM2.5 concentration was 0.98.

Population dynamics of an Arctiid caterpillar–tachinid parasitoid system using state‐space models

1. Population dynamics of insect host-parasitoid systems are important in many natural and managed ecosystems and have inspired much ecological theory. However, ecologists have a limited knowledge about the relative strengths of species interactions, abiotic effects and density dependence in natural host-parasitoid dynamics. Statistical time-series analyses would be more informative by incorporating multiple factors, measurement error and noisy dynamics. 2. We use a novel maximum likelihood and model-selection analysis of a state-space model for host-parasitoid dynamics to examine 21 years of annual census data for woolly bear caterpillars (Platyprepia virginalis) and their locally host-specific tachinid parasitoids (Thelaira americana). 3. Caterpillar densities varied by three orders of magnitude and were driven by density dependence and precipitation from the previous March but not detectably by parasitoids, despite variable and sometimes high (>50%) parasitism. 4. Fly fluctuations, as estimated from per cent parasitism, were affected by density dependence and precipitation from the previous July. There was marginal evidence that host abundance drives fly fluctuations as a generic linear effect but no evidence for classical Nicholson-Bailey coupling. 5. The state-space model analysis includes new methods for likelihood calculation and allows a balanced consideration of effect magnitude and statistical significance in a nonlinear model with multiple alternative explanatory variables.

Hierarchical Bayesian analysis of the seemingly unrelated regression and simultaneous equations models using a combination of direct Monte Carlo and importance sampling techniques

Computationally efficient simulation methods for hierarchical Bayesian analysis of the seemingly unrelated regression (SUR) and simultaneous equations models (SEM) are proposed and applied. These methods combine a direct Monte Carlo (DMC) approach and an importance sampling procedure to calculate Bayesian estimation and prediction results, namely, Bayesian posterior densities for parameters, predictive densities for future values of variables and associated moments, intervals and other quantities. The results obtained by our approach are compared to those yielded by use of MCMC techniques. Finally, we show that our algorithm can be applied to the Bayesian analysis of state space models.

Network-Based Predictions and Simulations by Biological State Space Models: Search for Drug Mode of Action

Since time-course microarray data are short but contain a large number of genes, most of statistical models should be extended so that they can handle such statistically irregular situations. We introduce biological state space models that are established as suitable computational models for constructing gene networks from microarray gene expression data. This chapter elucidates theory and methodology of our biological state space models together with some representative analyses including discovery of drug mode of action. Through the applications we show the whole strategy of biological state space model analysis involving experimental design of time-course data, model building and analysis of the estimated networks.

Behavioural estimation of blue whale movements in the Northeast Pacific from state-space model analysis of satellite tracks

Baleen whale migrations typically consist of annual movements between productive, high-latitude feeding grounds and unproductive, low-latitude breeding grounds. However, the actual migratory path and whales' behaviour in these locations are poorly known. The objectives of this study were to apply a switching state-space model to the satellite tracks of blue whales Balaen- optera musculus in the Northeast Pacific to improve location estimation and gain insight into the migratory (transiting) and foraging (area-restricted search, ARS) behaviours of this population. Dur- ing the period 1993 to 2007, Argos satellite tags were attached to 159 whales, mainly off the coast of California during late summer, of which 92 tracks were >7 d in duration. There was generally a southward movement during the winter to Baja California and to an area west of the Costa Rica Dome, in the eastern tropical Pacific (ETP). Travel speeds during transit were significantly faster than during ARS movements (mean = 3.70 and 1.05 km h -1 , respectively). On average, 29% of the track time was spent in ARS, and the mean time within an ARS patch was 21 d. The occurrence of ARS behaviour throughout the migration cycle suggests that these animals may forage year-round, but could also indicate limited movements during the reproductive season. The extent of their northward migration from Baja California to Washington varied significantly interannually, likely in response to environmental changes affecting their prey. The long track durations obtained from electronic tagging have provided essential new information about the critical habitats of Northeast Pacific blue whales.

FIELD-SCALE ROLES OF DENSITY, TEMPERATURE, NITROGEN, AND PREDATION ON APHID POPULATION DYNAMICS

Robust analyses of noisy, stage-structured, irregularly spaced, field-scale data incorporating multiple sources of variability and nonlinear dynamics remain very limited, hindering understanding of how small-scale studies relate to large-scale population dynamics. We used a novel, complementary Bayesian and frequentist state-space model analysis to ask how density, temperature, plant nitrogen, and predators affect cotton aphid (Aphis gossypii) population dynamics in weekly data from 18 field-years and whether estimated effects are consistent with small-scale studies. We found clear roles of density and temperature but not of plant nitrogen or predators, for which Bayesian and frequentist evidence differed. However, overall predictability of field-scale dynamics remained low. This study demonstrates stage-structured state-space model analysis incorporating bottom-up, top-down, and density-dependent effects for within-season (nearly continuous time), nonlinear population dynamics. The analysis combines Bayesian posterior evidence with maximum-likelihood estimation and frequentist hypothesis testing using average one-step-ahead residuals.

Use of a State Space Model to Study the Effect of Outdoor Air Quality on Indoor Air in Fairbanks Alaska

A usual method for studying the effective penetration efficiency of pollutants into buildings consists in performing a linear regression of outdoor and indoor samples. But, because of the dynamic relationship between outdoor and indoor concentrations, this method requires either long-term averages or steady-state conditions. Other methods use dynamic models but these normally require the knowledge of model parameters, such as the ventilation rate. This paper presents a state-space model analysis method that can be used for transient samples and doesn't require the knowledge of model parameters. It was used to study PM2.5 and CO in Fairbanks, Alaska. The effective penetration efficiency for PM2.5 ranged from 0.16 to 0.69, and was close to unity for CO. The outdoor generated PM2.5 was responsible in average for about 67% of the indoor PM2.5 in residences, and close to 100% in office environments.

State-space model of grid-connected inverters under current control mode

Growth of distributed generation has led to distribution systems with a mixture of rotating machine generators and inverter interfaced generators. The stability of such networks needs to be studied through the analysis of state-space models, and so suitable models of inverters are needed to complement the well-established models of rotating machines. As machine models include features such as automatic voltage regulators and wash-out functions, the inverter model also includes phase-locking functions and internal control loops. The model for voltage source inverters with an internal current control loop, an outer power regulation loop, a measurement of average power and a phase-locked loop has been developed. The model is presented in detail and is formed with a state-vector, similar to that used for rotating machines. The model includes nonlinear terms but can be linearised about an operating point. The state-space model is verified against a component-level time-step simulation in Simulink/PLECS.

Stability robustness analysis of state-space models for uncertain Linear time-varying systems

The stability robustness of linear-variant systems in the time domain is considered using the Lyapunov approach and the maximum singular values of a time-variant matrix. Bounds on linear time-varying perturbations that maintain the stability of a uniformly asymptotically stable linear time-variant system are obtained for both unstructured and structured independent perturbations. Bounds are also derived assuming that various elements of the system matrix are perturbed dependently. The result for the structural perturbation case is extended to the stability analysis of time-variant interval matrices.