First-order Markov Process Research Articles

Information bounds for Gaussian copula parameter in stationary semiparametric Markov models

Let {Vt}t=1n be any univariate stationary first-order semiparametric Markov process generated from an unknown invariant marginal distribution and a bivariate Gaussian copula with unknown correlation coefficient α0∈(−1,1). We prove that 1−α02 is the semiparametric efficient variance bound for estimating the correlation parameter α0 in any Gaussian copula generated first-order stationary Markov models. Surprisingly, this variance bound is strictly larger than 1−α022 (when α0≠0), which is the semiparametric efficient variance bound derived by Klaassen and Wellner (1997) for estimating the correlation parameter using any i.i.d. data {(Xi,Yi)}i=1n generated from a bivariate Gaussian copula with two unknown marginal distributions.

A TDOA sequence estimation method of underwater sound source based on hidden Markov model

To address the time difference of arrival (TDOA) estimation problem in the passive positioning system with wideband underwater motion sound sources and distributed hydrophones, a hidden Markov model-based (HMM) TDOA sequence estimation method is proposed in this paper. The method estimates the TDOA with multi-frame output of cross-correlated signals received on hydrophones. The transfer equation of the TDOA is established as a first-order hidden Markov process by analyzing the motion characteristics of the moving sound source and delays obtained from different hydrophones. Dynamic assignment of the HMM parameters is proposed to address the inconsistent change rate of the TDOA. We then achieve an HMM expression of the TDOA sequence by fitting the transfer equation and dynamic assignment of parameters into the HMM. Then, the Viterbi algorithm (VA) is applied to distinguish the optimal sequence of the TDOA among ambiguous estimations. To deal with the problem of data loss or unreliable issues caused by interferences, a data prediction algorithm which could produce possible time delays is added to VA to avoid the impact of outliers on the estimation results. By utilizing multi-frame processing, the proposed method reduces the signal-to-noise ratio (SNR) requirement of single frames since it does not require accurate estimations of TDOA for each frame. Moreover, the method adapts to a lower SNR, which has significant advantages in terms of whole sequence estimation compared with common methods. The results from the simulations and lake experiments validated the proposed TDOA sequence estimation method.

Filtering and smoothing estimation algorithms from uncertain nonlinear observations with time-correlated additive noise and random deception attacks

ABSTRACT This paper discusses the problem of estimating a stochastic signal from nonlinear uncertain observations with time-correlated additive noise described by a first-order Markov process. Random deception attacks are assumed to be launched by an adversary, and both this phenomenon and the uncertainty in the observations are modelled by two sets of Bernoulli random variables. Under the assumption that the evolution model generating the signal to be estimated is unknown and only the mean and covariance functions of the processes involved in the observation equation are available, recursive algorithms based on linear approximations of the real observations are proposed for the least-squares filtering and fixed-point smoothing problems. Finally, the feasibility and effectiveness of the developed estimation algorithms are verified by a numerical simulation example, where the impact of uncertain observation and deception attack probabilities on estimation accuracy is evaluated.

ESTIMATION OF WORKING LIFE EXPECTANCY: APPLICATION OF A MULTISTATE MARKOV MODEL

Abstract Longer life expectancy in Western countries has led to concerns about sustainable workforces amid the rising costs of securing aging populations. Retirement age is no more a good indicator of the end of the working life, because many older workers move in-and-out of workforce. A more useful measure is working life expectancy (WLE), which is the expected number of remaining years from a given age that a person will work. This measure considers transitions across different employment states. The method adopted for estimation of WLE is along the same line to estimate health expectancy (HE) based on cross-sectional data without considering transitions in different states of work over time. A better approach is based on multi-state survival models considering transitions among states over time using longitudinal data. These models assume a Markov Process to estimate transition probabilities. WLE is the weighted sum of duration of stay in a state weighted by the transition probabilities. The method adopted in IDEAR consortium is a multistate survival model assuming a first-order Markov process in continuous time to estimate transition probabilities. Transition probabilities are estimated by the msm package. This model takes care of interval censoring where the exact dates of transitions from one state to another is not known. WLEs are estimated by using the package elect (van den Hout, 2019) incorporating age as a time dependent variable by using a Gompertz model instead of the exponential model. The method is demonstrated to estimate WLE using Swedish Longitudinal Occupational Survey of Health (SLOSH).

SOCIOECONOMIC STATUS AND WORKING LIFE EXPECTANCY IN SWEDEN

Abstract Longer life expectancy and fertility decline have increased concerns about the security of old-age pensions. Raising retirement ages is one strategy to offset rising costs, though the option to retire varies considerably by socioeconomic status (SES) and sex. The level of variation in SES may depend the measure used. Also, many workers now transition into retirement slowly, e.g., move from full- to part-time work. Thus, retirement age may not sufficiently capture how long people work. Working life expectancy (WLE)—the expected average number of years worked—better measures total working life. We use data from the Swedish Longitudinal Occupational Survey of Health (SLOSH) from 2008 to 2020 (n=4,940 people age 50+ and n=74,093 person-observations) to examine WLE by SES. We estimate a three-state multistate model (i.e., working, not working, dead) and a four-state model (working part-time, working full-time, not working, and dead); both assume a continuous-time first-order Markov process. Models are sex-stratified models, cross-classified by: 1) occupation; 2) education; 3) income. We find that professionals work full-time 1 year more than routine workers, regardless of sex. The low educated work full-time 1 year less than the highly educated. In our weighted three-state model, where part-time work contributed ½ of full-time work, the difference increased to 1.14 and 1.05 years, respectively. Our unweighted three-state model showed slightly larger education differences. Findings suggest that WLE differs by SES, regardless of sex, and the differences are greater by education than occupation. This has implications for extending working life policies.

고령층 소득의 비선형적 지속성 분석

This study estimates income risk observed among the elderly using the Korean Retirement and Income Study data. In order to decompose household income into permanent and transitory components, the quantile-based panel data framework is employed. The permanent component is assumed to follow a first-order Markov process, and the transitory component is assumed to be independent over time and also independent of the persistent components. I estimate the income persistence from the estimated permanent income component, and analyze the dynamic effects of permanent income shocks on income through simulations. The results show the presence of nonlinear persistence in the household income of the elderly. Furthermore, it is observed that the dynamic effects of permanent income shocks vary depending on the past income history. These findings differ from studies focused on the age groups participating in the labor market. In particular, the permanent income shocks have a significant impact on the income of elderly households. In particular, the permanent income shocks have a significant impact on the income of elderly households.

Creation and Destruction of Jobs in Urban Labour Market: Role of Gender, Caste and Religion in India.

This study analyses labour market transitions from job to jobless or jobless to job by using Periodic Labour Force Survey (PLFS)of India in urban labour market by applying first-order Markov process in constructing transition matrices and panel logit regression model using personal level information from the PLFS in India for 2019-20. While education is assumed to be the most important factor influencing the process of transitions in the labour market, the circumstance variables like gender, caste and religion are expected to have significant effects on it in a country like India. The empirical results show a significant difference in labour market transitions between men and women. The movement of workers between job status was very low and the major part of the transition occurred in the form of job losses for each type of workers both among men and women and also among all working age group and young age group.

Adaptive Modified Unbiased Minimum-Variance Estimation for Highly Maneuvering Target Tracking With Model Mismatch

Due to the complexity, time variability, and mutability of the noncooperative maneuvering target, the dynamic tracking model of the target does not match with the actual state, which reduces the tracking accuracy or even completely tracking loss. In this article, an expectation maximization-based adaptive modified unbiased minimum-variance estimation (EM-AMUMVE) algorithm is proposed for highly maneuvering target tracking with model mismatch. First, the virtual maneuvering noise and the first-order Markov process model are integrated to quantitatively describe the maneuvering acceleration according to the boundness of the maneuvering acceleration. Then, the maneuvering acceleration and state estimation are derived based on the unbiased minimum-variance criterion, and the expectation maximization (EM) is introduced in the updating procedure of the quadratic Bayesian filter to adaptively estimate the mean and covariance of virtual maneuvering noise and thus to improve the accuracy of maneuvering acceleration estimation. Finally, the optimality of the adaptive modified maneuvering acceleration estimation is theoretically proved, and the tracking scenarios of time-varying maneuvering target with model mismatch and reentry gliding trajectory of typical hypersonic vehicle hypersonic technology vehicle 2 (HTV-2) are built to demonstrate the validness, convergence, sensitivity, and engineering practicability of the proposed algorithm.

Duals of multiplicative relationships involving beta and gamma random variables

By interpreting four known multiplicative relationships involving independent beta and gamma random variables as scale mixtures, their ‘dual’ mixture relationships are obtained, making links to a variety of other distributional relationships. One consequence of these dual relationships is the provision of a number of first-order Markov processes with beta and gamma marginals.

Memory Channel Models of a Hybrid PLC-VLC Link for a Smart Underground Mine

In this article, discrete memory channel models of a low-cost, visible light communication (VLC) and a hybrid amplify-and-forward (AF) powerline communication (PLC) and VLC channel are derived using data obtained from an underground mining testbed. The testbed is set up close to the mining face, where blasting occurs. Then, the noise distributions as a result of the connection of a blasting equipment and the mains switchboard supply on the powerline channel are modeled. The baseband signals are communicated over software-defined radios, using multicarrier modulation in the VLC and hybrid AF PLC-VLC channels. Aided by a Fritchman 3-state semi-hidden Markov model (SHMM) for channel state classification, the channels are modeled using a first-order (FO) Markov process, which considers only one previous state in the channel. In addition, the block diagonal (BD) Markov model, which groups similar successive states of the channel, is implemented in order to reduce the training complexity. The models for the error distribution are then derived for both VLC and hybrid PLC-VLC channels. Results show that the probability of error obtained from the trained models closely matches the probability of error obtained from the channel measurements, validating the suitability of the SHMM for modeling VLC and hybrid PLC-VLC channels. In addition, the modified BD Markov model, which groups the channel states shows better performance with reduced complexity when compared with the FO Markov model.

Ex-ante effects of the 2018 Agricultural Improvement Act’s grassland initiative

The Grassland Conservation Initiative (GCI) was introduced under the United States 2018 Agricultural Improvement Act. The goal of the GCI is to conserve pasture and grassland. This study analyzes the ex-ante impacts of the GCI on crop returns and land-use acreage for Oklahoma farmers and ranchers. Oklahoma’s agricultural landscape is diverse. As with most agricultural policies focusing on land use, the distributional effects of GCI program will be conditional upon dominant land use types and grassland/pasture resources. Regions endowed with relatively more land resources in pasture and grassland are more likely to have more eligible acres, thereby potentially signaling to landowners in those regions opportunities to accrue land-holding rents. Land-use dynamics are estimated as a first-order Markov process. Not all regions benefit from this program. Findings suggest that aggregate net returns to cropland decrease. However, locations with above average pasture and grassland acreage experience gains in returns under certain policy assumptions. Counties experiencing gains from the GCI policy could experience higher returns to cattle and wheat compared to other counties with limited grassland and pasture acreage.

Gaussian estimation for non‐linear stochastic uncertain systems with time‐correlated additive noises and packet dropout compensations

This paper discusses the problem of state estimation for non-linear stochastic uncertain systems with time-correlated additive noise and packet dropout compensations. Both process noise and measurement noise are additive forms of noise that can be described as Gaussian first-order Markov processes. The stochastic uncertainty of the system is described by synchronous correlated white multiplicative noise. When the measurement information from the current epoch is lost, a compensation strategy based on measurement information prediction is used. First, the state information, process noise, and measurement noise are augmented to enable the construction of a new vector to be estimated, and the filter, predictor, and smoother of the system are designed using a Gaussian iterative estimation algorithm based on innovation analysis. The multiplicative noise in the process equation is estimated in real time. Second, a numerical implementation of the proposed algorithm is derived based on the third-degree spherical-radial Cubature Kalman filter(CKF). Finally, the proposed algorithm is compared with an extended Kalman filter (EKF) based on Taylor series expansion. The effectiveness of the proposed algorithm is verified by comparing the simulation results.

Bayesian Forecasting with a Regime-Switching Zero-Inflated Multilevel Poisson Regression Model: An Application to Adolescent Alcohol Use with Spatial Covariates.

In this paper, we present and evaluate a novel Bayesian regime-switching zero-inflated multilevel Poisson (RS-ZIMLP) regression model for forecasting alcohol use dynamics. The model partitions individuals' data into two phases, known as regimes, with: (1) a zero-inflation regime that is used to accommodate high instances of zeros (non-drinking) and (2) a multilevel Poisson regression regime in which variations in individuals' log-transformed average rates of alcohol use are captured by means of an autoregressive process with exogenous predictors and a person-specific intercept. The times at which individuals are in each regime are unknown, but may be estimated from the data. We assume that the regime indicator follows a first-order Markov process as related to exogenous predictors of interest. The forecast performance of the proposed model was evaluated using a Monte Carlo simulation study and further demonstrated using substance use and spatial covariate data from the Colorado Online Twin Study (CoTwins). Results showed that the proposed model yielded better forecast performance compared to a baseline model which predicted all cases as non-drinking and a reduced ZIMLP model without the RS structure, as indicated by higher AUC (the area under the receiver operating characteristic (ROC) curve) scores, and lower mean absolute errors (MAEs) and root-mean-square errors (RMSEs). The improvements in forecast performance were even more pronounced when we limited the comparisons to participants who showed at least one instance of transition to drinking.

Markov Multi-Beamtracking on 60 GHz Mobile Channel Measurements

Beamforming training refers to the exhaustive scan over which the transmitter and receiver jointly steer their beams along a predefined set of double-directional angles to determine the beam pairs that coincide with the dominant propagation paths of the channel, for spatial multiplexing at millimeter-wave. When mobile, training necessitates a high refresh rate to maintain connectivity and so, to reduce overhead, beamtracking algorithms exploit the spatial-temporal consistency of the channel to localize the scan around the beam pairs determined at a previous time. The algorithms&#x2019; true performance, however, is still unknown since results reported to date are based on oversimplified channel models. In this paper, we propose a novel beamtracking algorithm formulated as a first-order Markov process that supports multiple beam pairs. The algorithm is evaluated through actual channel measurements &#x2013; <i>not a channel model</i> &#x2013; recorded with our high-precision 3D double-directional 60 GHz channel sounder. The measurement campaign, to our knowledge, is unprecedented: with 10, 895 large-scale measurements, spaced 8.8 cm apart on average to emulate continuous motion, over which the mobile receiver traversed a total of 900.2 m. We demonstrate that four beam pairs can be sustained always and that eight pairs can be sustained 57&#x0025; of the time.

A Beidou + UWB + inertial Navigation Integrated Indoor and Outdoor Multi-Source Information Fusion Positioning System

The article analyses the high-precision indoor and outdoor positioning system and its positioning method based on Beidou/UWB. And analyse the principles and characteristics of UWB technology. The article proposes a sequential filtering fusion algorithm for the ship’s integrated navigation system. The basic idea of the algorithm is to use the first-order Markov process to establish the noise model of ship motion, and use the state expansion method to transform the state equation into a basic equation that conforms to the standard Kalman filter. Theoretical research and experimental simulation prove that the filter introduced in the article is matched with the system and has high filtering performance and accuracy.

An MSI-VAR Approach on investigating the broad money supply and consumer price index in Malaysia

According to monetarism, the money supply is the leading cause of increasing price level in the short and long run. Previous works investigated the effect of money supply on inflation in several countries; however, inconsistent arguments from these studies resulted in the exploration of the correlations between money supply and inflation via a different approach in this work. This study investigates the broad money supply and consumer price index (CPI) using the Markov switching vector autoregressive model. The CPI, with 2010 as its base year, was used as a proxy for Malaysia's inflation. The broad money supply is defined as the sum of money and quasi-money. Other countries use different measurements; therefore, M3 was selected based on the monetary authority measurement of the money supply in this study. The transition probabilities and expected duration of the recession and upturn/normal states were examined using a two-regime switching VAR model. Furthermore, the Augmented Dickey-Fuller test, Johansen cointegration, and intercept adjusted MS-VAR model with the first-order Markov process was also used in this study to estimate the observables variables. The results confirmed significant transition probabilities in the state shifting and an asymmetric economic model representing broad money and inflation correlations in Malaysia. Keywords: Broad Money; Consumer Price Index, Malaysia, Regime Switching, MS-VAR

Modeling and forecasting of rainfall reoccurrence changes using Markov Switching in Iran

This paper represents the recurrence (reoccurrence) changes in the rainfall series using Markov Switching models (MSM). The switching employs a dynamic pattern that allows a linear model to be combined with nonlinearity models a discrete structure. The result is the Markov Switching models (MSM) reoccurrence predicting technique. Markov Switching models (MSM) were employed to analyze rainfall reoccurrence with spatiotemporal regime probabilities. In this study, Markov Switching models (MSM) were used based on the simple exogenous probability frame by identifying a first-order Markov process for the regime probabilities. The Markov transition matrix and regime probabilities were used to analyze the rainfall reoccurrence in 167 synoptic and climatology stations. The analysis results show a low distribution from 0.0 to 0.2 (0–20%) per day spatially from selecting stations, probability mean of daily rainfall recurrence is 0.84, and a different distribution based on the second regime was found to be more remarkable to the rainfall variability. The rainfall reoccurrence in daily rainfall was estimated with relatively low variability and strong reoccurrence daily with ranged from 0.851 to 0.995 (85.1–99.5%) per day based on the spatial distribution. The variability analysis of rainfall in the intermediate and long variability and irregular variability patterns would be helpful for the rainfall variability for environmental planning.

An adaptive non-zero mean damping model for trajectory tracking of hypersonic glide vehicles

In this paper, we proposed an adaptive non-zero mean damping oscillation model, aiming to solve the trajectory tracking problem of hypersonic glide vehicles (HGVs). To this end, an adaptive non-zero mean damping oscillation model (ANMDO) is established based on the maneuver patterns of HGVs, the proposed model consists of the mean and maneuvering components of HGV's accelerations. In particular, a sine autocorrelation random process is applied to model the mean component, while a first-order Markov process is introduced to compensate its maneuvering counterpart that is taken as the perturbation. Moreover, we proceed to introduce the Kalman filter to estimate the trajectory, while the dynamic errors of the proposed model are analytically developed. Simulation results verified that the proposed model can achieve a better tracking accuracy and reasonable convergence compared with the conventional sine correlation model and the Singer model.

Characteristics of human mobility patterns revealed by high-frequency cell-phone position data

Human mobility is an important characteristic of human behavior, but since tracking personalized position to high temporal and spatial resolution is difficult, most studies on human mobility patterns rely on sparsely sampled position data. In this work, we re-examined human mobility patterns via comprehensive cell-phone position data recorded at a high frequency up to every second. We constructed human mobility networks and found that individuals exhibit origin-dependent, path-preferential patterns in their short time-scale mobility. These behaviors are prominent when the temporal resolution of the data is high, and are thus overlooked in most previous studies. Incorporating measured quantities from our high frequency data into conventional human mobility models shows inconsistent statistical results. We finally revealed that the individual preferential transition mechanism characterized by the first-order Markov process can quantitatively reproduce the observed travel patterns at both individual and population levels at all relevant time-scales.

Anti-disturbance control for dynamic positioning system of ships with disturbances

A robust anti-disturbance control (RADC) strategy is investigated for the ship dynamic positioning (DP) systems with unknown time-varying disturbances. The disturbances are brought about by wind, second-order wave drift, ocean currents as well as unmodeled dynamics, which are modelled by the first-order Markov process. The disturbance observer (DO) is established to online estimate disturbances. Then, the anti-disturbance controller for the ship DP system is designed and the stability analysis of the composite system is presented by using stochastic stability theory. The DOBC and the pole placement methods are implemented to improve the robustness against ocean environmental disturbances. The unknown time-varying disturbances can be attenuated such that the yaw angle and position of the ship reach the desired value with high accuracy. Finally, simulation on a supply ship is given to illustrate the validity of the proposed control strategy.