Intra-patient Arrhythmia Heartbeat Modeling by Gibbs Sampling

For fully taking into account the feature of environmental data set the Gaussian mixture model (GMM) is combined with the Dirichlet Process (DP) to solve the problem of specifying the initial cluster number. The Gibbs sampling algorithm is also used as the substitute of the Expectation Maximization algorithm to estimate the parameter of the model with Dirichlet Process. The clustering process is implemented under the framework of Spark so as to deal with farm environmental data set stored in distributed computer cluster. Experiment results with external criterion show that the improved clustering method has a better ability in data anomaly detection compared with other common cluster methods. Farm environmental data anomaly detection is implemented by the improved clustering method.

The transcription start site (TSS) has been located for an increasing number of genes across several organisms. Statistical tests have shown that some cis-acting regulatory elements have positional preferences with respect to the TSS, but few strategies have emerged for locating elements by their positional preferences. This paper elaborates such a strategy. First, we align promoter regions without gaps, anchoring the alignment on each promoter's TSS. Second, we apply a novel word-specific mask. Third, we apply a clustering test related to gapless BLAST statistics. The test examines whether any specific word is placed unusually consistently with respect to the TSS. Finally, our program A-GLAM, an extension of the GLAM program, uses significant word positions as new 'anchors' to realign the sequences. A Gibbs sampling algorithm then locates putative cis-acting regulatory elements. Usually, Gibbs sampling requires a preliminary masking step, to avoid convergence onto a dominant but uninteresting signal from a DNA repeat. However, since the positional anchors focus A-GLAM on the motif of interest, masking DNA repeats during Gibbs sampling becomes unnecessary. In a set of human DNA sequences with experimentally characterized TSSs, the placement of 791 octonucleotide words was unusually consistent (multiple test corrected P < 0.05). Alignments anchored on these words sometimes located statistically significant motifs inaccessible to GLAM or AlignACE. The A-GLAM program and a list of statistically significant words are available at ftp://ftp.ncbi.nih.gov/pub/spouge/papers/archive/AGLAM/.

This dissertation consists of five chapters with three distinct but related research projects. In Chapter 1, we introduce some necessary definitions related to the research work. In Chapter 2, we develop Bayes factor based testing procedures for a general linear hypothesis of the regression coefficients in the context of the normal linear models. We propose two calibration schemes to deal with asymmetry in information of Bayes factor: (i) by controlling Type I error probability of the Bayes factor and (ii) by balancing Type I and Type II error probabilities of the Bayes factor. We evaluate the finite sample performance of the proposed Bayes factors via simulation studies and a real-data application. Experimental results have shown than the proposed Bayes factors perform well in testing the general linear hypothesis of the regression coefficient. In Chapter 3, we consider Bayesian quantile analysis for testing constrained hypotheses in linear models, in which the quantiles the parameters satisfy a simple order restriction. We develop a Bayesian hierarchical model based on the specification the asymmetric Laplace distribution for the error component. We propose a non-iterative sampling algorithm in the Expectation-Maximization (EM) structure to generate independently and identically distributed posterior samples from their posterior distributions of the parameters. Then we adopt the Savage-Dickey density ratios to conduct the multiple comparison with simply order constraints. Simulation studies were conducted to compare the finite sample performance of the proposed non-iterative sampling algorithm with the Gibbs sampling algorithm. In Chapter 4, we consider objective Bayesian analysis for the concordance correlation coefficient (CCC), which is one of the most commonly used metrics to assess agreement of different methods in many practical applications. We develop an objective Bayesian framework for estimating the CCC based a combined use of the multivariate student's t-distribution with noninformative Independence Jeffreys prior for the unknown parameters. Extensive simulation studies are conducted to compare the performance of the proposed Bayesian estimates with the ones under the subjective priors in the literature. In Chapter 5, we discuss some ongoing projects related to our research work mentioned above and some interesting problems for future work.

Many different algorithms developed in statistical physics, coding theory, signal processing, and artificial intelligence can be expressed by graphical models and solved (either exactly or approximately) with iterative message-passing algorithms on the model. One quantity of interest in these algorithms is the partition function. In graphical models without cycle (trees), the partition function can be computed efficiently by means of message-passing algorithms, like GDL or the sum-product algorithm. In contrast, when graphical models contain cycles, the computation of the partition function is in general intractable. Our contributions in this dissertation are: deriving deterministic upper and lower bounds on partition function, and developing methods to approximate this quantity with Monte Carlo methods. Specifically, we obtain subtree-based upper and lower bounds which lead to theoretical results on optimality properties of the minimum entropy sub-tree and finally lead to a greedy algorithm. At last, we introduce and analyze a number of estimators that use Gibbs sampling to draw samples from different target distributions to estimate the value of the partition function. In one estimator, we demonstrate a novel strategy which combines Gibbs sampling and message-passing algorithms on trees.

Models are often defined through conditional rather than joint distributions, but it can be difficult to check whether the conditional distributions are compatible,i.e.whether there exists a joint probability distribution which generates them. When they are compatible, a Gibbs sampler can be used to sample from this joint distribution. When they are not, the Gibbs sampling algorithm may still be applied, resulting in a “pseudo-Gibbs sampler”. We show its stationary probability distribution to be the optimal compromise between the conditional distributions, in the sense that it minimizes a mean squared misfit between them and its own conditional distributions. This allows us to perform Objective Bayesian analysis of correlation parameters in Kriging models by using univariate conditional Jeffreys-rule posterior distributions instead of the widely used multivariate Jeffreys-rule posterior. This strategy makes the full-Bayesian procedure tractable. Numerical examples show it has near-optimal frequentist performance in terms of prediction interval coverage.

Drug coating is one of the most important processes in the modern pharmaceutical industry. Improving the utilization rate of raw materials (URRM) in the drug coating process is thus important for cost saving and efficiency enhancement. There is little existing research on this topic in the literature of applied statistics. In this paper, motivated by a real dataset collected from a pharmaceutical company in China, we propose to use a novel predictive model that integrates a Bayesian framework with the Gibbs sampling algorithm to characterize the pattern of URRM. Based on certain prior distributional assumptions, the Gibbs sampling algorithm is then applied to sample the posterior distribution of the parameters to obtain more accurate and robust estimation results. By using the proposed method, the drugs can be properly separated into several categories with different patterns of URRM, and the pattern of each category can be properly recognized with selected covariates, which achieves the goals of clustering, variable selection, and regression simultaneously, and provides valuable insights into the improvement of the URRM for drug coating. Numerical studies show that the proposed method works well in practice.

In this article we present a Bayesian prediction of multiplicative seasonal autoregressive moving average (SARMA) processes using the Gibbs sampling algorithm. First, we estimate the unobserved errors using the nonlinear least squares (NLS) method to approximate the likelihood function. Second, we employ conjugate priors on the model parameters and initial values and assume the model errors are normally distributed to derive the conditional posterior and predictive distributions. In particular, we show that the conditional posterior distribution of the model parameters and the variance are multivariate normal and inverse gamma respectively, and the conditional predictive distribution of the future observations is a multivariate normal. Finally, we use these closed-form conditional posterior and predictive distributions to apply the Gibbs sampling algorithm to approximate empirically the marginal posterior and predictive distributions, enabling us easily to carry out multiple-step ahead predictions. We evaluate our proposed Bayesian method using simulation study and real-world time series datasets.

&amp;lt;p&amp;gt;Throughput is an important measure of performance of production system. Analyzing and modeling of production throughput is complex in today-s dynamic production systems due to uncertainties of production system. The main reasons are that uncertainties are materialized when the production line faces changes in setup time, machinery break down, lead time of manufacturing, and scraps. Besides, demand changes are fluctuating from time to time for each product type. These uncertainties affect the production performance. This paper proposes Bayesian inference for throughput modeling under five production uncertainties. Bayesian model utilized prior distributions related to previous information about the uncertainties where likelihood distributions are associated to the observed data. Gibbs sampling algorithm as the robust procedure of Monte Carlo Markov chain was employed for sampling unknown parameters and estimating the posterior mean of uncertainties. The Bayesian model was validated with respect to convergence and efficiency of its outputs. The results presented that the proposed Bayesian models were capable to predict the production throughput with accuracy of 98.3%.&amp;lt;/p&amp;gt;

In data analysis, change point problems correspond to abrupt changes in stochastic mechanisms generating data. The detection of change points is a relevant problem in the analysis and prediction of time series. In this paper, we consider a class of conjugate prior distributions obtained from conditional specification methodology for solving this problem. We illustrate the application of such distributions in Bayesian change point detection analysis with Poisson processes. We obtain the posterior distribution of model parameters using general bivariate distribution with gamma conditionals. Simulation from the posterior are readily implemented using a Gibbs sampling algorithm. The Gibbs sampling is implemented even when using conditional densities that are incompatible or only compatible with an improper joint density. The application of such methods will be demonstrated using examples of simulated and real data.

In this article we develop an estimation method based on the augmented data scheme and EM/SEM (Stochastic EM) algorithms for fitting one-parameter probit (Rasch) IRT (Item Response Theory) models. Instead of using the S steps of the SEM algorithm, that is, instead of simulating values for the unobserved variables (augmented data and the latent traits), we consider the conditional expectations of a set of unobserved variables on the other set of unobserved variables, the current estimates of the parameters and the observed data, based on the full conditional distributions from the Gibbs sampling algorithm. Our method, named the CADEM algorithm (conditional augmented data EM), presents straightforward E steps, which avoid the need to evaluate the usual integrals, also facilitating the M steps, without the need to use numerical methods of optimization. We use the CADEM algorithm to obtain both maximum likelihood estimates and maximum a posteriori estimates of the difficulty parameters for the one-parameter probit (Rasch) model. Also, we obtain estimates for the latent traits, based on conditional expectations. In addition, we show how to calculate the associated standard errors. Some directions are provided to extend our approach to other IRT models. In this respect, we perform a simulation study to compare the estimation methods. The results indicated that our approach is quite comparable to the usual marginal maximum likelihood (MML) and Gibbs sampling methods (GS) in terms of parameter recovery. However, CADEM is as fast as MML and as flexible as GS.

Mixture distributions are widely used to model data with distinct groups, providing a flexible approach to estimating density. However, Bayesian approaches for mixture models pose challenges, such as label switching in the Gibbs sampler output due to the non-identifiability of component parameters. We review advanced methods for Bayesian analysis, including the Markov chain Monte Carlo (MCMC) reversible jump algorithm and model comparison based on joint measures of fit and complexity. We also present a Bayesian regression model based on a two-component mixture model, implemented using the Gibbs sampler algorithm and applied to a dataset of time measurement differences between two clocks. Our theoretical investigation highlights the importance of latent variables in implementing the Bayesian normal mixture model with two components. When applied to the dataset, our model effectively assigned probabilities to the two states of the phenomenon under study and identified two processes with identical slopes, intercepts, and variances. Our findings demonstrate the power of Bayesian mixture models in uncovering hidden structures within complex datasets. In general, our review and application provide insight into the challenges and potential solutions for Bayesian mixture modeling and highlight the usefulness of these methods in various fields.

In this paper, we proposed a classification method based on a nature-inspired algorithm, i.e., modified artificial bee colony (MABC). This method was applied to electrocardiogram (ECG) heartbeat classification. ECG data was obtained from MITBIH database. Eight different types of heartbeats (N, j, V, F, f, A, a, and R) were analyzed. For a better classification result, both time domain and frequency domain features were used. Feature selection was done by divergence analysis. MABC classification accuracy and heartbeat sensitivity values were compared with the results of other methods. Among other classifiers, k-nearest neighbor (KNN), Kohonen's self-organizing map (SOM), and ant colony optimization (ACO) were the best performing ones, and therefore their results are presented. The MABC classifier achieved 97.18 % accuracy on the analyzed dataset, as well as high sensitivity values for heartbeat types.

The expectation maximisation (EM) algorithm is an iterative maximum likelihood procedure often used for estimating the parameters of a mixture model. Theoretically, increases in the likelihood function are guaranteed as the algorithm iteratively improves upon previously derived parameter estimates. The algorithm is considered to converge when all parameter estimates become stable and no further improvements can be made to the likelihood value. However, to reduce computational time, it is often common practice for the algorithm to be stopped before complete convergence using heuristic approaches. In this paper, we consider various stopping criteria and evaluate their effect on fitting Gaussian mixture models (GMMs) to patient length of stay (LOS) data. Although the GMM can be successfully fitted to positively skewed data such as LOS, the fitting procedure often requires many iterations of the EM algorithm. To our knowledge, no previous study has evaluated the effect of different stopping criteria on fitting GMMs to skewed distributions. Hence, the aim of this paper is to evaluate the effect of various stopping criteria in order to select and justify their use within a patient spell classification methodology. Results illustrate that criteria based on the difference in the likelihood value and on the GMM parameters may not always be a good indicator for stopping the algorithm. In fact we show that the values of the difference in the variance parameters should be used instead, as these parameters are the last to stabilise. In addition, we also specify threshold values for the other stopping criteria.

As the result of legal construction, market trading mechanism, transaction body,investor psychology immature and other reasons, China stock market, as an emerging market is vulnerable to the influence of external factors and presents large fluctuations. In the framework of Bayesian theory of econometrics, this article for the first time introduced the binomial distribution to AR (p) model with structure change in its lag coefficients, considering the mean mutation and variance mutation, and comprehensively analyzed the mutations of the time trend, intercept,lag coefficient and variance. Based on Bayesian theory, this paper constructed likelihood function, and at the same time introduced the hierarchical prior distribution by using a priori information and sample information. Then we used Gibbs sampling and MH algorithm to complete the judgment of change point number and location. After introducing the method, this paper discussed the structure change point of the Shanghai index. The results showed that in May 1992 to April 2012, the Shanghai index had 14 structural breaks:4 mean-variance change points, 1 mean change point, 9 variance change points.

In this paper, we consider Bayesian estimation and prediction problem for the parameters and unobserved lifetimes of exponentiated Weibull distribution based on a progressively type II censored samples. By using an extended likelihood function and informative joint prior distributions, the joint posterior density for the parameters and unobserved lifetimes of units censored at the failure time is obtained. Since the closed form of Bayes estimators does not exist, we use Markov Chain Monte Carlo (MCMC) method such as Gibbs sampling and MetropolisHastings algorithm to generate the posterior conditional probabilities of interest. Monte Carlo simulations and real data analysis are conducted to observe the behaviour of the proposed method.