The idea of the inheritance of biological processes, such as the developmental process or the life cycle of an organism, has been discussed in the biology literature, but formal mathematical descriptions and plausible data analysis frameworks are lacking. We introduce an extension of the nested Dirichlet Process (nDP) to a multiscale model to aid in understanding the mechanisms by which biological processes are inherited, remain stable, and are modified across generations. To address these issues, we introduce Nested Inheritance Dynamics Algorithm (NIDA). At its primary level, NIDA encompasses all processes unfolding within an individual organism's lifespan. The secondary level delineates the dynamics through which these processes evolve or remain stable over time. This framework allows for the specification of a physical system model at either scale, thus promoting seamless integration with established models of development and heredity.

Normalizing flow is a generative modeling approach with efficient sampling. However, Flow-based models suffer two issues: 1) If the target distribution is manifold, due to the unmatch between the dimensions of the latent target distribution and the data distribution, flow-based models might perform badly. 2) Discrete data might make flow-based models collapse into a degenerate mixture of point masses. To sidestep such two issues, we propose PaddingFlow, a novel dequantization method, which improves normalizing flows with padding-dimensional noise. To implement PaddingFlow, only the dimension of normalizing flows needs to be modified. Thus, our method is easy to implement and computationally cheap. Moreover, the padding-dimensional noise is only added to the padding dimension, which means PaddingFlow can dequantize without changing data distributions. Implementing existing dequantization methods needs to change data distributions, which might degrade performance. We validate our method on the main benchmarks of unconditional density estimation, including five tabular datasets and four image datasets for Variational Autoencoder (VAE) models, and the Inverse Kinematics (IK) experiments which are conditional density estimation. The results show that PaddingFlow can perform better in all experiments in this paper, which means PaddingFlow is widely suitable for various tasks. The code is available at: https://github.com/AdamQLMeng/PaddingFlow.

As a key part of modern online platforms, online decision-making plays a crucial role in a variety of settings, particularly related to the Internet. Two landmark examples that have been widely studied are dynamic pricing and online reviews. Online review systems constitute powerful platforms for users to get informed about the product and for the firm to understand how a given market is receiving the product. The study of these systems has been vast for the last two decades [6, 10], and more recently, modeling simple like/dislike reviews as bandits problems have become standard [1, 2, 3, 13, 16, 18]. Dynamic pricing, on the other hand, is an active area of research in economics, computer science, and operations research [12, 14], and has become a common practice in several industries such as transportation and retail. There has been a growing interest in combining the two areas as a way to design more effective pricing mechanisms that gather information from current reviews to update prices and make the product more attractive [5, 11, 17]. In particular, [5] considers social learning with non-Bayesian agents in a market with like & dislike reviews, and the resulting pricing decision of a monopolist.

Graduate School of Information Science and Technology Osaka University Osaka, Japan thanasutives@ai.sanken.osaka-u.ac.jp Ken-ichi Fukui SANKEN (The Institute of Scientific and Industrial Research) Osaka University Osaka, Japan fukui@ai.sanken.osaka-u.ac.jp The uncertainty-penalized information criterion (UBIC) has been proposed as a new model-selection criterion for data-driven partial differential equation (PDE) discovery. In this paper, we show that using the UBIC is equivalent to employing the conventional BIC to a set of overparameterized models derived from the potential regression models of different complexity measures. The result indicates that the asymptotic property of the UBIC and BIC holds indifferently.

In engineering, accurately modeling nonlinear dynamic systems from data contaminated by noise is both essential and complex. Established Sequential Monte Carlo (SMC) methods, used for the Bayesian identification of these systems, facilitate the quantification of uncertainty in the parameter identification process. A significant challenge in this context is the numerical integration of continuous-time ordinary differential equations (ODEs), crucial for aligning theoretical models with discretely sampled data. This integration introduces additional numerical uncertainty, a factor that is often over looked. To address this issue, the field of probabilistic numerics combines numerical methods, such as numerical integration, with probabilistic modeling to offer a more comprehensive analysis of total uncertainty. By retaining the accuracy of classical deterministic methods, these probabilistic approaches offer a deeper understanding of the uncertainty inherent in the inference process. This paper demonstrates the application of a probabilistic numerical method for solving ODEs in the joint parameter-state identification of nonlinear dynamic systems. The presented approach efficiently identifies latent states and system parameters from noisy measurements. Simultaneously incorporating probabilistic solutions to the ODE in the identification challenge. The methodology's primary advantage lies in its capability to produce posterior distributions over system parameters, thereby representing the inherent uncertainties in both the data and the identification process.

Surrogate models provide a quick-to-evaluate approximation to complex computational models and are essential for multi-query problems like design optimisation. The inputs of current computational models are usually high-dimensional and uncertain. We consider Bayesian inference for constructing statistical surrogates with input uncertainties and intrinsic dimensionality reduction. The surrogates are trained by fitting to data from prevalent deterministic computational models. The assumed prior probability density of the surrogate is a Gaussian process. We determine the respective posterior probability density and parameters of the posited statistical model using variational Bayes. The non-Gaussian posterior is approximated by a simpler trial density with free variational parameters and the discrepancy between them is measured using the Kullback-Leibler (KL) divergence. We employ the stochastic gradient method to compute the variational parameters and other statistical model parameters by minimising the KL divergence. We demonstrate the accuracy and versatility of the proposed reduced dimension variational Gaussian process (RDVGP) surrogate on illustrative and robust structural optimisation problems with cost functions depending on a weighted sum of the mean and standard deviation of model outputs.

In this paper, we explore the optimization of metal recycling with a focus on real-time differentiation between alloys of copper and aluminium. Spectral data, obtained through Prompt Gamma Neutron Activation Analysis (PGNAA), is utilized for classification. The study compares data from two detectors, cerium bromide (CeBr$_{3}$) and high purity germanium (HPGe), considering their energy resolution and sensitivity. We test various data generation, preprocessing, and classification methods, with Maximum Likelihood Classifier (MLC) and Conditional Variational Autoencoder (CVAE) yielding the best results. The study also highlights the impact of different detector types on classification accuracy, with CeBr$_{3}$ excelling in short measurement times and HPGe performing better in longer durations. The findings suggest the importance of selecting the appropriate detector and methodology based on specific application requirements.

Each decision-making tool should be tested and validated in real case studies to be practical and fit to global problems. The application of multi-criteria decision-making methods (MCDM) is currently a trend to rank alternatives. In the literature, there are several multi-criteria decision-making methods according to their classification. During our experimentation on the Combined Compromise Solution (CoCoSo) method, we encountered its limits for real cases. The authors examined the applicability of the CoCoFISo method (improved version of combined compromise solution), by a real case study in a university campus and compared the obtained results to other MCDMs such as Preference Ranking Organisation Method for Enrichment Evaluations (PROMETHEE), Weighted Sum Method (WSM) and Technique for Order Preference by Similarity to the Ideal Solution (TOPSIS). Our research finding indicates that CoCoSo is an applied method that has been developed to solve complex multi variable assessment problems, while CoCoFISo can improve the shortages observed in CoCoSo and deliver stable outcomes compared to other developed tools. The findings imply that application of CoCoFISo is suggested to decision makers, experts and researchers while they are facing practical challenges and sensitive questions regarding the utilization of a reliable decision-making method. Unlike many prior studies, the current version of CoCoSo is unique, original and is presented for the first time. Its performance was approved using several strategies and examinations.

Graphical models, including Graph Neural Networks (GNNs) and Probabilistic Graphical Models (PGMs), have demonstrated their exceptional capabilities across numerous fields. These models necessitate effective uncertainty quantification to ensure reliable decision-making amid the challenges posed by model training discrepancies and unpredictable testing scenarios. This survey examines recent works that address uncertainty quantification within the model architectures, training, and inference of GNNs and PGMs. We aim to provide an overview of the current landscape of uncertainty in graphical models by organizing the recent methods into uncertainty representation and handling. By summarizing state-of-the-art methods, this survey seeks to deepen the understanding of uncertainty quantification in graphical models, thereby increasing their effectiveness and safety in critical applications.

In this study, we address the challenge of constructing continuous three-dimensional (3D) models that accurately represent uncertain surfaces, derived from noisy and incomplete LiDAR scanning data. Building upon our prior work, which utilized the Gaussian Process (GP) and Gaussian Mixture Model (GMM) for structured building models, we introduce a more generalized approach tailored for complex surfaces in urban scenes, where GMM Regression and GP with derivative observations are applied. A Hierarchical GMM (HGMM) is employed to optimize the number of GMM components and speed up the GMM training. With the prior map obtained from HGMM, GP inference is followed for the refinement of the final map. Our approach models the implicit surface of the geo-object and enables the inference of the regions that are not completely covered by measurements. The integration of GMM and GP yields well-calibrated uncertainty estimates alongside the surface model, enhancing both accuracy and reliability. The proposed method is evaluated on real data collected by a mobile mapping system. Compared to the performance in mapping accuracy and uncertainty quantification of other methods, such as Gaussian Process Implicit Surface map (GPIS) and log-Gaussian Process Implicit Surface map (Log-GPIS), the proposed method achieves lower RMSEs, higher log-likelihood values and lower computational costs for the evaluated datasets.