Problem Of Point Estimation Research Articles

Neural Bayes Estimators for Irregular Spatial Data using Graph Neural Networks

Neural Bayes estimators are neural networks that approximate Bayes estimators in a fast and likelihood-free manner. Although they are appealing to use with spatial models, where estimation is often a computational bottleneck, neural Bayes estimators in spatial applications have, to date, been restricted to data collected over a regular grid. These estimators are also currently dependent on a prescribed set of spatial locations, which means that the neural network needs to be re-trained for new data sets; this renders them impractical in many applications and impedes their widespread adoption. In this work, we employ graph neural networks (GNNs) to tackle the important problem of parameter point estimation from data collected over arbitrary spatial locations. In addition to extending neural Bayes estimation to irregular spatial data, the use of GNNs leads to substantial computational benefits, since the estimator can be used with any configuration or number of locations and independent replicates, thus amortising the cost of training for a given spatial model. We also facilitate fast uncertainty quantification by training an accompanying neural Bayes estimator that approximates a set of marginal posterior quantiles. We illustrate our methodology on Gaussian and max-stable processes. Finally, we showcase our methodology on a data set of global sea-surface temperature, where we estimate the parameters of a Gaussian process model in 2161 spatial regions, each containing thousands of irregularly-spaced data points, in just a few minutes with a single graphics processing unit.

CamoDiffusion: Camouflaged Object Detection via Conditional Diffusion Models

Camouflaged Object Detection (COD) is a challenging task in computer vision due to the high similarity between camouflaged objects and their surroundings. Existing COD methods struggle with nuanced object boundaries and overconfident incorrect predictions. In response, we propose a new paradigm that treats COD as a conditional mask-generation task leveraging diffusion models. Our method, dubbed CamoDiffusion, employs the denoising process to progressively refine predictions while incorporating image conditions. Due to the stochastic sampling process of diffusion, our model is capable of sampling multiple possible predictions, avoiding the problem of overconfident point estimation. Moreover, we develop specialized network architecture, training, and sampling strategies, to enhance the model’s expressive power, refinement capabilities and suppress overconfident mis-segmentations, thus aptly tailoring the diffusion model to the demands of COD. Extensive experiments on three COD datasets attest to the superior performance of our model compared to existing state-of-the-art methods, particularly on the most challenging COD10K dataset, where our approach achieves 0.019 in terms of MAE. Codes and models are available at https://github.com/Rapisurazurite/CamoDiffusion.

Optimal estimation of reliability parameter for inverse Pareto distribution with application to insurance data

PurposeThe purpose of this paper is to develop optimal estimation procedures for the stress-strength reliability (SSR) parameter R = P(X > Y) of an inverse Pareto distribution (IPD).Design/methodology/approachWe estimate the SSR parameter R = P(X > Y) of the IPD under the minimum risk and bounded risk point estimation problems, where X and Y are strength and stress variables, respectively. The total loss function considered is a combination of estimation error (squared error) and cost, utilizing which we minimize the associated risk in order to estimate the reliability parameter. As no fixed-sample technique can be used to solve the proposed point estimation problems, we propose some “cost and time efficient” adaptive sampling techniques (two-stage and purely sequential sampling methods) to tackle them.FindingsWe state important results based on the proposed sampling methodologies. These include estimations of the expected sample size, standard deviation (SD) and mean square error (MSE) of the terminal estimator of reliability parameters. The theoretical values of reliability parameters and the associated sample size and risk functions are well supported by exhaustive simulation analyses. The applicability of our suggested methodology is further corroborated by a real dataset based on insurance claims.Originality/valueThis study will be useful for scenarios where various logistical concerns are involved in the reliability analysis. The methodologies proposed in this study can reduce the number of sampling operations substantially and save time and cost to a great extent.

Point estimation and related classification problems for several Lindley populations with application using COVID-19 data

ABSTRACT The problems of point estimation and classification under the assumption that the training data follow a Lindley distribution are considered. Bayes estimators are derived for the parameter of the Lindley distribution applying the Markov chain Monte Carlo (MCMC), and Tierney and Kadane's [Tierney and Kadane, Accurate approximations for posterior moments and marginal densities, J. Amer. Statist. Assoc. 81 (1986), pp. 82–86] methods. In the sequel, we prove that the Bayes estimators using Tierney and Kadane's approximation and Lindley's approximation both converge to the maximum likelihood estimator (MLE), as n → ∞ , where n is the sample size. The performances of all the proposed estimators are compared with some of the existing ones using bias and mean squared error (MSE), numerically. It has been noticed from our simulation study that the proposed estimators perform better than some of the existing ones. Applying these estimators, we construct several plug-in type classification rules and a rule that uses the likelihood accordance function. The performances of each of the rules are numerically evaluated using the expected probability of misclassification (EPM). Two real-life examples related to COVID-19 disease are considered for illustrative purposes.

Inference of improved adaptive progressively censored competing risks data for Weibull lifetime models

Recently, an improved adaptive Type-II progressive censoring scheme is proposed to ensure that the experimental time will not pass a pre-fixed time and ends the test after recording a pre-fixed number of failures. This paper studies the inference of the competing risks model from Weibull distribution under the improved adaptive progressive Type-II censoring. For this goal, we used the latent failure time model with Weibull lifetime distributions with common shape parameters. The point and interval estimation problems of parameters, reliability and hazard rate functions using the maximum likelihood and Bayesian estimation methods are considered. Moreover, making use of the asymptotic normality of classical estimators and delta method, approximate intervals are constructed via the observed Fisher information matrix. Following the assumption of independent gamma priors, the Bayes estimates of the scale parameters have closed expressions, but when the common shape parameter is unknown, the Bayes estimates cannot be formed explicitly. To solve this difficulty, we recommend using Markov chain Monte Carlo routine to compute the Bayes estimates and to construct credible intervals. A comprehensive Monte Carlo simulation is conducted to judge the behavior of the offered methods. Ultimately, analysis of electrodes data from the life-test of high-stress voltage endurance is provided to illustrate all proposed inferential procedures.

Parameters Estimation for the Unit log-log Distribution

In this paper, point estimation problem of two unknown parameters of the unit log-log distribution is examined. For point estimation, six methods of estimate such as maximum likelihood, maximum product spacing, Anderson-Darling, least squares, weighted least squares, and Cramer-von Mises are examined in detail. Extensive simulation experiments are conducted to compare the effectiveness of these estimators based on bias and mean squared errors. According to the simulation results, it is seen that all estimators performed well in terms of two criteria and take close values in case of large sample. Moreover, practical data applications are performed for all estimators. Results of the Kolmogorov-Smirnov statistics are reported for all estimators in practical applications.

Triple Sampling Inference Procedures for the Mean of the Normal Distribution When the Population Coefficient of Variation Is Known

This paper discusses the triple sampling inference procedures for the mean of a symmetric distribution—the normal distribution when the coefficient of variation is known. We use the Searls’ estimator as an initial estimate for the unknown population mean rather than the classical sample mean. In statistics literature, the normal distribution under investigation underlines almost all the natural phenomena with applications in many fields. First, we discuss the minimum risk point estimation problem under a squared error loss function with linear sampling cost. We obtained all asymptotic results that enhanced finding the second-order asymptotic risk and regret. Second, we construct a fixed-width confidence interval for the mean that satisfies at least a predetermined nominal value and find the second-order asymptotic coverage probability. Both estimation problems are performed under a unified optimal framework. The theoretical results reveal that the performance of the triple sampling procedure depends on the numerical value of the coefficient of variation—the smaller the coefficient of variation, the better the performance of the procedure.

Three-stage minimum risk point estimation with termination defined via Gini’s mean difference

In this article, we revisit the classic inference problem of minimum risk point estimation for an unknown normal mean when the variance also remains unknown. We propose an alternative three-stage sampling procedure with termination defined via Gini’s mean difference rather than the traditional sample standard deviation. A number of asymptotic properties are investigated both theoretically and empirically. An extensive set of simulations is conducted to demonstrate the remarkable performance of the new procedure. For practical purposes, we also include illustrations using real data sets on the number of days marigold seeds need to flower.

A possibilistic analogue to Bayes estimation with fuzzy data and its application in machine learning.

A Bayesian approach in a possibilistic context, when the available data for the underlying statistical model are fuzzy, is developed. The problem of point estimation with fuzzy data is studied in the possibilistic Bayesian approach introduced. For calculating the point estimation, we introduce a method without considering a loss function, and one considering a loss function. For the point estimation with a loss function, we first define a risk function based on a possibilistic posterior distribution, and then the unknown parameter is estimated based on such a risk function. Briefly, the present work extended the previous works in two directions: First the underlying model is assumed to be probabilistic rather than possibilistic, and second is that the problem of Bayes estimation is developed based on two cases of without and with considering loss function. Then, the applicability of the proposed approach to concept learning is investigated. Particularly, a naive possibility Bayes classifier is introduced and applied to some real-world concept learning problems.

A new formulation of minimum risk fixed-width confidence interval (MRFWCI) estimation problems for a normal mean with illustrations and simulations: Applications to air quality data

Research on classical fixed-width confidence interval (FWCI) estimation problems for a normal mean when the variance remains unknown have steadily moved along under a zero-one loss function. On the other hand, minimum risk point estimation (MRPE) problems have grown largely under a squared error loss function plus sampling cost. However, the FWCI problems customarily do not take into account any sampling cost in their formulations. This fundamental difference between the two treatments has led the literature on the FWCI and MRPE problems to grow in multiple directions in their own separate ways from one another. In this article, we introduce a new formulation combining both MRPE and FWCI methodologies with desired asymptotic first-order (Theorems 2.1–2.2) and asymptotic second-order characteristics (Theorem 2.3) under a single unified structure, allowing us to develop a genuine minimum risk fixed-width confidence interval (MRFWCI) estimation strategy. Fruitful ideas are proposed by incorporating illustrations from purely sequential and other multistage MRFWCI problems with an explicit presence of a cost function incurred due to sampling. We supplement the general theory and methodology by means of illustrations and analyses from simulated data along with applications to air quality data.

Asymptotic Efficiency of Point Estimators in Bayesian Predictive Inference

The point estimation problems that emerge in Bayesian predictive inference are concerned with random quantities which depend on both observable and non-observable variables. Intuition suggests splitting such problems into two phases, the former relying on estimation of the random parameter of the model, the latter concerning estimation of the original quantity from the distinguished element of the statistical model obtained by plug-in of the estimated parameter in the place of the random parameter. This paper discusses both phases within a decision theoretic framework. As a main result, a non-standard loss function on the space of parameters, given in terms of a Wasserstein distance, is proposed to carry out the first phase. Finally, the asymptotic efficiency of the entire procedure is discussed.

Using Collocated Vision and Tactile Sensors for Visual Servoing and Localization

Coordinating proximity and tactile imaging by collocating cameras with tactile sensors can 1) provide useful information before contact such as object pose estimates and visually servo a robot to a target with reduced occlusion and higher resolution compared to head-mounted or external depth cameras, 2) simplify the contact point and pose estimation problems and help tactile sensing avoid erroneous matches when a surface does not have significant texture or has repetitive texture with many possible matches, and 3) use tactile imaging to further refine contact point and object pose estimation. We demonstrate our results with objects that have more surface texture than most objects in standard manipulation datasets. We learn that optic flow needs to be integrated over a substantial amount of camera travel to be useful in predicting movement direction. Most importantly, we also learn that state of the art vision algorithms do not do a good job localizing tactile images on object models, unless a reasonable prior can be provided from collocated cameras.

Second-order asymptotics for comparing treatment means from purely sequential estimation strategies under possible outlying observations

We consider two independent populations, and with all four parameters assumed unknown, and In this paper, our goal is to revisit sequential minimum risk point estimation (MRPE) problems for the parameter say) under the squared error loss (SEL) plus linear cost of sampling in our quest for comparing two treatments. We explicitly consider two separate scenarios: (i) but is assumed unknown, and (ii) are unknown and unequal. In defining the relevant purely sequential stopping rules, customarily one incorporates multiples of sample standard deviations to set up requisite boundary crossing conditions. We set out to replace the multiples of sample standard deviations used in defining requisite boundary crossing conditions with Gini’s mean difference (GMD), mean absolute deviation (MAD), along with a number of combinations of the sample standard deviations, the GMD’s, and the MAD’s. We prove that the ensuing body of such newly developed purely sequential MRPE strategies have associated second-order regret expansions and that the GMD-based as well as the MAD-based strategies are better equipped to withstand occurrences of possible outlying observations. Our theory and methodologies are amply supported by both large-scale simulations and the illustrations with real data.

A comparative inference on reliability estimation for a multi-component stress-strength model under power Lomax distribution with applications

<abstract><p>In this article, reliability estimation for a system of multi-component stress-strength model is considered. Working under progressively censored samples is of great advantage over complete and usual censoring samples, therefore Type-II right progressive censored sample is selected. The lifetime of the components and the stress and strength components are following the power Lomax distribution. Consequently, the problem of point and interval estimation has been studied from different points of view. The maximum likelihood estimate and the maximum product spacing of reliability are evaluated. Also approximate confidence intervals are constructed using the Fisher information matrix. For the traditional methods, bootstrap confidence intervals are calculated. Bayesian estimation is obtained under the squared error and linear-exponential loss functions, where the numerical techniques such as Newton-Raphson and the Markov Chain Monte Carlo algorithm are implemented. For dependability, the largest posterior density credible intervals are generated. Simulations are used to compare the results of the proposed estimation methods, where it shows that the Bayesian estimation method of the reliability function is significantly better than the other methods. Finally, a real data of the water capacity of the Shasta reservoir is examined for illustration.</p></abstract>

MSAGNet: Multi-Stream Attribute-Guided Network for Occluded Pedestrian Detection

Pedestrian detection plays an indispensable role in human-centric applications. Although having enjoyed the merits of generic object detectors based on deep learning frameworks, pedestrian detection is still a persistent crucial task since the pedestrians often gather together and occlude each other. In this study, we propose a simple yet effective Multi-Stream Attribute-Guided Network (MSAGNet) to regard occluded pedestrian detection as a standard central point and height estimation problem. Specifically, we focus on searching for the central points of the pedestrians and predicting the scales and offsets of the corresponding pedestrians. Meanwhile, an adaptive weighting parameter, i.e., Intersection over the Visible part region of ground truth (IoV), is utilized to conduct accurate bounding box regression. Furthermore, a novel nonlinear Non-Maximum Suppression (NMS) is proposed to flexibly prune false positives and decrease the miss rate of adjacent overlapping pedestrians. Experimental results on Caltech-USA, CityPersons, CrowdHuman and WiderPerson pedestrian datasets show that the proposed MSAGNet can obtain significant performance boosts, while maintaining a reasonable run-time speed.

On robust learning in the canonical change point problem under heavy tailed errors in finite and growing dimensions

This paper presents a number of new findings about the canonical change point estimation problem. The first part studies the estimation of a change point on the real line in a simple stump model using the robust Huber estimating function which interpolates between the ℓ1 (absolute deviation) and ℓ2 (least squares) based criteria. While the ℓ2 criterion has been studied extensively, its robust counterparts and in particular, the ℓ1 minimization problem have not. We derive the limit distribution of the estimated change point under the Huber estimating function and compare it to that under the ℓ2 criterion. Theoretical and empirical studies indicate that it is more profitable to use the Huber estimating function (and in particular, the ℓ1 criterion) under heavy tailed errors as it leads to smaller asymptotic confidence intervals at the usual levels compared to the ℓ2 criterion. We also compare the ℓ1 and ℓ2 approaches in a parallel setting, where one has m independent single change point problems and the goal is to control the maximal deviation of the estimated change points from the true values, and establish rigorously that the ℓ1 estimation criterion provides a superior rate of convergence to the ℓ2, and that this relative advantage is driven by the heaviness of the tail of the error distribution. Finally, we derive minimax optimal rates for the change plane estimation problem in growing dimensions and demonstrate that Huber estimation attains the optimal rate while the ℓ2 scheme produces a rate sub-optimal estimator for heavy tailed errors. In the process of deriving our results, we establish a number of properties about the minimizers of compound Binomial and compound Poisson processes which are of independent interest.

Minimum risk point estimation of the size of a finite population under mark–recapture strategy

In this article, we address the problem of minimum risk point estimation for the size of a closed population using the weighted squared error loss function with a penalty of cost for each observation under the well-known mark–recapture strategy. In order to achieve minimum risk, a crucial point is to determine the number of items to obtain in the recapture phase. We first develop a purely sequential sampling scheme that will require much less sampling operations without losing accuracy of the estimation. Then, we develop a novel practical accelerated sequential method that will further accelerate the whole recapture process when sampling can be easily done in batches. The stopping rules of both purely sequential and accelerated sequential sampling schemes possess desirable asymptotic properties. All theoretical findings are double validated by extensive data analyses.

Uncertainty Inspired RGB-D Saliency Detection.

We propose the first stochastic framework to employ uncertainty for RGB-D saliency detection by learning from the data labeling process. Existing RGB-D saliency detection models treat this task as a point estimation problem by predicting a single saliency map following a deterministic learning pipeline. We argue that, however, the deterministic solution is relatively ill-posed. Inspired by the saliency data labeling process, we propose a generative architecture to achieve probabilistic RGB-D saliency detection which utilizes a latent variable to model the labeling variations. Our framework includes two main models: 1) a generator model, which maps the input image and latent variable to stochastic saliency prediction, and 2) an inference model, which gradually updates the latent variable by sampling it from the true or approximate posterior distribution. The generator model is an encoder-decoder saliency network. To infer the latent variable, we introduce two different solutions: i) a Conditional Variational Auto-encoder with an extra encoder to approximate the posterior distribution of the latent variable; and ii) an Alternating Back-Propagation technique, which directly samples the latent variable from the true posterior distribution. Qualitative and quantitative results on six challenging RGB-D benchmark datasets show our approach's superior performance in learning the distribution of saliency maps. The source code is publicly available via our project page: https://github.com/JingZhang617/UCNet.

Multistage Estimation of the Rayleigh Distribution Variance

In this paper we discuss the multistage sequential estimation of the variance of the Rayleigh distribution using the three-stage procedure that was presented by Hall (Ann. Stat. 9(6):1229–1238, 1981). Since the Rayleigh distribution variance is a linear function of the distribution scale parameter’s square, it suffices to estimate the Rayleigh distribution’s scale parameter’s square. We tackle two estimation problems: first, the minimum risk point estimation problem under a squared-error loss function plus linear sampling cost, and the second is a fixed-width confidence interval estimation, using a unified optimal stopping rule. Such an estimation cannot be performed using fixed-width classical procedures due to the non-existence of a fixed sample size that simultaneously achieves both estimation problems. We find all the asymptotic results that enhanced finding the three-stage regret as well as the three-stage fixed-width confidence interval for the desired parameter. The procedure attains asymptotic second-order efficiency and asymptotic consistency. A series of Monte Carlo simulations were conducted to study the procedure’s performance as the optimal sample size increases. We found that the simulation results agree with the asymptotic results.

A double-sequential sampling scheme

In this article, we have developed a new sequential sampling scheme, called the double-sequential sampling scheme, in which sampling is proceeded k-at-a-time () part of way, and then one-at-a-time sequentially. Requiring the same projected sample size as the Anscombe-Chow-Robbins (ACR) scheme, it further helps to save sampling operations. We include the statistical inference problems of fixed-width confidence interval estimation and minimum risk point estimation for a normal mean when the population variance also remains unknown as two illustrations. These are followed by extensive sets of simulations and real-data illustrations using horticulture data, showing great practical applicability of this new sequential sampling scheme.