Abstract: This paper employs the Jeffrey's prior technique in the
process of estimating the periodograms and frequency of sinusoidal
model for unknown noisy time variants or oscillating events (data) in
a Bayesian setting. The non-informative Jeffrey's prior was adopted
for the posterior trigonometric function of the sinusoidal model
such that Cramer-Rao Lower Bound (CRLB) inference was used
in carving-out the minimum variance needed to curb the invariance
structure effect for unknown noisy time observational and repeated
circular patterns. An average monthly oscillating temperature series
measured in degree Celsius (0C) from 1901 to 2014 was subjected to
the posterior solution of the unknown noisy events of the sinusoidal
model via Markov Chain Monte Carlo (MCMC). It was not only
deduced that two minutes period is required before completing a cycle
of changing temperature from one particular degree Celsius to another
but also that the sinusoidal model via the CRLB-Jeffrey's prior for
unknown noisy events produced a miniature posterior Maximum A
Posteriori (MAP) compare to a known noisy events.
Abstract: In this paper, we propose a condition-based
maintenance policy for multi-unit systems considering the
existence of economic dependency among units. We consider a
system composed of N identical units, where each unit deteriorates
independently. Deterioration process of each unit is modeled as a
three-state continuous time homogeneous Markov chain with two
working states and a failure state. The average production rate of
units varies in different working states and demand rate of the
system is constant. Units are inspected at equidistant time epochs,
and decision regarding performing maintenance is determined by the
number of units in the failure state. If the total number of units in the
failure state exceeds a critical level, maintenance is initiated, where
units in failed state are replaced correctively and deteriorated state
units are maintained preventively. Our objective is to determine the
optimal number of failed units to initiate maintenance minimizing
the long run expected average cost per unit time. The problem is
formulated and solved in the semi-Markov decision process (SMDP)
framework. A numerical example is developed to demonstrate the
proposed policy and the comparison with the corrective maintenance
policy is presented.
Abstract: In this work, we introduce the qualitative and
quantitative concept of the strong stability method in the risk process
modeling two lines of business of the same insurance company or
an insurance and re-insurance companies that divide between them
both claims and premiums with a certain proportion. The approach
proposed is based on the identification of the ruin probability
associate to the model considered, with a stationary distribution of a
Markov random process called a reversed process. Our objective, after clarifying the condition and the perturbation
domain of parameters, is to obtain the stability inequality of the ruin
probability which is applied to estimate the approximation error of a
model with disturbance parameters by the considered model. In the
stability bound obtained, all constants are explicitly written.
Abstract: In this paper, we study the performance of the strong
stability method of the univariate classical risk model. We interest to
the stability bounds established using two approaches. The first based
on the strong stability method developed for a general Markov chains.
The second approach based on the regenerative processes theory . By
adopting an algorithmic procedure, we study the performance of the
stability method in the case of exponential distribution claim amounts.
After presenting numerically and graphically the stability bounds, an
interpretation and comparison of the results have been done.
Abstract: Wireless Body Area Networks (WBANs) are essential for real-time health monitoring of patients and in diagnosing of many diseases. WBANs comprise many sensors to monitor a large range of ambient conditions. Quality of Service (QoS) is a key challenge in WBAN, because the different state information of the neighboring nodes has to be monitored in an accurate manner. However, energy consumption gets increased while predicting and maintaining the exact information in highly dynamic environments. In order to reduce energy consumption and end to end delay, Markov Chain Based Quality of Service Support (MC-QoSS) method is designed in the health monitoring services of WBAN communication. The energy consumption gets reduced by forming a Markov chain with high energy nodes in the sensor networks communication path. The low energy level sensor nodes are removed using transitional probability in order to reduce end to end delay. High energy nodes are formed in the chain structure of its corresponding path to enhance communication. After choosing the communication path through high energy nodes, the packets are sent to the sink node from the source node with a higher Packet Delivery Ratio. The simulation result shows that MC-QoSS method improves the packet delivery ratio and reduces energy consumption with minimum end to end delay, compared to existing methods.
Abstract: The primary approach for estimating bridge deterioration uses Markov-chain models and regression analysis. Traditional Markov models have problems in estimating the required transition probabilities when a small sample size is used. Often, reliable bridge data have not been taken over large periods, thus large data sets may not be available. This study presents an important change to the traditional approach by using the Small Data Method to estimate transition probabilities. The results illustrate that the Small Data Method and traditional approach both provide similar estimates; however, the former method provides results that are more conservative. That is, Small Data Method provided slightly lower than expected bridge condition ratings compared with the traditional approach. Considering that bridges are critical infrastructures, the Small Data Method, which uses more information and provides more conservative estimates, may be more appropriate when the available sample size is small. In addition, regression analysis was used to calculate bridge deterioration. Condition ratings were determined for bridge groups, and the best regression model was selected for each group. The results obtained were very similar to those obtained when using Markov chains; however, it is desirable to use more data for better results.
Abstract: This paper is to compare the parameter estimation of
the mean in normal distribution by Maximum Likelihood (ML),
Bayes, and Markov Chain Monte Carlo (MCMC) methods. The ML
estimator is estimated by the average of data, the Bayes method is
considered from the prior distribution to estimate Bayes estimator,
and MCMC estimator is approximated by Gibbs sampling from
posterior distribution. These methods are also to estimate a parameter
then the hypothesis testing is used to check a robustness of the
estimators. Data are simulated from normal distribution with the true
parameter of mean 2, and variance 4, 9, and 16 when the sample
sizes is set as 10, 20, 30, and 50. From the results, it can be seen
that the estimation of MLE, and MCMC are perceivably different
from the true parameter when the sample size is 10 and 20 with
variance 16. Furthermore, the Bayes estimator is estimated from the
prior distribution when mean is 1, and variance is 12 which showed
the significant difference in mean with variance 9 at the sample size
10 and 20.
Abstract: Piecewise polynomial regression model is very flexible model for modeling the data. If the piecewise polynomial regression model is matched against the data, its parameters are not generally known. This paper studies the parameter estimation problem of piecewise polynomial regression model. The method which is used to estimate the parameters of the piecewise polynomial regression model is Bayesian method. Unfortunately, the Bayes estimator cannot be found analytically. Reversible jump MCMC algorithm is proposed to solve this problem. Reversible jump MCMC algorithm generates the Markov chain that converges to the limit distribution of the posterior distribution of piecewise polynomial regression model parameter. The resulting Markov chain is used to calculate the Bayes estimator for the parameters of piecewise polynomial regression model.
Abstract: Allocating limited budget to maintain bridge networks and selecting effective maintenance strategies for each bridge represent challenging tasks for maintenance managers and decision makers. In Egypt, bridges are continuously deteriorating. In many cases, maintenance works are performed due to user complaints. The objective of this paper is to develop a practical and reliable framework to manage the maintenance, repair, and rehabilitation (MR&R) activities of Bridges network considering performance and budget limits. The model solves an optimization problem that maximizes the average condition of the entire network given the limited available budget using Genetic Algorithm (GA). The framework contains bridge inventory, condition assessment, repair cost calculation, deterioration prediction, and maintenance optimization. The developed model takes into account multiple parameters including serviceability requirements, budget allocation, element importance on structural safety and serviceability, bridge impact on network, and traffic. A questionnaire is conducted to complete the research scope. The proposed model is implemented in software, which provides a friendly user interface. The framework provides a multi-year maintenance plan for the entire network for up to five years. A case study of ten bridges is presented to validate and test the proposed model with data collected from Transportation Authorities in Egypt. Different scenarios are presented. The results are reasonable, feasible and within acceptable domain.
Abstract: The cumulative costs for O&M may represent as
much as 65%-90% of the turbine's investment cost. Nowadays the
cost effectiveness concept becomes a decision-making and
technology evaluation metric. The cost of energy metric accounts for
the effect replacement cost and unscheduled maintenance cost
parameters. One key of the proposed approach is the idea of
maintaining the WTs which can be captured via use of a finite state
Markov chain. Such a model can be embedded within a probabilistic
operation and maintenance simulation reflecting the action to be
done. In this paper, an approach of estimating the cost of O&M is
presented. The finite state Markov model is used for decision
problems with number of determined periods (life cycle) to predict
the cost according to various options of maintenance.
Abstract: Although there has been a growing interest in the
hybrid free-space optical link and radio frequency FSO/RF
communication system, the current literature is limited to results
obtained in moderate or cold environment. In this paper, using a soft
switching approach, we investigate the effect of weather
inhomogeneities on the strength of turbulence hence the channel
refractive index under Qatar harsh environment and their influence
on the hybrid FSO/RF availability. In this approach, either FSO/RF
or simultaneous or none of them can be active. Based on soft
switching approach and a finite state Markov Chain (FSMC) process,
we model the channel fading for the two links and derive a
mathematical expression for the outage probability of the hybrid
system. Then, we evaluate the behavior of the hybrid FSO/RF under
hazy and harsh weather. Results show that the FSO/RF soft switching
renders the system outage probability less than that of each link
individually. A soft switching algorithm is being implemented on
FPGAs using Raptor code interfaced to the two terminals of a
1Gbps/100 Mbps FSO/RF hybrid system, the first being implemented
in the region. Experimental results are compared to the above
simulation results.
Abstract: This paper presents the application of finite dynamic
programming, specifically the "Markov Chain" model, as part of the
decision making process of a company in the cosmetics sector located
in the vicinity of Bogota DC. The objective of this process was to
decide whether the company should completely reconstruct its
wastewater treatment plant or instead optimize the plant through the
addition of equipment. The goal of both of these options was to make
the required improvements in order to comply with parameters
established by national legislation regarding the treatment of waste
before it is released into the environment. This technique will allow
the company to select the best option and implement a solution for
the processing of waste to minimize environmental damage and the
acquisition and implementation costs.
Abstract: This paper proposes a linear mixed model (LMM) with spatial effects to forecast rice and cassava yields in Thailand at the same time. A multivariate conditional autoregressive (MCAR) model is assumed to present the spatial effects. A Bayesian method is used for parameter estimation via Gibbs sampling Markov Chain Monte Carlo (MCMC). The model is applied to the rice and cassava yields monthly data which have been extracted from the Office of Agricultural Economics, Ministry of Agriculture and Cooperatives of Thailand. The results show that the proposed model has better performance in most provinces in both fitting part and validation part compared to the simple exponential smoothing and conditional auto regressive models (CAR) from our previous study.
Abstract: A forecasting model for steel demand uncertainty in Thailand is proposed. It consists of trend, autocorrelation, and outliers in a hierarchical Bayesian frame work. The proposed model uses a cumulative Weibull distribution function, latent first-order autocorrelation, and binary selection, to account for trend, time-varying autocorrelation, and outliers, respectively. The Gibbs sampling Markov Chain Monte Carlo (MCMC) is used for parameter estimation. The proposed model is applied to steel demand index data in Thailand. The root mean square error (RMSE), mean absolute percentage error (MAPE), and mean absolute error (MAE) criteria are used for model comparison. The study reveals that the proposed model is more appropriate than the exponential smoothing method.
Abstract: In this paper, we present a simplified higher-order Markov chain model for multiple categorical data sequences also called as simplified higher-order multivariate Markov chain model.
Abstract: Inferring the network structure from time series data
is a hard problem, especially if the time series is short and noisy.
DNA microarray is a technology allowing to monitor the mRNA
concentration of thousands of genes simultaneously that produces
data of these characteristics. In this study we try to investigate the
influence of the experimental design on the quality of the result.
More precisely, we investigate the influence of two different types of
random single gene perturbations on the inference of genetic networks
from time series data. To obtain an objective quality measure for
this influence we simulate gene expression values with a biologically
plausible model of a known network structure. Within this framework
we study the influence of single gene knock-outs in opposite to
linearly controlled expression for single genes on the quality of the
infered network structure.
Abstract: Missing data yields many analysis challenges. In case of complex survey design, in addition to dealing with missing data, researchers need to account for the sampling design to achieve useful inferences. Methods for incorporating sampling weights in neural network imputation were investigated to account for complex survey designs. An estimate of variance to account for the imputation uncertainty as well as the sampling design using neural networks will be provided. A simulation study was conducted to compare estimation results based on complete case analysis, multiple imputation using a Markov Chain Monte Carlo, and neural network imputation. Furthermore, a public-use dataset was used as an example to illustrate neural networks imputation under a complex survey design
Abstract: By systematically applying different engineering
methods, difficult financial problems become approachable. Using a
combination of theory and techniques such as wavelet transform,
time series data mining, Markov chain based discrete stochastic
optimization, and evolutionary algorithms, this work formulated a
strategy to characterize and forecast non-linear time series. It
attempted to extract typical features from the volatility data sets of
S&P100 and S&P500 indices that include abrupt drops, jumps and
other non-linearity. As a result, accuracy of forecasting has reached
an average of over 75% surpassing any other publicly available
results on the forecast of any financial index.
Abstract: In this paper we present a novel error model for
packet loss and subsequent error description. The proposed model
simulates the error performance of wireless communication link. The
model is designed as two independent Markov chains, where the first
one is used for packet generation and the second one generates
correctly and incorrectly transmitted bits for received packets from
the first chain. The statistical analyses of real communication on the
wireless link are used for determination of model-s parameters. Using
the obtained parameters and the implementation of the generator, we
collected generated traffic. The obtained results generated by
proposed model are compared with the real data collection.
Abstract: The cumulative conformance count (CCC) charts are
widespread in process monitoring of high-yield manufacturing.
Recently, it is found the use of variable sampling interval (VSI)
scheme could further enhance the efficiency of the standard CCC
charts. The average time to signal (ATS) a shift in defect rate has
become traditional measure of efficiency of a chart with the VSI
scheme. Determining the ATS is frequently a difficult and tedious
task. A simple method based on a finite Markov Chain approach for
modeling the ATS is developed. In addition, numerical results are
given.