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: 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: 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: This paper proposes a GLMM with spatial and
temporal effects for malaria data in Thailand. A Bayesian method is
used for parameter estimation via Gibbs sampling MCMC. A
conditional autoregressive (CAR) model is assumed to present the
spatial effects. The temporal correlation is presented through the
covariance matrix of the random effects. The malaria quarterly data
have been extracted from the Bureau of Epidemiology, Ministry of
Public Health of Thailand. The factors considered are rainfall and
temperature. The result shows that rainfall and temperature are
positively related to the malaria morbidity rate. The posterior means
of the estimated morbidity rates are used to construct the malaria
maps. The top 5 highest morbidity rates (per 100,000 population) are
in Trat (Q3, 111.70), Chiang Mai (Q3, 104.70), Narathiwat (Q4,
97.69), Chiang Mai (Q2, 88.51), and Chanthaburi (Q3, 86.82).
According to the DIC criterion, the proposed model has a better
performance than the GLMM with spatial effects but without
temporal terms.
Abstract: Parametric models have been quite popular for
studying human growth, particularly in relation to biological
parameters such as peak size velocity and age at peak size velocity.
Longitudinal data are generally considered to be vital for fittinga
parametric model to individual-specific data, and for studying the
distribution of these biological parameters in a human population.
However, cross-sectional data are easier to obtain than longitudinal
data. In this paper, we present a method of combining longitudinal
and cross-sectional data for the purpose of estimating the distribution
of the biological parameters. We demonstrate, through simulations in
the special case ofthePreece Baines model, how estimates based on
longitudinal data can be improved upon by harnessing the
information contained in cross-sectional data.We study the extent of
improvement for different mixes of the two types of data, and finally
illustrate the use of the method through data collected by the Indian
Statistical Institute.
Abstract: Several combinations of the preprocessing algorithms,
feature selection techniques and classifiers can be applied to the data
classification tasks. This study introduces a new accurate classifier,
the proposed classifier consist from four components: Signal-to-
Noise as a feature selection technique, support vector machine,
Bayesian neural network and AdaBoost as an ensemble algorithm.
To verify the effectiveness of the proposed classifier, seven well
known classifiers are applied to four datasets. The experiments show
that using the suggested classifier enhances the classification rates for
all datasets.
Abstract: Among various HLM techniques, the Multivariate Hierarchical Linear Model (MHLM) is desirable to use, particularly when multivariate criterion variables are collected and the covariance structure has information valuable for data analysis. In order to reflect prior information or to obtain stable results when the sample size and the number of groups are not sufficiently large, the Bayes method has often been employed in hierarchical data analysis. In these cases, although the Markov Chain Monte Carlo (MCMC) method is a rather powerful tool for parameter estimation, Procedures regarding MCMC have not been formulated for MHLM. For this reason, this research presents concrete procedures for parameter estimation through the use of the Gibbs samplers. Lastly, several future topics for the use of MCMC approach for HLM is discussed.
Abstract: Using Dynamic Bayesian Networks (DBN) to model genetic regulatory networks from gene expression data is one of the major paradigms for inferring the interactions among genes. Averaging a collection of models for predicting network is desired, rather than relying on a single high scoring model. In this paper, two kinds of model searching approaches are compared, which are Greedy hill-climbing Search with Restarts (GSR) and Markov Chain Monte Carlo (MCMC) methods. The GSR is preferred in many papers, but there is no such comparison study about which one is better for DBN models. Different types of experiments have been carried out to try to give a benchmark test to these approaches. Our experimental results demonstrated that on average the MCMC methods outperform the GSR in accuracy of predicted network, and having the comparable performance in time efficiency. By proposing the different variations of MCMC and employing simulated annealing strategy, the MCMC methods become more efficient and stable. Apart from comparisons between these approaches, another objective of this study is to investigate the feasibility of using DBN modeling approaches for inferring gene networks from few snapshots of high dimensional gene profiles. Through synthetic data experiments as well as systematic data experiments, the experimental results revealed how the performances of these approaches can be influenced as the target gene network varies in the network size, data size, as well as system complexity.
Abstract: In this paper we present a novel approach for human
Body configuration based on the Silhouette. We propose to address
this problem under the Bayesian framework. We use an effective
Model based MCMC (Markov Chain Monte Carlo) method to solve
the configuration problem, in which the best configuration could be
defined as MAP (maximize a posteriori probability) in Bayesian
model. This model based MCMC utilizes the human body model to
drive the MCMC sampling from the solution space. It converses the
original high dimension space into a restricted sub-space constructed
by the human model and uses a hybrid sampling algorithm. We
choose an explicit human model and carefully select the likelihood
functions to represent the best configuration solution. The
experiments show that this method could get an accurate
configuration and timesaving for different human from multi-views.
Abstract: In high powered dense wavelength division
multiplexed (WDM) systems with low chromatic dispersion,
four-wave mixing (FWM) can prove to be a major source of noise.
The MultiCanonical Monte Carlo Method (MCMC) and the Split
Step Fourier Method (SSFM) are combined to accurately evaluate the
probability density function of the decision variable of a receiver,
limited by FWM. The combination of the two methods leads to more
accurate results, and offers the possibility of adding other optical
noises such as the Amplified Spontaneous Emission (ASE) noise.
Abstract: In unsupervised segmentation context, we propose a bi-dimensional hidden Markov chain model (X,Y) that we adapt to the image segmentation problem. The bi-dimensional observed process Y = (Y 1, Y 2) is such that Y 1 represents the noisy image and Y 2 represents a noisy supplementary information on the image, for example a noisy proportion of pixels of the same type in a neighborhood of the current pixel. The proposed model can be seen as a competitive alternative to the Hilbert-Peano scan. We propose a bayesian algorithm to estimate parameters of the considered model. The performance of this algorithm is globally favorable, compared to the bi-dimensional EM algorithm through numerical and visual data.