scholarly journals A Bayesian Method for Dynamic Origin–Destination Demand Estimation Synthesizing Multiple Sources of Data

Sensors ◽  
2021 ◽  
Vol 21 (15) ◽  
pp. 4971
Author(s):  
Hang Yu ◽  
Senlai Zhu ◽  
Jie Yang ◽  
Yuntao Guo ◽  
Tianpei Tang
Keyword(s):  
Posterior Distribution ◽  
Demand Uncertainty ◽  
Bayesian Method ◽  
Total Error ◽  
Demand Estimation ◽  
Estimation Accuracy ◽  
Multiple Sources ◽  
Traffic Counts ◽  
Traffic Count ◽  
Relative Errors

In this paper a Bayesian method is proposed to estimate dynamic origin–destination (O–D) demand. The proposed method can synthesize multiple sources of data collected by various sensors, including link counts, turning movements at intersections, flows, and travel times on partial paths. Time-dependent demand for each O–D pair at each departure time is assumed to satisfy the normal distribution. The connections among multiple sources of field data and O–D demands for all departure times are established by their variance-covariance matrices. Given the prior distribution of dynamic O–D demands, the posterior distribution is developed by updating the traffic count information. Then, based on the posterior distribution, both point estimation and the corresponding confidence intervals of O–D demand variables are estimated. Further, a stepwise algorithm that can avoid matrix inversion, in which traffic counts are updated one by one, is proposed. Finally, a numerical example is conducted on Nguyen–Dupuis network to demonstrate the effectiveness of the proposed Bayesian method and solution algorithm. Results show that the total O–D variance is decreasing with each added traffic count, implying that updating traffic counts reduces O–D demand uncertainty. Using the proposed method, both total error and source-specific errors between estimated and observed traffic counts decrease by iteration. Specifically, using 52 multiple sources of traffic counts, the relative errors of almost 50% traffic counts are less than 5%, the relative errors of 85% traffic counts are less than 10%, the total error between the estimated and “true” O–D demands is relatively small, and the O–D demand estimation accuracy can be improved by using more traffic counts. It concludes that the proposed Bayesian method can effectively synthesize multiple sources of data and estimate dynamic O–D demands with fine accuracy.

scholarly journals ANALISIS SISTEM PELAYANAN KERETA API DI STASIUN SEMARANG TAWANG MENGGUNAKAN PROSES BAYESIAN

2020 ◽  
Vol 9 (4) ◽  
pp. 495-504
Author(s):  
Lifana Nugraeni ◽  
Sugito Sugito ◽  
Dwi Ispriyanti
Keyword(s):  
Poisson Distribution ◽  
Posterior Distribution ◽  
Public Transportation ◽  
Bayesian Method ◽  
Service System ◽  
Likelihood Function ◽  
Performance Standard ◽  
Sample Distribution ◽  
Service Patterns ◽  
Transportation Facilities

Along with the times, transportation has progressed. Regarding the means of transportation, one of the phenomenon that is easily encountered in everyday life is the queue at public transportation facilities. One of the queues that occurred at public transportation facilities is  the train queue at Semarang Tawang Station. The number of trains that passes the station can cause the train service at the station busy. This study aims to see whether the train service system of Semarang Tawang Station is good or not. This can be consider by the queues method, determining the distribution of arrival patterns and service patterns to obtain a queues system model and a system performance standard. In this study, the distribution of arrival patterns and service patterns are determined by calculating the posterior distribution using the Bayesian method. The bayesian method was chosen because it is able to combine the sample distribution in the current study with the previous information for the same cases. The prior distribution and the likelihood function are the elements needed to obtain the posterior distribution. The distribution of arrival patterns and service patterns obtained from previous information follows the Poisson distribution. Based on the calculation of the posterior distribution, the result shows that the distribution of the arrival pattern is a discrete uniform distribution and the distribution of the service pattern is a Poisson distribution. The result shows that the train service system at Semarang Tawang Station has a model (Uniform Discrete / Gamma / 7: GD / ~ / ~) and has good service based on the performance values obtained.

Extending production models to include process error in the population dynamics

2003 ◽  
Vol 60 (10) ◽  
pp. 1217-1228 ◽  
Author(s):  
Andre E Punt
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Population Dynamics ◽  
Total Error ◽  
Error Estimator ◽  
Observation Error ◽  
Production Models ◽  
Fitting Production ◽  
Process Error ◽  
Relative Errors

Four methods for fitting production models, including three that account for the effects of error in the population dynamics equation (process error) and when indexing the population (observation error), are evaluated by means of Monte Carlo simulation. An estimator that represents the distributions of biomass explicitly and integrates over the unknown process errors numerically (the NISS estimator) performs best of the four estimators considered, never being the worst estimator and often being the best in terms of the medians of the absolute values of the relative errors. The total-error approach outperforms the observation-error estimator conventionally used to fit dynamic production models, and the performance of a Kalman filter based estimator is particularly poor. Although the NISS estimator is the best-performing estimator considered, its estimates of quantities of management interest are severely biased and highly imprecise for some of the scenarios considered.

scholarly journals ANALISIS METODE BAYESIAN PADA SISTEM ANTREAN RAWAT JALAN DI RSUP Dr. KARIADI DENGAN DISTRIBUSI SAMPEL POISSON DAN GEOMETRIK

2021 ◽  
Vol 10 (3) ◽  
pp. 413-422
Author(s):  
Nur Azizah ◽  
Sugito Sugito ◽  
Hasbi Yasin
Keyword(s):  
Internal Medicine ◽  
Posterior Distribution ◽  
Prior Distribution ◽  
Bayesian Method ◽  
Likelihood Function ◽  
Queuing System ◽  
Hospital Service ◽  
Queuing Model ◽  
Sample Distribution ◽  
New Information

Hospital service facilities cannot be separated from queuing events. Queues are an unavoidable part of life, but they can be minimized with a good system. The purpose of this study was to find out how the queuing system at Dr. Kariadi. Bayesian method is used to combine previous research and this research in order to obtain new information. The sample distribution and prior distribution obtained from previous studies are combined with the sample likelihood function to obtain a posterior distribution. After calculating the posterior distribution, it was found that the queuing model in the outpatient installation at Dr. Kariadi Semarang is (G/G/c): (GD/∞/∞) where each polyclinic has met steady state conditions and the level of busyness is greater than the unemployment rate so that the queuing system at Dr. Kariadi is categorized as good, except in internal medicine poly. 

scholarly journals A novel Bayesian method for inferring and interpreting the dynamics of adaptive landscapes from phylogenetic comparative data

2014 ◽  
Author(s):  
Josef C Uyeda ◽  
Luke J Harmon
Keyword(s):  
Large Scale ◽  
Bayesian Method ◽  
A Priori ◽  
Model Fitting ◽  
Biological Data ◽  
Comparative Data ◽  
Adaptive Landscape ◽  
Multiple Sources ◽  
Adaptive Landscapes ◽  
Selection Parameters

Our understanding of macroevolutionary patterns of adaptive evolution has greatly increased with the advent of large-scale phylogenetic comparative methods. Widely used Ornstein-Uhlenbeck (OU) models can describe an adaptive process of divergence and selection. However, inference of the dynamics of adaptive landscapes from comparative data is complicated by interpretational difficulties, lack of identifiability among parameter values and the common requirement that adaptive hypotheses must be assigneda priori. Here we develop a reversible-jump Bayesian method of fitting multi-optima OU models to phylogenetic comparative data that estimates the placement and magnitude of adaptive shifts directly from the data. We show how biologically informed hypotheses can be tested against this inferred posterior of shift locations using Bayes Factors to establish whether oura priorimodels adequately describe the dynamics of adaptive peak shifts. Furthermore, we show how the inclusion of informative priors can be used to restrict models to biologically realistic parameter space and test particular biological interpretations of evolutionary models. We argue that Bayesian model-fitting of OU models to comparative data provides a framework for integrating of multiple sources of biological data--such as microevolutionary estimates of selection parameters and paleontological timeseries--allowing inference of adaptive landscape dynamics with explicit, process-based biological interpretations.

Terminal filtering of stochastic processes observed on a finite time interval

2021 ◽  
Author(s):  
S.V. Sokolov ◽  
E.G. Chub ◽  
A.A. Manin
Keyword(s):  
Time Series ◽  
Stochastic Processes ◽  
Posterior Distribution ◽  
Finite Time ◽  
Distribution Density ◽  
Optimal Estimation ◽  
Observation Time ◽  
Estimation Accuracy ◽  
Time Interval ◽  
Finite Time Interval

Annotation. Currently, the problem of evaluating stochastic processes observed under noisy conditions on a finite time interval is solved only for datasets in the form of time series using a limited number of statistical variational or spectral analysis methods, as well as various modifications of regression methods. In this case, parametric criteria are used that depend on individual parameters of the distribution density of the observed process, and not on the density itself, which significantly limits the possibilities of increasing the estimation accuracy. To solve the problem of high-precision estimation of stochastic processes on a finite time interval of their observation, an approach is proposed, firstly, providing optimal estimation according to the criterion depending on the posterior distribution density - the most informative characteristic of the observed process, and secondly, taking into account the dynamic structure of the process and the finiteness of the interval observation. A numerical example is considered to illustrate the effectiveness of the developed approach. Relevance. Currently, the problem of evaluating stochastic processes observed under noisy conditions on a finite time interval (terminal filtering problem) is solved only for datasets in the form of time series using a limited number of statistical variational or spectral analysis methods, as well as various modifications of regression methods. In this case, parametric criteria are used that depend on individual parameters of the distribution density of the observed process, and not on the density itself, which significantly limits the possibilities of increasing the estimation accuracy. Target. In this regard, for stochastic processes of a general form - described by nonlinear stochastic differential equations, it is necessary to develop a method of terminal filtering according to a criterion that takes into account the finiteness of the observation time interval and depends on the posterior distribution density - the most informative characteristic of the observed process (and not on its individual parameters). Results. The proposed solution to the problem of high-precision terminal filtering of stochastic processes - their optimal estimation over a finite observation time interval - is based on the use of a terminal criterion that depends directly on the posterior distribution density and takes into account the finiteness of the observation time interval. When describing the observed stochastic processes, their most general representation was used - nonlinear stochastic differential equations, which significantly expands the field of application of the results obtained in comparison, for example, with time series. The general solution to the problem of optimal terminal filtering is obtained using the Pontryagin maximum principle, the solution to the problem of suboptimal filtering, which significantly reduces computational costs, is based on the method of invariant immersion. Practical significance. A numerical example is considered to illustrate the effectiveness of the developed method. The proposed approach can be widely used in various fields of scientific and technical research: radio engineering, Earth sensing, satellite navigation, astronomy, seismology, geodesy, etc.

Interval Estimation of Bivariate Correlations With Missing Data on Both Variables: A Bayesian Approach

1997 ◽  
Vol 22 (4) ◽  
pp. 407-424 ◽  
Author(s):  
Alan L. Gross
Keyword(s):  
Missing Data ◽  
Posterior Distribution ◽  
Prior Distribution ◽  
Bayesian Method ◽  
Interval Estimation ◽  
Data Set ◽  
Interval Estimates ◽  
Bivariate Correlation ◽  
Missing Completely At Random ◽  
Sample Correlation

The posterior distribution of the bivariate correlation ( ρxy) is analytically derived given a data set consisting N1 cases measured on both x and y, N2 cases measured only on x, and N3 cases measured only on y. The posterior distribution is shown to be a function of the subsample sizes, the sample correlation ( rxy) computed from the N1 complete cases, a set of four statistics which measure the extent to which the missing data are not missing completely at random, and the specified prior distribution for ρxy. A sampling study suggests that in small ( N = 20) and moderate ( N = 50) sized samples, posterior Bayesian interval estimates will dominate maximum likelihood based estimates in terms of coverage probability and expected interval widths when the prior distribution for ρxy is simply uniform on (0, 1). The advantage of the Bayesian method when more informative priors based on beta densities are employed is not as consistent.

Bayesian Estimation of Gold Index's Change Point of Time Series Model

2013 ◽  
Vol 709 ◽  
pp. 538-541
Author(s):  
Ying Xiang
Keyword(s):  
Time Series ◽  
Posterior Distribution ◽  
Change Point ◽  
Prior Information ◽  
Bayesian Method ◽  
Time Sequence ◽  
Time Series Model ◽  
Conjugate Prior ◽  
Parameter Values ◽  
Iterative Error

The thesis mainly estimates the change point of time series model through Bayesian method. First, through establishing the time series model, adopting conjugate prior distribution, linear regression and prior information, the parameter values related to distribution can be got. Then posterior distribution and change point can be got through computation. To reduce iterative error, Peak Algorithm is used to check the posterior distribution. Finally, the gold indexs change point of time sequence model can be got through this method.

scholarly journals 2-D DOA estimation method based on coprime array MIMO radar

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Fei Zhang ◽  
Zijing Zhang ◽  
Aisuo Jin ◽  
Chuantang Ji ◽  
Yi Wang
Keyword(s):  
Degrees Of Freedom ◽  
Estimation Method ◽  
Doa Estimation ◽  
Mimo Radar ◽  
Estimation Methods ◽  
Estimation Accuracy ◽  
Multiple Sources ◽  
Source Estimation ◽  
Array Aperture ◽  
Coprime Array

AbstractAiming at the problem that traditional direction of arrival (DOA) estimation methods cannot handle multiple sources with high accuracy while increasing the degrees of freedom (DOF), a new method for 2-D DOA estimation based on coprime array MIMO radar (SA-MIMO-CA) is proposed. First of all, in order to ensure the accuracy of multi-source estimation when the number of elements is finite, a new coprime array model based on MIMO (MIMO-CA) is proposed. This method is based on a new MIMO array-based co-prime array model (MIMO-CA), which improves the accuracy of multi-source estimation when the number of array elements is limited, and obtains a larger array aperture with a smaller number of array elements, and improves the estimation accuracy of 2-D DOA. Finally, the effectiveness and reliability of the proposed SM-MIMO-CA method in improving the DOF of array and DOA accuracy are verified by experiments.

Sign in / Sign up

Export Citation Format

Share Document