Marginal and simultaneous predictive classification using stratified graphical models

Computed tomography (CT) angiography (CTA) is a non-invasive imaging method used to detect arteries and examine various brain diseases. When CTA is performed for follow-up or postoperative evaluation, reproducibility of vessel delineation is required. A reproducible and stable contrast enhancement can be achieved by manipulating the factors affecting it. Previous studies have investigated several factors that alter the contrast enhancement of arteries. However, no reports establishing the effect of different operators on contrast enhancement exist. To assess the differences between inter-operator arterial contrast enhancement in cerebral CTA using Bayesian statistical modeling. Image data were obtained using a multistage sampling method from the cerebral CTA scans of patients who underwent the process between January 2015 and December 2018. Several Bayesian statistical models were developed, and the objective variable was the mean CT number of the bilateral internal carotid arteries after contrast enhancement. The explanatory variables were sex, age, fractional dose (FD), and the operator's information. The posterior distributions of the parameters were computed via Bayesian inference using the Markov chain Monte Carlo (MCMC) method, with the Hamiltonian Monte Carlo method employed as the algorithm. The posterior predictive distributions were computed using the posterior distributions of the parameters. Finally, the differences between inter-operator arterial contrast enhancement on the CT number in cerebral CTA were estimated. The posterior distributions showed that all parameters representing the difference between operators included zero at the 95% credible intervals (CIs). The maximum mean difference between inter-operator CT number in the posterior predictive distribution was only 12.59 Hounsfield units (HUs). The Bayesian statistical modeling results suggest that contrast enhancement of cerebral CTA examination between operator-to-operator differences in postcontrast CT number was small compared to those within-operator differences resulting from factors not considered in the model.

Infrared (IR) images are essential to improve the visibility of dark or camouflaged objects. Object recognition and segmentation based on a neural network using IR images provide more accuracy and insight than color visible images. But the bottleneck is the amount of relevant IR images for training. It is difficult to collect real-world IR images for special purposes, including space exploration, military and fire-fighting applications. To solve this problem, we created color visible and IR images using a Unity-based 3D game editor. These synthetically generated color visible and IR images were used to train cycle consistent adversarial networks (CycleGAN) to convert visible images to IR images. CycleGAN has the advantage that it does not require precisely matching visible and IR pairs for transformation training. In this study, we discovered that additional synthetic data can help improve CycleGAN performance. Neural network training using real data (N = 20) performed more accurate transformations than training using real (N = 10) and synthetic (N = 10) data combinations. The result indicates that the synthetic data cannot exceed the quality of the real data. Neural network training using real (N = 10) and synthetic (N = 100) data combinations showed almost the same performance as training using real data (N = 20). At least 10 times more synthetic data than real data is required to achieve the same performance. In summary, CycleGAN is used with synthetic data to improve the IR image conversion performance of visible images.

Graphical models are a useful tool with increasing diffusion. In the categorical variable framework, they provide important visual support to understand the relationships among the considered variables. Besides, particular chain graphical models are suitable to represent multivariate regression models. However, the associated parameterization, such as marginal log-linear models, is often difficult to interpret when the number of variables increases because of a large number of parameters involved. On the contrary, conditional and marginal independencies reduce the number of parameters needed to represent the joint probability distribution of the variables. In compliance with the parsimonious principle, it is worthwhile to consider also the so-called context-specific independencies, which are conditional independencies holding for particular values of the variables in the conditioning set. In this work, we propose a particular chain graphical model able to represent these context-specific independencies through labeled arcs. We provide also the Markov properties able to describe marginal, conditional, and context-specific independencies from this new chain graph. Finally, we show the results in an application to a real data set.

Bayesian estimation of the mixture of Burr Type-XII distributions using doubly censored data

Accurately modelled computer-generated data can be used in place of real-world signals for the design, test and validation of signal processing techniques in situations where real data is difficult to obtain. Bio-signal processing researchers interested in working with fNIRS data are restricted due to the lack of freely available fNIRS data and by the prohibitively expensive cost of fNIRS systems. We present a simplified mathematical description and associated MATLAB implementation of model-based synthetic fNIRS data which could be used by researchers to develop fNIRS signal processing techniques. The software, which is freely available, allows users to generate fNIRS data with control over a wide range of parameters and allows for fine-tuning of the synthetic data. We demonstrate how the model can be used to generate raw fNIRS data similar to recorded fNIRS signals. Signal processing steps were then applied to both the real and synthetic data. Visual comparisons between the temporal and spectral properties of the real and synthetic data show similarity. This paper demonstrates that our model for generating synthetic fNIRS data can replicate real fNIRS recordings.

Formulation of the Tree Approximation Problem as a Detection Problem and Relation between the AUC and Information Theory Divergences

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.

Error handling in multimodal voice-enabled interfaces of tour-guide robots using graphical models

Approximated sensitivity analysis in posterior predictive distribution

Bayesian Methods and Simulation-Based Computation for Contingency Tables

In this paper, the Bayesian analysis of scale parameter of inverse Gaussian distribution has been considered. The Bayes estimators along with corresponding risks have been derived under a class of priors and using various loss functions. The Bayesian credible intervals have been derived for the said parameter. In order to predict the future values of the variable the posterior predictive distributions have been constructed under different priors. A simulation study has been conducted for different parametric values to assess and compare the performance of different estimators.

The hazard and increased risk associated with slope failures in the natural habitat are attributed to uncertainty in soil parameters. These soil parameters, that is, cohesion, internal friction angle, and shear modulus, are estimated using the back-analysis method. The method incorporates machine learning algorithms such as particle swarm optimization and support vector machine. However, to capture the uncertainties in the soil parameters, probabilistic analysis is required. This study implements support vector machine for estimating soil parameters as the function of displacement in the soil. The Bayesian method is used to account for uncertainty in soil parameters. The Noto Hanto earthquake in 2007 and the consequent slope failure at Noto Yuryo Road, Japan, is considered as the case study for the proposed model. The finite-element method is used to simulate this slope failure. The soil parameters are treated as random variables to account for uncertainties in these parameters. The predicted displacement is comparable with the measured displacement in the field, which validates the application of the proposed model. The proposed method can efficiently predict experiment soil parameters by capturing uncertainty in soil parameters through a probabilistic approach.

We have discussed various statistical models and their implementation so far. However, the ways we used the MCMC samples from the posterior distributions and predictive distributions were only kept on very basic levels, such as computing the intervals and visualizations. In this chapter, we will introduce more advanced usages of the MCMC sample. They would be helpful in practice because it is very common to encounter the situation where we need to extract more information from the MCMC sample.

Chapter 5 - Fitting Models Using the Bayesian Modeling Software BUGS and JAGS

Non-overlapping classification of hyperspectral imagery with superpixel segmentation