Adversarial EM for variational deep learning: Application to semi-supervised image quality enhancement in low-dose PET and low-dose CT.

In positron emission tomography (PET) and X-ray computed tomography (CT), reducing radiation dose can cause significant degradation in image quality. For image quality enhancement in low-dose PET and CT, we propose a novel theoretical adversarial and variational deep neural network (DNN) framework relying on expectation maximization (EM) based learning, termed adversarial EM (AdvEM). AdvEM proposes an encoder-decoder architecture with a multiscale latent space, and generalized-Gaussian models enabling datum-specific robust statistical modeling in latent space and image space. The model robustness is further enhanced by including adversarial learning in the training protocol. Unlike typical variational-DNN learning, AdvEM proposes latent-space sampling from the posterior distribution, and uses a Metropolis-Hastings scheme. Unlike existing schemes for PET or CT image enhancement which train using pairs of low-dose images with their corresponding normal-dose versions, we propose a semi-supervised AdvEM (ssAdvEM) framework that enables learning using a small number of normal-dose images. AdvEM and ssAdvEM enable per-pixel uncertainty estimates for their outputs. Empirical analyses on real-world PET and CT data involving many baselines, out-of-distribution data, and ablation studies show the benefits of the proposed framework.

A Semiparametric Bayesian Approach to Heterogeneous Spatial Autoregressive Models.

Many semiparametric spatial autoregressive (SSAR) models have been used to analyze spatial data in a variety of applications; however, it is a common phenomenon that heteroscedasticity often occurs in spatial data analysis. Therefore, when considering SSAR models in this paper, it is allowed that the variance parameters of the models can depend on the explanatory variable, and these are called heterogeneous semiparametric spatial autoregressive models. In order to estimate the model parameters, a Bayesian estimation method is proposed for heterogeneous SSAR models based on B-spline approximations of the nonparametric function. Then, we develop an efficient Markov chain Monte Carlo sampling algorithm on the basis of the Gibbs sampler and Metropolis-Hastings algorithm that can be used to generate posterior samples from posterior distributions and perform posterior inference. Finally, some simulation studies and real data analysis of Boston housing data have demonstrated the excellent performance of the proposed Bayesian method.

Estimation for two Gompertz populations under a balanced joint progressive Type-II censoring scheme.

Comparative lifetime experiments are remarkable when the study is to ascertain the relative merits of two competing products regarding the duration of their service life. This paper considers the comparative lifetime experiments of two Gompertz populations under a balanced joint progressive Type-II censoring scheme. The lifetime distributions of the units are assumed to follow the Gompertz distribution with a common shape but different scale parameters. The maximum likelihood estimates of the unknown parameters are derived. The existence of the maximum likelihood estimates is proved. Expectation-maximization and stochastic expectation-maximization algorithms are provided to calculate the estimates. The bootstrap-p, bootstrap-t, and approximate confidence intervals are established. To obtain the Bayesian estimates, it is assumed that the prior of scale parameters is a Beta-Gamma distribution and the prior of the common shape parameter is an independent Gamma distribution. Under squared error loss and LINEX loss functions, the Metropolis-Hastings algorithm is provided to compute the Bayes estimates and the credible intervals. Further, the statistical inferences with order restriction are studied when it is known a priori that the expectation of the lifespan of one population is shorter than that of the other population. A wide range of simulation experiments is conducted to evaluate the performance of the proposed methods. Finally, the lifetimes of white organic light-emitting diodes and the breaking strengths of jute fiber of gauge lengths are analyzed to illustrate the practical application of the proposed model and methods.

Bayesian mixture modelling with ranked set samples.

We consider the Bayesian estimation of the parameters of a finite mixture model from independent order statistics arising from imperfect ranked set sampling designs. As a cost-effective method, ranked set sampling enables us to incorporate easily attainable characteristics, as ranking information, into data collection and Bayesian estimation. To handle the special structure of the ranked set samples, we develop a Bayesian estimation approach exploiting the Expectation-Maximization (EM) algorithm in estimating the ranking parameters and Metropolis within Gibbs Sampling to estimate the parameters of the underlying mixture model. Our findings show that the proposed RSS-based Bayesian estimation method outperforms the commonly used Bayesian counterpart using simple random sampling. The developed method is finally applied to estimate the bone disorder status of women aged 50 and older.

Bayesian hidden mark interaction model for detecting spatially variable genes in imaging-based spatially resolved transcriptomics data.

Recent technology breakthroughs in spatially resolved transcriptomics (SRT) have enabled the comprehensive molecular characterization of cells whilst preserving their spatial and gene expression contexts. One of the fundamental questions in analyzing SRT data is the identification of spatially variable genes whose expressions display spatially correlated patterns. Existing approaches are built upon either the Gaussian process-based model, which relies on ad hoc kernels, or the energy-based Ising model, which requires gene expression to be measured on a lattice grid. To overcome these potential limitations, we developed a generalized energy-based framework to model gene expression measured from imaging-based SRT platforms, accommodating the irregular spatial distribution of measured cells. Our Bayesian model applies a zero-inflated negative binomial mixture model to dichotomize the raw count data, reducing noise. Additionally, we incorporate a geostatistical mark interaction model with a generalized energy function, where the interaction parameter is used to identify the spatial pattern. Auxiliary variable MCMC algorithms were employed to sample from the posterior distribution with an intractable normalizing constant. We demonstrated the strength of our method on both simulated and real data. Our simulation study showed that our method captured various spatial patterns with high accuracy; moreover, analysis of a seqFISH dataset and a STARmap dataset established that our proposed method is able to identify genes with novel and strong spatial patterns.

Uncertainty Computation at Finite Distance in Nonlinear Mixed Effects Models-a New Method Based on Metropolis-Hastings Algorithm.

The standard errors (SE) of the maximum likelihood estimates (MLE) of the population parameter vector in nonlinear mixed effect models (NLMEM) are usually estimated using the inverse of the Fisher information matrix (FIM). However, at a finite distance, i.e. far from the asymptotic, the FIM can underestimate the SE of NLMEM parameters. Alternatively, the standard deviation of the posterior distribution, obtained in Stan via the Hamiltonian Monte Carlo algorithm, has been shown to be a proxy for the SE, since, under some regularity conditions on the prior, the limiting distributions of the MLE and of the maximum a posterior estimator in a Bayesian framework are equivalent. In this work, we develop a similar method using the Metropolis-Hastings (MH) algorithm in parallel to the stochastic approximation expectation maximisation (SAEM) algorithm, implemented in the saemix R package. We assess this method on different simulation scenarios and data from a real case study, comparing it to other SE computation methods. The simulation study shows that our method improves the results obtained with frequentist methods at finite distance. However, it performed poorly in a scenario with the high variability and correlations observed in the real case study, stressing the need for calibration.

Estimation and prediction for Burr type III distribution based on unified progressive hybrid censoring scheme.

The present communication develops the tools for estimation and prediction of the Burr-III distribution under unified progressive hybrid censoring scheme. The maximum likelihood estimates of model parameters are obtained. It is shown that the maximum likelihood estimates exist uniquely. Expectation maximization and stochastic expectation maximization methods are employed to compute the point estimates of unknown parameters. Based on the asymptotic distribution of the maximum likelihood estimators, approximate confidence intervals are proposed. In addition, the bootstrap confidence intervals are constructed. Furthermore, the Bayes estimates are derived with respect to squared error and LINEX loss functions. To compute the approximate Bayes estimates, Metropolis-Hastings algorithm is adopted. The highest posterior density credible intervals are obtained. Further, maximum a posteriori estimates of the model parameters are computed. The Bayesian predictive point, as well as interval estimates, are proposed. A Monte Carlo simulation study is employed in order to evaluate the performance of the proposed statistical procedures. Finally, two real data sets are considered and analysed to illustrate the methodologies established in this paper.

Emergent communication of multimodal deep generative models based on Metropolis-Hastings naming game.

Deep generative models (DGM) are increasingly employed in emergent communication systems. However, their application in multimodal data contexts is limited. This study proposes a novel model that combines multimodal DGM with the Metropolis-Hastings (MH) naming game, enabling two agents to focus jointly on a shared subject and develop common vocabularies. The model proves that it can handle multimodal data, even in cases of missing modalities. Integrating the MH naming game with multimodal variational autoencoders (VAE) allows agents to form perceptual categories and exchange signs within multimodal contexts. Moreover, fine-tuning the weight ratio to favor a modality that the model could learn and categorize more readily improved communication. Our evaluation of three multimodal approaches - mixture-of-experts (MoE), product-of-experts (PoE), and mixture-of-product-of-experts (MoPoE)-suggests an impact on the creation of latent spaces, the internal representations of agents. Our results from experiments with the MNIST + SVHN and Multimodal165 datasets indicate that combining the Gaussian mixture model (GMM), PoE multimodal VAE, and MH naming game substantially improved information sharing, knowledge formation, and data reconstruction.

Bayesian Hidden Mark Interaction Model for Detecting Spatially Variable Genes in Imaging-Based Spatially Resolved Transcriptomics Data.

Recent technology breakthroughs in spatially resolved transcriptomics (SRT) have enabled the comprehensive molecular characterization of cells whilst preserving their spatial and gene expression contexts. One of the fundamental questions in analyzing SRT data is the identification of spatially variable genes whose expressions display spatially correlated patterns. Existing approaches are built upon either the Gaussian process-based model, which relies on ad hoc kernels, or the energy-based Ising model, which requires gene expression to be measured on a lattice grid. To overcome these potential limitations, we developed a generalized energy-based framework to model gene expression measured from imaging-based SRT platforms, accommodating the irregular spatial distribution of measured cells. Our Bayesian model applies a zero-inflated negative binomial mixture model to dichotomize the raw count data, reducing noise. Additionally, we incorporate a geostatistical mark interaction model with a generalized energy function, where the interaction parameter is used to identify the spatial pattern. Auxiliary variable MCMC algorithms were employed to sample from the posterior distribution with an intractable normalizing constant. We demonstrated the strength of our method on both simulated and real data. Our simulation study showed that our method captured various spatial patterns with high accuracy; moreover, analysis of a seqFISH dataset and a STARmap dataset established that our proposed method is able to identify genes with novel and strong spatial patterns.

Random Change-Point Non-linear Mixed Effects Model for left-censored longitudinal data: An application to HIV surveillance.

A change-point model is essential in longitudinal data to infer an individual specific time to an event that induces a change of trend. However, in general, change points are not known for population-based data. We present an unknown change-point model that fits the linear and non-linear mixed effects for pre- and post-change points. We address the left-censored observations. Through stochastic approximation expectation maximization (SAEM) with the Metropolis Hasting sampler, we fit a random change-point non-linear mixed effects model. We apply our method on the longitudinal viral load (VL) data reported to the HIV surveillance registry from New York City.

Comparação entre modelos para predição do nitrogênio mineralizado: uma abordagem bayesiana / Comparison of the models for prediction of the mineralized nitrogen: a bayesian approach

Neste trabalho, desenvolveu-se uma abordagem bayesiana para predizer as quantidades de nitrogênio mineralizados por intermédio de modelos não lineares. Os modelos não lineares considerados para avaliar a dinâmica da mineralização do nitrogênio e para ilustrar o procedimento bayesiano foram: modelo de Cabrera, Marion, Stanford e Smith. A comparação dos modelos foi feita por meio do Fator de Bayes (FB) e do Critério de Informação Bayesiano (BIC). A inferência sobre os parâmetros realizou-se por intermédio do Amostrador de Gibbs e do Metropolis Hastings. O modelo de Cabrera (1993) foi o que proporcionou melhor qualidade de ajuste ao conjunto de dados de mineralização de nitrogênio, sendo seguido pelo modelo de Stanford & Smith (1972) e, por último, o de Marion et al. (1981).

In this work one developed a Bayesian approach to predict the amount of mineralized nitrogen through nonlinear models. The nonlinear models considered to evaluate the mineralization of organic nitrogen and to illustrate the Bayesian procedure were: models of Cabrera, Marion, Stanford and Smith. The comparison of the models was promoted through the Bayes Factor (FB) and Bayes Information Criterion (BIC). Inference on the parameters was carried out through the Gibbs Sampling and Metropolis Hastings. The model that provided better adjustment quality to the group of data was Cabrera's model (1993), followed by the model of Stanford & Smith (1972) and the last one by Marion et al. (1981).