Prior Information Research Articles

Bayesian prediction of the stock price rate in the Iraq stock market based on the symmetric heavy tails regression model

In this paper, we investigate the estimation of generalized modified Bessel regression model by using the Bayesian techniques under the assumption that the scale parameter and shape parameters are known. We use the informative priors for estimating of model. Then we derive a prediction distribution of the future response variable ▁Y_f by using informative priors for predictive future. Our work applied our results to real data which represent the Iraqi market for securities having taken monthly data for the services sector and of Baghdad sector of Iraq for public transport for the year 2018, as the stock variable rate response variables affecting it are closing price variable, the stock turnover variable. Through the study shows that the explanatory variables are the most important influence on the stock price rate variables through variance inflation factor, the estimated model was appropriate for the data studied.

Spatial Prior-Guided Bi-Directional Cross-Attention Transformers for Tooth Instance Segmentation.

Tooth instance segmentation of dental panoramic X-ray images represents a task of significant clinical importance. Teeth demonstrate symmetry within the upper and lower jawbones and are arranged in a specific order. However, previous studies frequently overlook this crucial spatial prior information, resulting in misidentifications of tooth categories for adjacent or similarly shaped teeth. In this paper, we propose SPGTNet, a spatial prior-guided transformer method, designed to both the extracted tooth positional features from CNNs and the long-range contextual information from vision transformers for dental panoramic X-ray image segmentation. Initially, a center-based spatial prior perception module is employed to identify each tooth's centroid, thereby enhancing the spatial prior information for the CNN sequence features. Subsequently, a bi-directional cross-attention module is designed to facilitate the interaction between the spatial prior information of the CNN sequence features and the long-distance contextual features of the vision transformer sequence features. Finally, an instance identification head is employed to derive the tooth segmentation results. Extensive experiments on three public benchmark datasets have demonstrated the effectiveness and superiority of our proposed method in comparison with other state-of-the-art approaches. The proposed method demonstrates the capability to accurately identify and analyze tooth structures, thereby providing crucial information for dental diagnosis, treatment planning, and research.

Dynamic simultaneous localization and mapping based on object tracking in occluded environment

Abstract In practical applications, many robots equipped with embedded devices have limited computing capabilities. These limitations often hinder the performance of existing dynamic SLAM algorithms, especially when faced with occlusions or processor constraints. Such challenges lead to subpar positioning accuracy and efficiency. This paper introduces a novel lightweight dynamic SLAM algorithm designed primarily to mitigate the interference caused by moving object occlusions. Our proposed approach combines a deep learning object detection algorithm with a Kalman filter. This combination offers prior information about dynamic objects for each SLAM algorithm frame. Leveraging geometric techniques like RANSAC and the epipolar constraint, our method filters out dynamic feature points, focuses on static feature points for pose determination, and enhances the SLAM algorithm’s robustness in dynamic environments. We conducted experimental validations on the TUM public dataset, which demonstrated that our approach elevates positioning accuracy by approximately 54% and boosts the running speed by 75.47% in dynamic scenes.

Probabilistic Prediction of Floating Offshore Wind Turbine Platform Motions via Uncertainty Quantification and Information Integration

The accurate prediction of short-term platform motions in a real environment is crucial for the safe design, operation, and maintenance of floating offshore wind turbines (FOWTs). Numerical simulations of motions are typically associated with high uncertainties due to abstracted theoretical models, empirical parameters, initial environment parameters, etc. Therefore, it is necessary to integrate other sources of information associated with less uncertainty, e.g., monitoring data, for accurate predictions. In this paper, we propose a probabilistic prediction based on the Bayesian approach that logically integrates motion monitoring data with simulated motion predictions of FOWTs, considering uncertainties in the environment model, structural properties, motion prediction method, monitoring data, etc. The approach consists of constructing a prior probability density function (PDF) of a random variable (which characterizes the largest value of the initial motion response) via numerical simulations and a likelihood function based on platform motion monitoring data and deriving a posterior PDF of the random variable by Bayesian updating. Then, posterior distributions of short-term extreme motion responses are derived using the posterior PDF of the random variable, representing lower uncertainty and improved accuracy. A Metropolis–Hastings algorithm is adopted to obtain PDFs of complex probability distributions. The effectiveness of the approach is demonstrated on a real FOWT platform in Scotland. The proposed probabilistic prediction approach results in posterior distributions of short-term extreme platform motions associated with less uncertainty and higher accuracy, which is attributed to integrating prior knowledge with monitoring data.

THE UNINFORMATIVE PRIOR OF JEFFREYS’ DISTRIBUTION IN BAYESIAN GEOGRAPHICALLY WEIGHTED REGRESSION

When using the Bayesian method for estimating parameters in a geographically weighted regression model, the choice of the prior distribution directly impacts the posterior distribution. The distribution known as the Jeffreys prior is an uninformative type of prior distribution and is invariant to reparameterization. In cases where information about the parameter is not available, the Jeffreys' prior is utilized. The data was fitted with an uninformative Jeffreys' prior distribution, which yielded a posterior distribution that was utilized for estimating parameters. This study aims to derive the prior and marginal posterior distributions of the Jeffreys' and in Bayesian geographically weighted regression (BGWR). The marginal posterior distributions of and can be obtained by integrating the other parameters of a common posterior distribution. Based on the results and discussion, the Jeffreys prior in BGWR with the likelihood function is . On the other hand, the marginal posterior distribution of follows a normal multivariate distribution, that is, , while the marginal posterior distribution of follows an inverse gamma distribution, that is, . As further research, it is necessary to follow up on several limitations of the results of this research, namely numerical simulations and application to a particular case that related to the results of the analytical studies that we have carried out.

Synergizing habits and goals with variational Bayes

Behaving efficiently and flexibly is crucial for biological and artificial embodied agents. Behavior is generally classified into two types: habitual (fast but inflexible), and goal-directed (flexible but slow). While these two types of behaviors are typically considered to be managed by two distinct systems in the brain, recent studies have revealed a more sophisticated interplay between them. We introduce a theoretical framework using variational Bayesian theory, incorporating a Bayesian intention variable. Habitual behavior depends on the prior distribution of intention, computed from sensory context without goal-specification. In contrast, goal-directed behavior relies on the goal-conditioned posterior distribution of intention, inferred through variational free energy minimization. Assuming that an agent behaves using a synergized intention, our simulations in vision-based sensorimotor tasks explain the key properties of their interaction as observed in experiments. Our work suggests a fresh perspective on the neural mechanisms of habits and goals, shedding light on future research in decision making.

Maximum information measurement for qubit states

We determine the optimal measurement that maximizes the average information gain about the state of a qubit system. The qubit is prepared in one of two known states with known prior probabilities. To treat the problem analytically we employ the formalism developed for the maximum confidence quantum state discrimination strategy and obtain the POVM which optimizes the information gain for the entire parameter space of the system. We show that the optimal measurement coincides exactly with the minimum-error quantum measurement only for two pure states, or when the two states have the same Bloch radius or they are on the same diagonal of the Bloch disk.

Combining prior and post‐release data while accounting for dispersal to improve predictions for reintroduction populations

AbstractAttempts to reintroduce species to managed areas may be compromised by dispersal into the surrounding landscape. Therefore, decisions regarding the selection and ongoing management of reintroduction areas require predicting dispersal as well as the survival and reproduction rates of the species to be reintroduced. Dispersal can potentially be measured directly by tracking animals, but this is often impractical. However, dispersal can also be inferred from re‐sighting surveys done within reintroduction areas if such data are available from multiple areas with varying connectivity to the surrounding landscape, allowing apparent survival and recruitment to be modelled as a function of connectivity metrics. Here, we show how data from 10 previous reintroductions of a New Zealand passerine, the toutouwai (Petroica longipes), were used to predict population dynamics at a predator‐controlled reintroduction area with high connectivity, and predictions then updated using post‐release data. Bayesian hierarchical modelling of the previous data produced prior distributions for productivity, adult survival and apparent juvenile survival rates that accounted for random variation among areas as well as rat density and connectivity. The modelling of apparent juvenile survival as a function of connectivity allowed it to be partitioned into estimates of survival and fidelity. Bayesian updating based on post‐release data produced posterior distributions for parameters that were consistent with the priors but much more precise. The prior data also allowed the recruitment rate estimated in the new area to be partitioned into separate estimates for productivity, juvenile survival and juvenile fidelity. Consequently, it was possible to not only estimate population growth under current management, but also predict the consequences of reducing the scale or intensity of predator control, facilitating adaptive management. The updated model could then be used to predict population growth as a function of the connectivity and predator control regime at proposed reintroduction areas while accounting for random variation among areas.

Bayesian earthquake forecasting approach based on the epidemic type aftershock sequence model

The epidemic type aftershock sequence (ETAS) model is used as a baseline model both for earthquake clustering and earthquake prediction. In most forecast experiments, the ETAS parameters are estimated based on a short and local catalog, therefore the model parameter optimization carried out by means of a maximum likelihood estimation may be not as robust as expected. We use Bayesian forecast techniques to solve this problem, where non-informative flat prior distributions of the parameters is adopted to perform forecast experiments on 3 mainshocks occurred in Southern California. A Metropolis–Hastings algorithm is employed to sample the model parameters and earthquake events. We also show, through forecast experiments, how the Bayesian inference allows to obtain a probabilistic forecast, differently from one obtained via MLE.Graphical

Stick–Slip Suppression in Drill String Systems Using a Novel Adaptive Sliding Mode Control Approach

A novel control technique is presented in this paper, which is based on a first-order adaptive sliding mode that ensures convergence in a finite time without any prior information on the upper limits of the parametric uncertainties and/or external disturbances. Based on an exponent reaching law, this controller uses two dynamically adaptive control gains. Once the sliding mode is reached, the dynamic gains decrease in order to loosen the system’s constraints, which guarantees minimal control effort. The proof of convergence was demonstrated according to Lyapunov’s criterion. The proposed algorithm was applied to a drill string system to evaluate its performance because such systems present variable operating conditions caused by, for example, the type of rock. The effectiveness of the proposed controller was evaluated by conducting a comparative study that involved comparing it against a commonly used sliding mode controller, as well as other recent adaptive sliding mode control techniques. The different mathematical performance measures included energy consumption. The proposed algorithm had the best performance measures with the lowest energy consumption and it was able to significantly improve the functioning of the drill string system. The results indicated that the proposed controller had 20% less chattering than the classic SM controller. Finally, the proposed controller was the most robust to uncertainties in system parameters and external disturbances, thus demonstrating the auto-adjustable features of the controller.

High‐dimensional sparse classification using exponential weighting with empirical hinge loss

In this study, we address the problem of high‐dimensional binary classification. Our proposed solution involves employing an aggregation technique founded on exponential weights and empirical hinge loss. Through the employment of a suitable sparsity‐inducing prior distribution, we demonstrate that our method yields favorable theoretical results on prediction error. The efficiency of our procedure is achieved through the utilization of Langevin Monte Carlo, a gradient‐based sampling approach. To illustrate the effectiveness of our approach, we conduct comparisons with the logistic Lasso on simulated data and a real dataset. Our method frequently demonstrates superior performance compared to the logistic Lasso.

The R2D2 Prior for Generalized Linear Mixed Models

In Bayesian analysis, the selection of a prior distribution is typically done by considering each parameter in the model. While this can be convenient, in many scenarios it may be desirable to place a prior on a summary measure of the model instead. In this work, we propose a prior on the model fit, as measured by a Bayesian coefficient of determination ( R 2 ) , which then induces a prior on the individual parameters. We achieve this by placing a beta prior on R 2 and then deriving the induced prior on the global variance parameter for generalized linear mixed models. We derive closed-form expressions in many scenarios and present several approximation strategies when an analytic form is not possible and/or to allow for easier computation. In these situations, we suggest approximating the prior by using a generalized beta prime distribution and provide a simple default prior construction scheme. This approach is quite flexible and can be easily implemented in standard Bayesian software. Lastly, we demonstrate the performance of the method on simulated and real-world data, where the method particularly shines in high-dimensional settings, as well as modeling random effects.

Bayesian benchmark dose risk assessment with mixed‐factor quantal data

AbstractBenchmark analysis is a general risk estimation strategy for identifying the benchmark dose (BMD) past which the risk of exhibiting an adverse environmental response exceeds a fixed, target value of benchmark response. Estimation of BMD and of its lower confidence limit (BMDL) is well understood for the case of an adverse response to a single stimulus. In many environmental settings, however, one or more additional, secondary, qualitative factor(s) may collude to affect the adverse outcome, such that the risk changes with differential levels of the secondary factor. Bayesian methods for estimation of the BMD and BMDL have grown in popularity, and a large variety of candidate dose–response models is available for applying these methods. This article applies Bayesian strategies to a mixed‐factor setting with a secondary qualitative factor possessing two levels to derive two‐factor Bayesian BMDs and BMDLs. We present reparameterized dose–response models that allow for explicit use of prior information on the target parameter of interest, the BMD. We also enhance our Bayesian estimation technique for BMD analysis by applying Bayesian model averaging to produce the BMDs and BMDLs, overcoming associated questions of model adequacy when multimodel uncertainty is present. An example from environmental carcinogenicity testing illustrates the calculations.

A Procedure for Revising Data-Based Priors in a Group

A group of individuals is interested in predicting the outcome of a current problem. Each individual has access to private data that are used to form a prior probability over possible outcomes. While individuals may be reluctant or unable to disclose their private data, they are willing to publish their priors. We characterize a procedure for revising the individuals’ prior probabilities based on the published priors of others and discuss its implications regarding the formation of a common prior in the group, both in the short and long run. This paper was accepted by Manel Baucells, behavioral economics and decision analysis. Funding: G. Gayer gratefully acknowledges support from ISF [Grant 1443/20].

Bayesian pairwise meta-analysis of time-to-event outcomes in the presence of non-proportional hazards: A simulation study of flexible parametric, piecewise exponential and fractional polynomial models.

Traditionally, meta-analysis of time-to-event outcomes reports a single pooled hazard ratio assuming proportional hazards (PH). For health technology assessment evaluations, hazard ratios are frequently extrapolated across a lifetime horizon. However, when treatment effects vary over time, an assumption of PH is not always valid. The Royston-Parmar (RP), piecewise exponential (PE), and fractional polynomial (FP) models can accommodate non-PH and provide plausible extrapolations of survival curves beyond observed data. Simulation study to assess and compare the performance of RP, PE, and FP models in a Bayesian framework estimating restricted mean survival time difference (RMSTD) at 50 years from a pairwise meta-analysis with evidence of non-PH. Individual patient data were generated from a mixture Weibull distribution. Twelve scenarios were considered varying the amount of follow-up data, number of trials in a meta-analysis, non-PH interaction coefficient, and prior distributions. Performance was assessed through bias and mean squared error. Models were applied to a metastatic breast cancer example. FP models performed best when the non-PH interaction coefficient was 0.2. RP models performed best in scenarios with complete follow-up data. PE models performed well on average across all scenarios. In the metastatic breast cancer example, RMSTD at 50-years ranged from -14.6 to 8.48 months. Synthesis of time-to-event outcomes and estimation of RMSTD in the presence of non-PH can be challenging and computationally intensive. Different approaches make different assumptions regarding extrapolation and sensitivity analyses varying key assumptions are essential to check the robustness of conclusions to different assumptions for the underlying survival function.

Single-photon lidar depth imaging based on sparsity adaptive matching pursuit method

Photon counting lidar has the ability to detect weak echo photons. However, in imaging applications, a small number of echo signals obtained in a very short acquisition time cannot get an accurate image estimation through the photon arrival time distribution histogram. Therefore, high-precision and fast imaging of an object using a small amount of weak echo photon signals is urgent to be solved. In this work, a sparse adaptive matching pursuit (SAMP) algorithm is proposed to process the echo photons without prior information to obtain the effective photon interval, which improves the reconstruction quality and imaging speed. By constructing a non-coaxial scanning imaging system to detect the face model, it has been experimentally proven that the proposed algorithm can achieve depth and reflectance image estimation under the condition of low power and low acquisition time of 4µs per pixel on average, and the mean absolute error (MAE) value is reduced by about 10 times compared to conventional reconstruction algorithm.

Data-driven estimation of the algebraic Riccati equation for the discrete-time inverse linear quadratic regulator problem

In this paper, we propose a method for estimating the algebraic Riccati equation (ARE) with respect to an unknown discrete-time system from the system state and input observation. The inverse optimal control (IOC) problem asks, “What objective function is optimized by a given control system?” The inverse linear quadratic regulator (ILQR) problem is an IOC problem that assumes a linear system and quadratic objective function. The ILQR problem can be solved by solving a linear matrix inequality that contains the ARE. However, the system model is required to obtain the ARE, and it is often unknown in fields in which the IOC problem occurs, for example, biological system analysis. Our method directly estimates the ARE from the observation data without identifying the system. This feature enables us to economize the observation data using prior information about the objective function. We provide a data condition that is sufficient for our method to estimate the ARE. We conducted a numerical experiment to demonstrate that our method can estimate the ARE with less data than system identification if the prior information is sufficient.

How pre-trained large model can help, when SAM meets image restoration

In the process of image capture, degradation is inevitable due to noise, motion, down-sampling and so on. Therefore, image restoration is essential to improve the quality of images to enhance their visual effects and benefit downstream tasks. Adding prior knowledge can help the model better understand the image content and restoration requirements, thus improving the quality and efficiency. Semantic-level prior information can be generated by pre-trained large-scale models, such as segment anything models (SAM), and applied to a large number of downstream tasks. SAM has demonstrated powerful robustness and stability in restoration tasks, such as denoising, super-resolution, low-light enhancement, etc. Meanwhile, as an interactive component, SAM brings more control for users during the repair process. In this paper, we focus on the importance of SAM as prior information and systematically summarize a series of recent works combining SAM prior and low-level image restoration from three perspectives. In addition, we have summarized some potential problems and future directions of SAM.

A capture-recapture modeling framework emphasizing expert opinion in disease surveillance.

In disease surveillance, capture-recapture methods are commonly used to estimate the number of diseased cases in a defined target population. Since the number of cases never identified by any surveillance system cannot be observed, estimation of the case count typically requires at least one crucial assumption about the dependency between surveillance systems. However, such assumptions are generally unverifiable based on the observed data alone. In this paper, we advocate a modeling framework hinging on the choice of a key population-level parameter that reflects dependencies among surveillance streams. With the key dependency parameter as the focus, the proposed method offers the benefits of (a) incorporating expert opinion in the spirit of prior information to guide estimation; (b) providing accessible bias corrections, and (c) leveraging an adapted credible interval approach to facilitate inference. We apply the proposed framework to two real human immunodeficiency virus surveillance datasets exhibiting three-stream and four-stream capture-recapture-based case count estimation. Our approach enables estimation of the number of human immunodeficiency virus positive cases for both examples, under realistic assumptions that are under the investigator's control and can be readily interpreted. The proposed framework also permits principled uncertainty analyses through which a user can acknowledge their level of confidence in assumptions made about the key non-identifiable dependency parameter.

The Impact of Skill Level on the Integration of Information and Post-Error Adjustment during Action Anticipation in Basketball.

The present study examined the impact of skill level on the integration of contextual prior information and kinematic information alongside post-error adjustment during action anticipation in basketball. Twenty-three collegiate basketball players and twenty-three control participants engaged in anticipating as quickly and accurately as possible the outcomes of free throws, utilizing video clips depicting basketball players' actions, both with and without contextual prior information. Anticipatory performance and the difference in anticipatory performance following errors and correct responses were analyzed based on skill level and the congruency of contextual prior information (none, congruent, and incongruent). The findings revealed that the congruency of contextual prior information significantly affects action anticipation, with skill level moderating this effect. Moreover, skill level influenced the congruency effect on accuracy discrepancies between post-error and post-correct trials during action anticipation, with controls showing greater sensitivity to previous trial performance compared to experts. These results provide further evidence for the notion that individuals employ Bayesian reliability-based strategies to integrate different information sources and underscore the role of skill level in adjusting anticipatory judgments following errors during action anticipation. These insights contribute to a deeper understanding of the cognitive and behavioral mechanisms that differentiate skill levels in action anticipation, potentially guiding the development of targeted training interventions.