MCMC

In multiple instance learning (MIL), a bag represents a sample that has a set of instances, each of which is described by a vector of explanatory variables, but the entire bag only has one label/response. Though many methods for MIL have been developed to date, few have paid attention to interpretability of models and results. The proposed Bayesian regression model stands on two levels of hierarchy, which transparently show how explanatory variables explain and instances contribute to bag responses. Moreover, two selection problems are simultaneously addressed; the instance selection to find out the instances in each bag responsible for the bag response, and the variable selection to search for the important covariates...

We present a fully Bayesian autoencoder model that treats both local latent variables and global decoder parameters in a Bayesian fashion. This approach allows for flexible priors and posterior approximations while keeping the inference costs low. To achieve this, we introduce an amortized MCMC approach by utilizing an implicit stochastic network to learn sampling from the posterior over local latent variables. Furthermore, we extend the model by incorporating a Sparse Gaussian Process prior over the latent space, allowing for a fully Bayesian treatment of inducing points and kernel hyperparameters and leading to improved scalability...

Tensor network (TN) has demonstrated remarkable efficacy in the compact representation of high-order data. In contrast to the TN methods with pre-determined structures, the recently introduced tensor network structure search (TNSS) methods automatically learn a compact TN structure from the data, gaining increasing attention. Nonetheless, TNSS requires time-consuming manual adjustments of the penalty parameters that control the model complexity to achieve better performance, especially in the presence of missing or noisy data...

The blue shark Prionace glauca plays a critical role as a predator in marine ecosystems but is threatened by by-catch. To obtain more precise biological data, a Bayesian approach was used, and 536 vertebrae samples collected during 1 year at the landing stage called "Playita Mía" Manta, Ecuador, were analysed. The objective was to estimate the age and growth parameters of the species. The size of the specimens varied between 116 and 310 cm in total length (TL). Using a Bayesian approach based on the Markov Chain Monte Carlo (MCMC) method, growth parameters were evaluated...

BACKGROUND: The analysis of dental caries has been a major focus of recent work on modeling dental defect data. While a dental caries focus is of major importance in dental research, the examination of developmental defects which could also contribute at an early stage of dental caries formation, is also of potential interest. This paper proposes a set of methods which address the appearance of different combinations of defects across different tooth regions. In our modeling we assess the linkages between tooth region development and both the type of defect and associations with etiological predictors of the defects which could be influential at different times during the tooth crown development...

Three-dimensional (3D) bioprinting of hydrogels with a wide spectrum of compositions has been widely investigated. Despite such efforts, a comprehensive understanding of the correlation among the process science, buildability, and biophysical properties of the hydrogels for a targeted clinical application has not been developed in the scientific community. In particular, the quantitative analysis across the entire developmental path for 3D extrusion bioprinting of such scaffolds is not widely reported. In the present work, we addressed this gap by using widely investigated biomaterials, such as gelatin methacryloyl (GelMA), as a model system...

Agronomy research traditionally relies on small, controlled trial plots, which may not accurately represent the complexities and variabilities found in larger, real-world settings. To address this gap, we introduce a Bayesian methodology for the analysis of yield monitor data, systematically collected across extensive agricultural landscapes during the 2020/21 and 2021/22 growing seasons. Utilizing advanced yield monitoring equipment, our method provides a detailed examination of the effects of green manure on wheat yields in a real-world context...

In the literature on deep neural networks, there is considerable interest in developing activation functions that can enhance neural network performance. In recent years, there has been renewed scientific interest in proposing activation functions that can be trained throughout the learning process, as they appear to improve network performance, especially by reducing overfitting. In this paper, we propose a trainable activation function whose parameters need to be estimated. A fully Bayesian model is developed to automatically estimate from the learning data both the model weights and activation function parameters...

Individual level models are a class of mechanistic models that are widely used to infer infectious disease transmission dynamics. These models incorporate individual level covariate information accounting for population heterogeneity and are generally fitted in a Bayesian Markov chain Monte Carlo (MCMC) framework. However, Bayesian MCMC methods of inference are computationally expensive for large data sets. This issue becomes more severe when applied to infectious disease data collected from spatially heterogeneous populations, as the number of covariates increases...

OBJECTIVES: Utility scores associated with preference-based health-related quality-of-life instruments such as the EQ-5D-3L are reported as point estimates. In this study, we develop methods for capturing the uncertainty associated with the valuation study of the UK EQ-5D-3L that arises from the variability inherent in the underlying data, which is tacitly ignored by point estimates. We derive a new tariff that properly accounts for this and assigns a specific closed-form distribution to the utility of each of the 243 health states of the EQ-5D-3L...

Metabolic reaction rates (fluxes) play a crucial role in comprehending cellular phenotypes and are essential in areas such as metabolic engineering, biotechnology, and biomedical research. The state-of-the-art technique for estimating fluxes is metabolic flux analysis using isotopic labelling (13 C-MFA), which uses a dataset-model combination to determine the fluxes. Bayesian statistical methods are gaining popularity in the field of life sciences, but the use of 13 C-MFA is still dominated by conventional best-fit approaches...

The increasing risk posed by space debris highlights the need for accurate localization techniques. Spaceborne single photon Lidar (SSPL) offers a promising solution, overcoming the limitations of traditional ground-based systems by providing expansive coverage and superior maneuverability without being hindered by weather, time, or geographic constraints. This study introduces a novel approach leveraging non-parametric Bayesian inference and the Dirichlet process mixture model (DPMM) to accurately determine the distance of space debris in low Earth orbit (LEO), where debris exhibits nonlinear, high dynamic motion characteristics...

We describe the design of optimized multilayer dielectric coatings for precision laser interferometry. By setting up an appropriate cost function and then using a global optimizer to find a minimum in the parameter space, we were able to realize coating designs that meet the design requirements for spectral reflectivity, thermal noise, absorption, and tolerances to coating fabrication errors. We also present application of a Markov-Chain Monte Carlo (MCMC) based parameter estimation algorithm that can infer thicknesses of dielectric layers in a coating, given a measurement of the spectral reflectivity...

Nadarajah and Haghighi distribution (NHD) inferences problem has been discussed under unified hybrid censoring scheme (UHCS) in the existence of competing risks model. Competing risks model is defined by time-to-failure under more than one cause of failure, which can be dependent or independent. This study focuses on discussing the case of failure partially observed causes of failure competing risks model. We obtain various inferences: we first obtain the MLE, in addition, we construct approximate confidence intervals (ACIs)...

The intensification of intervention activities against the fatal vector-borne disease gambiense human African trypanosomiasis (gHAT, sleeping sickness) in the last two decades has led to a large decline in the number of annually reported cases. However, while we move closer to achieving the ambitious target of elimination of transmission (EoT) to humans, pockets of infection remain, and it becomes increasingly important to quantitatively assess if different regions are on track for elimination, and where intervention efforts should be focused...

PURPOSE: This study aims to evaluate the effectiveness of mitigation strategies and analyze the impact of human behavior on the transmission of Mpox. The results can provide guidance to public health authorities on comprehensive prevention and control for the new Mpox virus strain in the Democratic Republic of Congo as of December 2023. METHODS: We develop a two-layer Watts-Strogatz network model. The basic reproduction number is calculated using the next-generation matrix approach...

Item response theory (IRT) has evolved as a standard psychometric approach in recent years, in particular for test construction based on dichotomous (i.e., true/false) items. Unfortunately, large samples are typically needed for item refinement in unidimensional models and even more so in the multidimensional case. However, Bayesian IRT approaches with hierarchical priors have recently been shown to be promising for estimating even complex models in small samples. Still, it may be challenging for applied researchers to set up such IRT models in general purpose or specialized statistical computer programs...

COVID-19 is a respiratory disease triggered by an RNA virus inclined to mutations. Since December 2020, variants of COVID-19 (especially Delta and Omicron) continuously appeared with different characteristics that influenced death and transmissibility emerged around the world. To address the novel dynamics of the disease, we propose and analyze a dynamical model of two strains, namely native and mutant, transmission dynamics with mutation and imperfect vaccination. It is also assumed that the recuperated individuals from the native strain can be infected with mutant strain through the direct contact with individual or contaminated surfaces or aerosols...

Genetic association studies for brain connectivity phenotypes have gained prominence due to advances in noninvasive imaging techniques and quantitative genetics. Brain connectivity traits, characterized by network configurations and unique biological structures, present distinct challenges compared to other quantitative phenotypes. Furthermore, the presence of sample relatedness in the most imaging genetics studies limits the feasibility of adopting existing network-response modeling. In this article, we fill this gap by proposing a Bayesian network-response mixed-effect model that considers a network-variate phenotype and incorporates population structures including pedigrees and unknown sample relatedness...

This paper examines the uncertainty of greenhouse gas (GHG) emissions during monorail construction. Firstly, a deterministic analysis is conducted. Subsequently, the obtained data are evaluated using the data quality indicator (DQI), and a Markov chain Monte Carlo (MCMC) simulation method is employed to assume different parameter distributions. The results of the deterministic calculation indicate that the calculated emissions per unit area of the station amount to 1.97 ton CO2 e/m2 , while the calculated emissions per unit section length reach 7...