Likelihood Research Articles

An improved uncertainty autoencoder with blurred measurements

AbstractCompressed sensing (CS) techniques have enabled efficient acquisition and recovery of sparse high‐dimensional data via succinct low‐dimensional projections, which usually consist of an encoder and a decoder. Unlike conventional CS techniques with the encoding–decoding architecture, the uncertainty autoencoder (UAE) can sample from the learned input data distribution without an explicit likelihood function and hence avoids potential uninformative latent representations. However, existing works on UAE mainly focus on the encoders and maximize the lower bound of the mutual information between input and measurements, rather than the decoders, which brings the shortcoming that the two may not cope well. In this work, the authors propose a novel training scheme for UAE that blurs the measurements to learn the encoder and decoder simultaneously. Experimental results show that the proposed method improves the reconstruction performances when applied to UAE.

Likelihood function modelling of radar targets under high‐speed observation

AbstractThe likelihood ratio function of the target plays a crucial role in applications such as tracking before detection (TBD). In the framework of random finite sets, the performance of radar target TBD based on particle filters is limited by the performance of the likelihood ratio function. Traditional likelihood ratio functions only consider the likelihood ratio between the target and background noise, thus requiring a high signal‐to‐noise (SNR) ratio for the input signal. In scenarios where the observation time interval is extremely short, there exists a strong autocorrelation between the complex amplitudes of the radar target at different time instants. Based on this characteristic, an autoregressive model is utilized to establish the autocorrelation of the target complex amplitudes and update the target's complex amplitudes using a Kalman filter. The likelihood ratio is derived from the model and it is compared with the traditional likelihood ratio under pulse‐Doppler radar. This comparison aims to demonstrate the effectiveness of the proposed likelihood ratio. Due to the fact that this likelihood ratio only requires the extraction of the complex amplitudes of the target scattering centre, without the need to extract the energy around the scattering centre like traditional point spread function methods, the algorithm complexity is greatly reduced, enabling real‐time operation of the proposed method.

Sequential Bayesian Planning for Accelerated Degradation Tests Considering Sensor Degradation

Most classical accelerated degradation test (ADT) planning models implicitly overlook the errors when measuring the degradation levels of the test units. However, the sensor measurement errors are inevitable and the magnitude of the errors may have a trend to increase over time due to sensor degradation. As a consequence improperly overlooking the sensor degradation in ADT planning could result in a test plan with unsatisfactory performance. This article addresses this issue by proposing a sequential ADT planning model that factors in sensor degradation. The system degradation level is periodically measured, based on which we dynamically adjust the stress level during ADT. We adopt a Bayesian framework that periodically updates the posterior distribution of model parameters considering the sensor degradation. An approximate Bayesian computation algorithm is developed to circumvent the difficulty of directly evaluating the complicated likelihood function in our problem. Numerical studies on a gas turbine reveal that our sequential model outperforms several traditional ADT designs that overlook the sensor degradation.

Reliability Analysis of Kavya Manoharan Kumaraswamy Distribution under Generalized Progressive Hybrid Data

Generalized progressive hybrid censoring approaches have been developed to reduce test time and cost. This paper investigates the difficulties associated with estimating the unobserved model parameters and the reliability time functions of the Kavya Manoharan Kumaraswamy (KMKu) distribution based on generalized type-II progressive hybrid censoring using classical and Bayesian estimation techniques. The frequentist estimators’ normal approximations are also used to construct the appropriate estimated confidence intervals for the unknown parameter model. Under symmetrical squared error loss, independent gamma conjugate priors are used to produce the Bayesian estimators. The Bayesian estimators and associated highest posterior density intervals cannot be derived analytically since the joint likelihood function is provided in a complicated form. However, they may be evaluated using Monte Carlo Markov chain (MCMC) techniques. Out of all the censoring choices, the best one is selected using four optimality criteria.

Reliability Estimation of Inverse Weibull Distribution Based on Intuitionistic Fuzzy Lifetime Data

As a commonly used model in reliability analysis, the inverse Weibull distribution (IWD) is widely applied in various scientific fields. This paper considers the reliability estimation of the IWD based on intuitionistic fuzzy lifetime data. Firstly, the related concepts of the fuzzy set theory are reviewed, and the concepts of the intuitionistic fuzzy conditional density, intuitionistic fuzzy likelihood function, and intuitionistic fuzzy conditional expectation are obtained by extension. In classical estimations, the maximum likelihood estimators of parameters and reliability are derived. Due to the nonlinearity, the EM algorithm is used to obtain the maximum likelihood estimates. In the Bayesian estimation, the gamma prior is selected, and the Bayesian estimation of the parameters and reliability is conducted under the symmetric entropy and the scale square error loss function, respectively. Since the integrals are complicated, the Lindley approximation is used to approximate the Bayesian estimates. Then, the performance of these estimators is evaluated by the Monte Carlo simulation. The simulation results show that the Bayesian estimation is more suitable than the maximum likelihood estimation for the reliability estimation. Finally, a set of real data is used to prove the effectiveness of these proposed methods. Through these methods, the reliability of the intuitive fuzzy life data is accurately estimated, which provides an important reference for the reliability analysis in the scientific field.

Guided wave-based characterisation of cracks in pipes utilising approximate Bayesian computation

This paper proposed a probabilistic framework of damage characterisation to detect and identify early-state cracks in pipe-like structures using ultrasonic guided waves. The crack location, crack sizes (e.g., depth and width of the crack), and Young's modulus are considered as unknown parameters in the model updating using a Bayesian approach, by which their values and the associated uncertainties are quantified. The proposed framework is developed based on approximate Bayesian computation (ABC) by subset simulation, which is a likelihood-free Bayesian approach. This algorithm estimates the posterior distributions of unknown parameters by directly accessing the similarity between the measured signals from experiments and the simulated guided wave (GW) signals from the numerical model. In this case, the evaluation of likelihood functions can be smartly circumvented during Bayesian inference. A time-domain spectral finite element (SFE) method with a cracked finite element model is employed to model the pipes to enhance the computational efficiency of the simulation and model updating. Numerical and experimental case studies are carried out to evaluate the performance of the proposed likelihood-free approach. Numerical results show the accuracy and robustness of the proposed approach in identifying unknown parameters under different scenarios. The associated uncertainties of each parameter are also quantified by analysing the statistical properties of the sample set, such as mean and coefficient of variation (COV) values. Experimental results show that the proposed method can accurately identify the unknown parameters, which further verifies the accuracy and practicability of the probabilistic damage characterisation framework.

Predicting maize yield in Northeast China by a hybrid approach combining biophysical modelling and machine learning

ContextChina produces more than 20 % of maize grain in the world, and Northeast China (NEC) accounts for ∼30 % of the nation's total maize production. Previous studies have used either climate data, satellite data, or crop growth model (CGM) to predict or forecast maize yield. However, maize is highly susceptible to the effect of extreme climate events (such as drought, heat) in NEC, and there is a lack of studies to predict/forecast maize yield by integrating climate data, satellite data, extreme climate events, and CGM-simulated data. ObjectiveWe aim to develop a hybrid approach with machine learning to blend different sources of data (climate data, satellite data, extreme climate events) and process-based modelling results to improve predictive accuracy of maize yield in NEC. MethodsUsing maize data from 44 sites during the period of 2000–2013 in NEC, we firstly optimized Agricultural Production System sIMulator (APSIM) using Differential Evolution Adaptive Metropolis combined with Gaussian likelihood function and Bayesian multiplication method. Next, we divided the growing season into five phases, and selected variables of different phases using exploratory data analysis and Random Forest. Then, we developed a hybrid model using Random Forest by blending of multiple sources of data and APSIM simulations to predict maize yield from the start to the end of the growing season, and quantified the relative contribution of predictors. Results and conclusionsA hybrid model developed with random forest by combining climate data, NDVI, extreme climate events and APSIM simulations can achieve high performance for predicting yield toward the end of the growing season. The accuracy of in-season yield prediction showed a linear increase with MAPE/KGE changing from 19 %/0.05 to 13 %/0.53 from start to end of the growing season. Yield forecasts are acceptable with RMSE/MAE of 1.20/1.01 Mg ha−1 (16 %/13 % of the observed mean yield) approximately one-month prior to harvest. The most important predictor that affect yield forecast was APSIM-simulated biomass or yield, and the most important extreme climate event was drought during early grain-filling stage. SignificanceWith the increasing availability of crop-related data, we expect that the in-season forecasting capacity of the proposed methodology could be further improved, and the methodology can be extended to other crops and other regions for yield forecast.

Analysis of the impact of ADDIE education model based on logistic regression model on teaching contemporary cultural and creative product design

Abstract Exploring the influence of the ADDIE education model on teaching cultural and creative product design to promote the improvement of the quality of teaching cultural and creative product design. Starting from the ADDIE education model, this paper analyzes the five components of the model and the specific functions of each component. The logistic regression algorithm that constitutes the analysis module of the ADDIE education model is introduced, and a sparse prior factor is introduced to optimize the logistic regression algorithm; then, a sparse logistic regression algorithm is constructed to solve the likelihood function of the weight vector. Finally, the ADDIE education model is used to analyze the indicators of cultural and creative product design teaching in two aspects: the teaching objectives and teaching principles of cultural and creative product design. From the teaching objectives, the influence of cognitive, skill, and emotional objectives accounted for 47.11%, 44.41% and 51.26%, respectively. From the teaching principles, the percentages of uniqueness, practicality, and attractiveness are 51.5%, 43.7%, and 40.3%, respectively. Based on the ADDIE education model can affect the emotional goals and uniqueness in the teaching of cultural and creative product design, and it is necessary to focus on the emotional teaching of product design as well as diversified and differentiated teaching in design teaching in order to enhance better the learners’ interest degree in cultural and creative product design.

Profile Likelihood for Hierarchical Models Using Data Doubling.

In scientific problems, an appropriate statistical model often involves a large number of canonical parameters. Often times, the quantities of scientific interest are real-valued functions of these canonical parameters. Statistical inference for a specified function of the canonical parameters can be carried out via the Bayesian approach by simply using the posterior distribution of the specified function of the parameter of interest. Frequentist inference is usually based on the profile likelihood for the parameter of interest. When the likelihood function is analytical, computing the profile likelihood is simply a constrained optimization problem with many numerical algorithms available. However, for hierarchical models, computing the likelihood function and hence the profile likelihood function is difficult because of the high-dimensional integration involved. We describe a simple computational method to compute profile likelihood for any specified function of the parameters of a general hierarchical model using data doubling. We provide a mathematical proof for the validity of the method under regularity conditions that assure that the distribution of the maximum likelihood estimator of the canonical parameters is non-singular, multivariate, and Gaussian.

Information criteria for matrix exponential spatial specifications

In this study, we suggest using information criteria for nested and non-nested model selection problems for the matrix exponential spatial specifications (MESS) under both homoskedasticity and heteroskedasticity. To this end, we consider the deviance information criterion, the Akaike information criterion and the Bayesian information criterion in a Bayesian setting. In the heteroskedastic case, we assume that the error terms have a scale mixture of normal distributions, where the scale mixture variables are latent variables that lead to different distributions. We demonstrate how the integrated likelihood function can be obtained analytically by integrating out the scale mixture variables from the complete-data likelihood function, and how this integrated likelihood function can be used to formulate the information criteria. We investigate the finite sample performance of these criteria in selecting the true model in a simulation study. The results show that these criteria perform satisfactorily and can be useful for selecting the correct model in specification search exercises. Finally, we apply the proposed information criteria to a spatially augmented growth model and a carbon emission model to show their usefulness for both nested and non-nested model selection problems.

A new reduced contagious zero-inflated model: An application to count data

In this paper, a reduced one-parameter contagious distribution was developed from the joint distribution of three-parameter gamma and Poisson distributions, on which Lakshmi’s three-parameter gamma distribution is based to model a count data. The distribution properties and some common descriptive measures relating to this contagious distribution are derived. The behavior of the probability mass function with changes in parameters was also studied. The parameter estimation by the maximum likelihood and moment-generating function methods is discussed. A simulation study was carried out with the proposed model to check for consistency and bias. The new model show consistency as the sample size increases. The model was applied to a real-life dataset and was seen to be more flexible in capturing excess zero, under, and over-dispersion in count data and proved to be a useful alternative to some existing zero-inflated models.

CoLFI: Cosmological Likelihood-free Inference with Neural Density Estimators

In previous works, we proposed to estimate cosmological parameters with an artificial neural network (ANN) and a mixture density network (MDN). In this work, we propose an improved method called a mixture neural network (MNN) to achieve parameter estimation by combining ANN and MDN, which can overcome shortcomings of the ANN and MDN methods. Besides, we propose sampling parameters in a hyperellipsoid for the generation of the training set, which makes the parameter estimation more efficient. A high-fidelity posterior distribution can be obtained using forward simulation samples. In addition, we develop a code named CoLFI for parameter estimation, which incorporates the advantages of MNN, ANN, and MDN, and is suitable for any parameter estimation of complicated models in a wide range of scientific fields. CoLFI provides a more efficient way for parameter estimation, especially for cases where the likelihood function is intractable or cosmological models are complex and resource-consuming. It can learn the conditional probability density p( θ ∣ d ) using samples generated by models, and the posterior distribution p( θ ∣ d 0) can be obtained for a given observational data d 0. We tested the MNN using power spectra of the cosmic microwave background and Type Ia supernovae and obtained almost the same result as the Markov Chain Monte Carlo method. The numerical difference only exists at the level of . The method can be extended to higher-dimensional data.

Estimation of the time of exposure based on interval and censored data using the ε-accelerated EM algorithm.

Accurately estimating the timing of pathogen exposure plays a crucial role in outbreak control for emerging infectious diseases, including the source identification, contact tracing, and vaccine research and development. However, since surveillance activities often collect data retrospectively after symptoms have appeared, obtaining accurate data on the timing of disease onset is difficult in practice and can involve "coarse" observations, such as interval or censored data. To address this challenge, we propose a novel likelihood function, tailored to coarsely observed data in rapid outbreak surveillance, along with an optimization method based on an -accelerated EM algorithm for faster convergence to find maximum likelihood estimates (MLEs). The covariance matrix of MLEs is also discussed using a nonparametric bootstrap approach. In terms of bias and mean-squared error, the performance of our proposed method is evaluated through extensive numerical experiments, as well as its application to a series of epidemiological surveillance focused on cases of mass food poisoning. The experiments show that our method exhibits less bias than conventional methods, providing greater efficiency across all scenarios.

Learning and reasoning with graph data.

Reasoning about graphs, and learning from graph data is a field of artificial intelligence that has recently received much attention in the machine learning areas of graph representation learning and graph neural networks. Graphs are also the underlying structures of interest in a wide range of more traditional fields ranging from logic-oriented knowledge representation and reasoning to graph kernels and statistical relational learning. In this review we outline a broad map and inventory of the field of learning and reasoning with graphs that spans the spectrum from reasoning in the form of logical deduction to learning node embeddings. To obtain a unified perspective on such a diverse landscape we introduce a simple and general semantic concept of a model that covers logic knowledge bases, graph neural networks, kernel support vector machines, and many other types of frameworks. Still at a high semantic level, we survey common strategies for model specification using probabilistic factorization and standard feature construction techniques. Based on this semantic foundation we introduce a taxonomy of reasoning tasks that casts problems ranging from transductive link prediction to asymptotic analysis of random graph models as queries of different complexities for a given model. Similarly, we express learning in different frameworks and settings in terms of a common statistical maximum likelihood principle. Overall, this review aims to provide a coherent conceptual framework that provides a basis for further theoretical analyses of respective strengths and limitations of different approaches to handling graph data, and that facilitates combination and integration of different modeling paradigms.

Approximate likelihood and pseudo-likelihood inference in meta-analysis of diagnostic accuracy studies accounting for disease prevalence and study design.

Bivariate random-effects models represent a recommended approach for meta-analysis of diagnostic test accuracy, jointly modeling study-specific sensitivity and specificity. As the severity of the disease status can vary across studies, a proper analysis should account for the dependence of the accuracy measures on the disease prevalence. To this aim, trivariate generalized linear mixed-effects models have been proposed in the literature, although computational difficulties strongly limit their applicability. In addition, the attention has been mainly paid to cohort studies, where the study-specific disease prevalence can be estimated from, while information from case-control studies is often neglected. To overcome such limits, this article introduces a trivariate approximate normal model, which accounts for disease prevalence along with accuracy measures in cohort studies and sensitivity and specificity in case-control studies. The model represents an extension of the bivariate normal mixed-effects model originally developed for meta-analysis not accounting for disease prevalence, under an approximate normal within-study distribution for the logit of estimated sensitivity and specificity. The components of the approximate within-study covariance matrix are derived and the likelihood function is obtained in closed-form. The approximate likelihood approach is compared to that based on the exact within-study distribution and to its modifications following a pseudo-likelihood strategy aimed at reducing the computational effort. The comparison is based on simulation studies in a variety of scenarios, and illustrated in a meta-analysis about the accuracy of a test to diagnose fungal infection and a meta-analysis of a noninvasive test to detect colorectal cancer.

Research on brand operation strategy of integrating traditional culture into the modern tourism industry based on big data analysis

Abstract The rich traditional culture is an inexhaustible treasure trove of resources for the brand operation of the modern tourism industry. This paper proposes an improved method for the LDA model of text big data mining, optimizing the topic representation of LDA by introducing the Topic2Vec model, optimizing the probability calculation of generated words by combining the original Dilley distribution and Bernoulli distribution and optimizing the assignment of topic words in the Gibbs adoption process of LDA model with the help of likelihood function. Then, the big data of tourism brand design text, promotion, and cultural products are mined and analyzed based on the improved LFV-LDA model. In the design of tourism brands focusing on traditional culture, the frequency of the keyword “pattern” was the highest, accounting for 8.20%. In brand promotion, the most distributed channel from 2017 to 2021 was a live broadcast, and the growth rate in 2020 and 2021 reached 22.71% and 36.29%. Regarding traditional cultural and creative products, tourism cultural and creative products have maintained a high growth momentum from 2012 to 2021, with an average annual growth rate of 154.25%. Based on the analysis of big data, it can guide the operation of tourism industry brands in all aspects, such as design, promotion, and landing, and give full play to the value connotation of traditional culture.

Testing symmetry of model errors for non linear multiplicative distortion measurement error models

To study the symmetry and asymmetry of the model error under multiplicative distortion measurement errors setting, we propose a correlation coefficient-based measure between the distribution function and the root of density function. The unknown distribution function and density function are estimated from four kinds of residuals: the conditional mean calibration-based residuals, the conditional absolute mean calibration-based residuals, the conditional variance calibration-based residuals, and the conditional absolute logarithmic calibration-based residuals. We study the asymptotic results of the estimators of correlation coefficient-based measure under four calibrations. Next, we consider statistical inference of the correlation coefficient-based measure by using the empirical likelihood method. The empirical likelihood statistics are shown to be an asymptotically standard chi-squared distribution. Simulation studies demonstrate the performance of the proposed estimators and test statistics. A real example is analyzed to illustrate its practical usage.

Consistent Model Selection Procedure for Random Coefficient INAR Models.

In the realm of time series data analysis, information criteria constructed on the basis of likelihood functions serve as crucial instruments for determining the appropriate lag order. However, the intricate structure of random coefficient integer-valued time series models, which are founded on thinning operators, complicates the establishment of likelihood functions. Consequently, employing information criteria such as AIC and BIC for model selection becomes problematic. This study introduces an innovative methodology that formulates a penalized criterion by utilizing the estimation equation within conditional least squares estimation, effectively addressing the aforementioned challenge. Initially, the asymptotic properties of the penalized criterion are derived, followed by a numerical simulation study and a comparative analysis. The findings from both theoretical examinations and simulation investigations reveal that this novel approach consistently selects variables under relatively relaxed conditions. Lastly, the applications of this method to infectious disease data and seismic frequency data produce satisfactory outcomes.

Conditional density estimation using population Monte Carlo based approximate Bayesian computation

Most statistical methods require likelihood evaluation to draw a statistical inference. However, in some situations, likelihood evaluation becomes difficult analytically or computationally. Different likelihood-free methods are available that eliminate the need to compute the likelihood function. Approximate Bayesian Computation (ABC) is a framework that implements likelihood-free inference and replaces the likelihood evaluation with simulations by using forward modeling. The goal of ABC methods is to approximate the posterior distribution. However, posterior approximation via ABC methods is still considerably expensive for high dimensions. ABC requires many simulations that become computationally infeasible for complex models. Here, a technique is proposed that combines a somewhat more efficient form of ABC (Population Monte Carlo, PMC) with a Conditional Density Estimation (CDE) approach. The proposed framework provides an estimation of the posterior distribution which is referred to as PMC-CDE. A simulation study is performed that provides empirical evidence to show the efficiency of PMC-CDE in terms of integrated squared error loss. Furthermore, real-life datasets manifest the application of the proposed method.

Semiparametric probit regression model with misclassified current status data.

Current status data arise when each subject under study is examined only once at an observation time, and one only knows the failure status of the event of interest at the observation time rather than the exact failure time. Moreover, the obtained failure status is frequently subject to misclassification due to imperfect tests, yielding misclassified current status data. This article conducts regression analysis of such data with the semiparametric probit model, which serves as an important alternative to existing semiparametric models and has recently received considerable attention in failure time data analysis. We consider the nonparametric maximum likelihood estimation and develop an expectation-maximization (EM) algorithm by incorporating the generalized pool-adjacent-violators (PAV) algorithm to maximize the intractable likelihood function. The resulting estimators of regression parameters are shown to be consistent, asymptotically normal, and semiparametrically efficient. Furthermore, the numerical results in simulation studies indicate that the proposed method performs satisfactorily in finite samples and outperforms the naive method that ignores misclassification. We then apply the proposed method to a real dataset on chlamydia infection.