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: 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: 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: 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: Quantitative trait loci (QTL) experiments have yielded
important biological and biochemical information necessary for
understanding the relationship between genetic markers and
quantitative traits. For many years, most QTL algorithms only
allowed one observation per genotype. Recently, there has been an
increasing demand for QTL algorithms that can accommodate more
than one observation per genotypic distribution. The Bayesian
hierarchical model is very flexible and can easily incorporate this
information into the model. Herein a methodology is presented that
uses a Bayesian hierarchical model to capture the complexity of the
data. Furthermore, the Markov chain Monte Carlo model composition
(MC3) algorithm is used to search and identify important markers. An
extensive simulation study illustrates that the method captures the
true QTL, even under nonnormal noise and up to 6 QTL.
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 this paper we investigate the influence of external
noise on the inference of network structures. The purpose of our
simulations is to gain insights in the experimental design of microarray
experiments to infer, e.g., transcription regulatory networks
from microarray experiments. Here external noise means, that the
dynamics of the system under investigation, e.g., temporal changes of
mRNA concentration, is affected by measurement errors. Additionally
to external noise another problem occurs in the context of microarray
experiments. Practically, it is not possible to monitor the mRNA
concentration over an arbitrary long time period as demanded by the
statistical methods used to learn the underlying network structure. For
this reason, we use only short time series to make our simulations
more biologically plausible.