Maximum Likelihood Estimation Research Articles

Analysis of leukemia and forest fires data using new Poisson Quasi-Shanker distribution

In this study, a new two-parameter discrete distribution is introduced by mixing Poisson and Quasi-Shanker distributions. The new model is named Poisson Quasi-Shanker-(PQS) distribution. Some important mathematical properties of the proposed distribution are derived including factorial moments, moment-generating function, variance, and dispersion index. The parameters of PQS distribution are estimated using the maximum likelihood estimation approach. A Monte Carlo simulation is carried out to illustrate the behavior of derived estimators. The applicability of the new model is assessed using two datasets from different areas. It is concluded the proposed distribution is more flexible as compared to the considered competitive distributions.

Maximum likelihood estimation for multi-factor uncertain differential equations

Multi-factor uncertain differential equation (MUDE) is widely used in dynamic systems with multiple types of uncertainties. After observing actual data, how to estimate unknown parameters based on these observations rationally is a key issue. Existing estimation methods are based on difference scheme of MUDE with a prerequisite that observation intervals are small enough. To overcome this shortage, a novel maximum likelihood method is proposed using the concept of residual for MUDE in this work. Both analytical and numerical methods for calculating residuals are also studied. In addition, uncertain hypothesis test is employed to verify the reasonableness of estimations. Numerical example and real data analyses show the proposed method in details.

STATISTICAL INFERENCE ON SINE-EXPONENTIAL DISTRIBUTION PARAMETER

The Sine-Exponential (Sine-E) distribution is a probability distribution that combines the periodic behavior of the sine function with the decay characteristic of the exponential function. This study addresses the problem of identifying the most accurate and reliable estimation method for the parameter of the Sine-E distribution. The objective is to evaluate various parameter estimation techniques, including Maximum Likelihood Estimation (MLE), Least Squares Estimation (LSE), Weighted Least Squares Estimation (WLSE), Maximum Product of Spacing Estimation (MPSE), Cramer-von-Mises Estimation (CVME), and Anderson-Darling Estimation (ADE), using Mean Square Error (MSE) as the criterion for determining the technique with the minimum error. The study’s findings reveal that as sample size increases, the parameter estimates for all techniques converge to the true parameter value, with decreases in bias, MSE, and mean relative estimates. Among the techniques evaluated, the MPSE method consistently provides estimates closest to the true parameter value and exhibits the least bias and lowest MSE across small, moderate, and large sample sizes, making it the best estimator for the Sine-E distribution.

Different sensory information is used for state estimation when stationary or moving.

The accurate estimation of limb state is necessary for movement planning and execution. While state estimation requires both feedforward and feedback information, we focus here on the latter. Prior literature has shown that integrating visual and proprioceptive feedback improves estimates of static limb position. However, differences in visual and proprioceptive feedback delays suggest that multisensory integration could be disadvantageous when the limb is moving. We formalized this hypothesis by modeling feedback-based state estimation using the longstanding maximum likelihood estimation model of multisensory integration, which we updated to account for sensory delays. Our model predicted that the benefit of multisensory integration was largely lost when the limb was passively moving. We tested this hypothesis in a series of experiments in human subjects that compared the degree of interference created by discrepant visual or proprioceptive feedback when estimating limb position either statically at the end of the movement or dynamically at movement midpoint. In the static case, we observed significant interference: discrepant feedback in one modality systematically biased sensory estimates based on the other modality. However, no interference was seen in the dynamic case: participants could ignore sensory feedback from one modality and accurately reproduce the motion indicated by the other modality. Together, these findings suggest that the sensory feedback used to compute a state estimate differs depending on whether the limb is stationary or moving. While the former may tend toward multimodal integration, the latter is more likely to be based on feedback from a single sensory modality.Significance statement The estimation of limb state involves feedforward and feedback information. While estimation based on feedback has been well studied when the limb is stationary, it is unknown if similar sensory processing supports limb position estimates when moving. Using a computational model and behavioral experiments, we show that feedback-based state estimation may involve multisensory integration in the static case, but it is likely based on a single modality when the limb is moving. We suggest that this difference may stem from visual and proprioceptive feedback delays.

Simple closed-form estimation of a binary latent variable model

Abstract This paper develops a closed-form nonparametric estimator of the conditional distribution function for a binary outcome variable given an unobserved latent variable. This type of function is commonly used in models that involve measurement error and dynamic models with agent-specific unobserved heterogeneity. This paper presents a consistent extremum sieve estimator with the following advantages: i) it has a closed-form expression for all the sieve coefficients; ii) it is computationally straightforward, equivalent to computing eigenvalues and eigenvectors of matrices without the use of iterative optimization algorithms. While as flexible as the sieve maximum likelihood estimator (MLE) previously proposed for this model, our estimator proves computationally simpler. The finite sample properties of the estimator are investigated through a Monte Carlo study, and the developed estimator is applied to a probit model to assess the targeting performance of a social welfare program.

How Product Standards Influence Tea Exports? Empirical Evidence from India

India has witnessed a declining trend in tea exports in the recent period, which can partly be attributed to competition from exporters (e.g., Kenya and Sri Lanka) enjoying price advantages over the Indian varieties. However, although after the inception of the World Trade Organization (WTO) in 1995, the tariff barriers on Indian tea exports have come down across developed partners, the incidence of non-tariff barriers (NTBs) has emerged as a challenge in many destinations, with a possible dampening effect on exports. The present analysis attempts to analyse whether the imposition of product standard related measures, particularly sanitary and phytosanitary (SPS) and Technical Barriers to Trade (TBT) interventions, may have negatively influenced Indian tea exports over the period 1996–2021. Rather than considering the mere presence of SPS–TBT standards in major partner countries, their potential impacts on Indian tea exports have been determined by analysing the stringency levels of the corresponding notifications submitted to the WTO. The constructed stringency patterns are then incorporated into the Poisson pseudo maximum likelihood estimation models. The observed negative influence of standard-related measures in partner countries on Indian tea exports calls for policy interventions to enable the sector to better ensure compliance in the future.

CURTAINs flows for flows: Constructing unobserved regions with maximum likelihood estimation

Model independent techniques for constructing background data templates using generative models have shown great promise for use in searches for new physics processes at the LHC. We introduce , a major improvement to the CURTAINs method by training the conditional normalizing flow between two side-band regions using maximum likelihood estimation instead of an optimal transport loss. The new training objective improves the robustness and fidelity of the transformed data and is much faster and easier to train. We compare the performance against the previous approach and the current state of the art using the LHC Olympics anomaly detection dataset, where we see a significant improvement in sensitivity over the original CURTAINs method. Furthermore, CURTAINsF4F requires substantially less computational resources to cover a large number of signal regions than other fully data driven approaches. When using an efficient configuration, an order of magnitude more models can be trained in the same time required for ten signal regions, without a significant drop in performance.

Estimating the risk of major adverse cardiac events following radiotherapy for left breast cancer using a modified generalized Lyman normal-tissue complication probability model

BackgroundWe introduced an adapted Lyman normal-tissue complication probability (NTCP) model, incorporating clinical risk factors and censored time-to-event data, to estimate the risk of major adverse cardiac events (MACE) following left breast cancer radiotherapy (RT). Materials and methodsClinical characteristics and MACE data of 1100 women with left-side breast cancer receiving postoperative RT from 2005 to 2017 were retrospectively collected. A modified generalized Lyman NTCP model based on the individual left ventricle (LV) equivalent uniform dose (EUD), accounting for clinical risk factors and censored data, was developed using maximum likelihood estimation. Subgroup analysis was performed for low-comorbidity and high-comorbidity groups. ResultsOver a median follow-up 7.8 years, 64 patients experienced MACE, with higher mean LV dose in affected individuals (4.1 Gy vs. 2.9 Gy). The full model accounting for clinical factors identified D50 = 43.3 Gy, m = 0.59, and n = 0.78 as the best-fit parameters. The threshold dose causing a 50 % probability of MACE was lower in the high-comorbidity group (D50 = 30 Gy) compared to the low-comorbidity group (D50 = 45 Gy). Predictions indicated that restricting LV EUD below 5 Gy yielded a 10-year relative MACE risk less than 1.3 and 1.5 for high-comorbidity and low-comorbidity groups, respectively. ConclusionPatients with comorbidities are more susceptible to cardiac events following breast RT. The proposed modified generalized Lyman model considers nondosimetric risk factors and addresses incomplete follow-up for late complications, offering comprehensive and individualized MACE risk estimates post-RT.

Transient and Persistent Technical Efficiencies in Rice Farming: A Generalized True Random-Effects Model Approach

This study estimates transient and persistent technical efficiencies (TEs) using a generalized true random-effects (GTRE) model. We estimate the GTRE model using maximum likelihood and Bayesian estimation methods, then compare it to three simpler models nested within it to evaluate the robustness of our estimates. We use a panel data set of 945 observations collected from 344 rice farming households in Vietnam’s Mekong River Delta. The results indicate that the GTRE model is more appropriate than the restricted models for understanding heterogeneity and inefficiency in rice production. The mean estimate of overall technical efficiency is 0.71 on average, with transient rather than persistent inefficiency being the dominant component. This suggests that rice farmers could increase output substantially and would benefit from policies that pay more attention to addressing short-term inefficiency issues.

History-restricted marginal structural model and latent class growth analysis of treatment trajectories for a time-dependent outcome.

In previous work, we introduced a framework that combines latent class growth analysis (LCGA) with marginal structural models (LCGA-MSM). LCGA-MSM first summarizes the numerous time-varying treatment patterns into a few trajectory groups and then allows for a population-level causal interpretation of the group differences. However, the LCGA-MSM framework is not suitable when the outcome is time-dependent. In this study, we propose combining a nonparametric history-restricted marginal structural model (HRMSM) with LCGA. HRMSMs can be seen as an application of standard MSMs on multiple time intervals. To the best of our knowledge, we also present the first application of HRMSMs with a time-to-event outcome. It was previously noted that HRMSMs could pose interpretation problems in survival analysis when either targeting a hazard ratio or a survival curve. We propose a causal parameter that bypasses these interpretation challenges. We consider three different estimators of the parameters: inverse probability of treatment weighting (IPTW), g-computation, and a pooled longitudinal targeted maximum likelihood estimator (pooled LTMLE). We conduct simulation studies to measure the performance of the proposed LCGA-HRMSM. For all scenarios, we obtain unbiased estimates when using either g-computation or pooled LTMLE. IPTW produced estimates with slightly larger bias in some scenarios. Overall, all approaches have good coverage of the 95 % confidence interval. We applied our approach to a population of older Quebecers composed of 57,211 statin initiators and found that a greater adherence to statins was associated with a lower combined risk of cardiovascular disease or all-cause mortality.

Gaussian process regression to predict dryout incipience quality of saturated flow boiling in mini/micro-channels

In the present study, a Gaussian process regression (GPR) model is developed to predict the dryout incipience quality for flow boiling in mini / micro – channels based on a consolidated database obtained from Purdue University Boiling and Two – Phase Flow Laboratory (PU – BTPFL) consisting of 997 points from 26 sources. The database includes 13 different working fluids over a wide range of operating conditions: hydraulic diameter (0.51 – 6.0 mm), mass velocities (29 – 2303 kg/ m2 s), liquid – only Reynolds number (125 – 53,770), boiling number (0.31 – 44.3 × 10-4), and reduced pressure (0.005 – 0.78). The inputs to the model were liquid – only Weber number (Wefo), reduced pressure (PR), boiling number (Bo), heated to frictional perimeter ratio(PH/PF), capillary number (Ca) and density ratio (ρg/ρf), and the output was dryout incipience quality. The database was randomly divided into training data to learn GPR kernel (covariance) parameters using maximum likelihood estimation, and test data to evaluate the prediction accuracy of the outputs based on mean absolute error (MAE). Six – different types of covariance functions were tested, and GPR model with automatic relevance detection (ARD) rational quadratic covariance function showed the best overall performance. A performance comparison of approved GPR model was made with an existing highly reliable universal correlation to predict dryout incipience quality for mini / micro – channels. Results show that the developed GPR model exhibits superior generalization ability with an overall MAE of 6.03 %, and a significant reduction of 51.76 % in MAE compared with the universal correlation. Overall, the GPR model was found to be a data efficient machine learning technique for predicting dryout incipience quality for flow boiling in mini / micro – channels based on a consolidated database.

Spatial clustering based on geographically weighted multivariate generalized gamma regression

Geographically Weighted Regression (GWR) is one of the local statistical models that can capture the effects of spatial heterogeneity. This model can be used for both univariate and multivariate responses. However, it should be noted that GWR models require the assumption of error normality. To overcome this problem, we propose a GWR model for generalized gamma distributed responses that can capture the phenomenon of some special continuous distributions. The proposed model is known as Geographically Weighted Multivariate Generalized Gamma Regression (GWMGGR). Parameter estimation is performed using the Maximum Likelihood Estimation (MLE) method optimized with the Bernt-Hall-Hall-Haussman (BHHH) algorithm. To determine the significance of the spatial heterogeneity effect, a hypothesis test was conducted using the Maximum Likelihood Ratio Test (MLRT) approach. We made a spatial cluster based on the estimated model parameters for each response using the k-means clustering method to interpret the obtained results. Some highlights of the proposed method are:•A new model for GWR with multivariate generalized gamma distributed responses to overcome the assumption of normally distributed errors.•Goodness of fit test to test the spatial effects in GWMGGR model.•Spatial clustering of districts/cities in Central Java based on three dimensions of educational indicators.

Almost unbiased ridge estimator in Bell regression model: theory and application to plastic polywood data

In this paper, a new regression estimator is proposed as an alternative to the ridge estimator in the case of multicollinearity in Bell regression model, called an almost unbiased ridge estimator. Also, we provide the theoretical properties of the new almost unbiased ridge estimator, and some theorems showing under which conditions that the almost unbiased ridge estimator is superior to its competitors. We consider a comprehensive simulation study to demonstrate the superiority of the almost unbiased ridge estimator compared to the usual Bell ridge estimator and the maximum likelihood estimator. The usefulness and superiority of the introduced regression estimator is shown via a real-world data example. According to the results of the simulation study and real-world data example, we conclude that the new almost unbiased ridge regression estimator is superior to its competitors in terms of the mean square error criterion.

Accounting for regression to the mean under the bivariate -distribution.

Regression to the mean occurs when an unusual observation is followed by a more typical outcome closer to the population mean. In pre- and post-intervention studies, treatment is administered to subjects with initial measurements located in the tail of a distribution, and a paired sample -test can be utilized to assess the effectiveness of the intervention. The observed change in the pre-post means is the sum of regression to the mean and treatment effects, and ignoring regression to the mean could lead to erroneous conclusions about the effectiveness of the treatment effect. In this study, formulae for regression to the mean are derived, and maximum likelihood estimation is employed to numerically estimate the regression to the mean effect when the test statistic follows the bivariate -distribution based on a baseline criterion or a cut-off point. The pre-post degrees of freedom could be equal but also unequal such as when there is missing data. Additionally, we illustrate how regression to the mean is influenced by cut-off points, mixing angles which are related to correlation, and degrees of freedom. A simulation study is conducted to assess the statistical properties of unbiasedness, consistency, and asymptotic normality of the regression to the mean estimator. Moreover, the proposed methods are compared with an existing one assuming bivariate normality. The -values are compared when regression to the mean is either ignored or accounted for to gauge the statistical significance of the paired -test. The proposed method is applied to real data concerning schizophrenia patients, and the observed conditional mean difference called the total effect is decomposed into the regression to the mean and treatment effects.

Utilizing large language models in infectious disease transmission modelling for public health preparedness

IntroductionOpenAI's ChatGPT, a Large Language Model (LLM), is a powerful tool across domains, designed for text and code generation, fostering collaboration, especially in public health. Investigating the role of this advanced LLM chatbot in assisting public health practitioners in shaping disease transmission models to inform infection control strategies, marks a new era in infectious disease epidemiology research. This study used a case study to illustrate how ChatGPT collaborates with a public health practitioner in co-designing a mathematical transmission model. MethodsUsing natural conversation, the practitioner initiated a dialogue involving an iterative process of code generation, refinement, and debugging with ChatGPT to develop a model to fit 10 days of prevalence data to estimate two key epidemiological parameters: i) basic reproductive number (Ro) and ii) final epidemic size. Verification and validation processes are conducted to ensure the accuracy and functionality of the final model. ResultsChatGPT developed a validated transmission model which replicated the epidemic curve and gave estimates of Ro of 4.19 (95 % CI: 4.13- 4.26) and a final epidemic size of 98.3 % of the population within 60 days. It highlighted the advantages of using maximum likelihood estimation with Poisson distribution over least squares method. ConclusionIntegration of LLM in medical research accelerates model development, reducing technical barriers for health practitioners, democratizing access to advanced modeling and potentially enhancing pandemic preparedness globally, particularly in resource-constrained populations.

A Generalized Class of Exponentiated Modified Weibull Distribution With Applications

Abstract: In this paper, a new class of five parameter gamma-exponentiated or generalized modified Weibull (GEMW) distribution which includes exponential, Rayleigh, Weibull, modified Weibull, exponentiated Weibull, exponentiated exponential, exponentiated modified Weibull, exponentiated modified exponential, gamma-exponentiated exponential, gamma exponentiated Rayleigh, gamma-modified Weibull, gamma-modified exponential, gamma-Weibull, gamma-Rayleigh and gamma-exponential distributions as special cases is proposed and studied. Mathematical properties of this new class of distributions including moments, mean deviations, Bonferroni and Lorenz curves, distribution of order statistics and Renyi entropy are presented. Maximum likelihood estimation technique is used to estimate the model parameters and applications to real data sets presented in order to illustrate the usefulness of this new class of distributions and its sub-models.

A GARCH model selection and estimation method based on neural network with the loss function of mean square error and model confidence set

AbstractThis paper proposes a method that uses mean square error (MSE) and model confidence set (MCS) as the loss function of back‐propagation neural network (BPNN), aiming to train and find a generalized autoregressive conditional heteroskedastic (GARCH) model that has the best forecasting performance of a time series. Combining MSE and the p‐value of MCS can not only estimate better parameters for the GARCH models but also find the best GARCH model to forecast the volatility of a time series. Meanwhile, we divide a time series into several parts and use each part as the input of the BPNN. Through the BPNN, each part of the time series will be turned into several forecasting values. These values will be used to calculate the MSE and the p‐value of MCS, which will then be used to update the parameters of the BPNN. In the end, we use MCS to choose the best GARCH model among the trained GARCH models and compare this method with maximum likelihood estimation (MLE) and the generalized least squares estimation (GLS). The result shows that the p‐value of MCS of the best model estimated by this method is higher than the p‐value of MCS of the best model estimated by MLE and GLS. According to the theory of MCS, a model that has a larger p‐value does have a better forecasting performance. The method proposed by this paper can provide a potential application of neural network in GARCH model forecasting and estimation.

ESG practices disclosure and initial performance of Malaysian IPOS

Companies’ decision to go public is risky because of the high uncertainty level from the companies’ unknown history prior to their listing. Recent studies in the Malaysian market reported the declining trend of companies’ initial performance, relating it to investors’ current demand for higher information transparency that can reflect companies’ sustainable evolution as a means to attract their demand in subscribing newly issued shares. Thus, this study aims to investigate the impact of disclosing ESG practices on companies’ initial performance. Using a linear regression with maximum likelihood (ML) estimation, this study examines 171 initial public offerings (IPOs) issued in the Malaysian market from 2015 to 2023. By using two ways of measuring companies’ initial performance (offer-to-open and offer-to-close), the findings show that higher information disclosure on ESG practices will only be reflective and positively affect companies’ performance by the end of the day. Further examination of individual ESG pillars indicates that environmental disclosures negatively influence companies’ initial performance, while social and governance disclosures positively influence companies’ initial performance. A large investment in maintaining a high level of environmental practice can be costly, negatively influencing companies’ performances. Higher social and governance disclosure attracts socially conscious investors and reflects good internal governance, increasing demand for the companies’ shares during the IPO and positively influencing companies’ performances. This study contributes to the growing literature concerning ESG and post-IPO performances specific to the Malaysian market and proposes recommendations on the importance of disclosing ESG practices prior to their IPO. AcknowledgmentsThe authors would like to acknowledge that this article is part of a research project funded by Universiti Teknologi MARA (UiTM) for the MyRA Grant Scheme, file no: 600-RMC 5/3/GPM (118/2022).

A new extension of the Gumbel distribution with biomedical data analysis

In the field of biomedical research, data characteristics often exhibit significant variability, challenging the applicability of classical Gumbel distribution for biomedical data modeling. To address this, this paper introduces a novel extension of the Gumbel model known as the odd beta prime Gumbel (OBP-Gum) model. Derived from the odd beta prime family, the new distribution exhibits greater kurtosis compared to the traditional Gumbel distribution. Importantly, the proposed distribution is designed to capture right-skewed, left-skewed, and nearly symmetric density functions, as well as increasing, decreasing, constant, and upside-down bathtub shapes for its hazard rate function, providing excellent curvature features for creating flexible statistical models for biomedical research. We derive the fundamental features of the OBP-Gum model, such as the quantile function, linear representations, moment generating function, moments, skewness, kurtosis, incomplete moments, and Rényi and Tsallis entropies. Parameter estimation for this new model is conducted using the maximum likelihood estimation method. A simulation study demonstrates the performance of the model parameters. The empirical findings, based on applications to two biomedical datasets, suggest that the OBP-Gum distribution outperforms existing models, particularly in handling extreme observations. Instead of relying on conventional models for decision-making, this research provides relevant stakeholders with an improved statistical distribution for more accurate biomedical data modeling.

An overview of floral and vegetative evolution in the Asian clade of Bulbophyllum (Orchidaceae)

Background and aims – Bulbophyllum, the largest genus in Orchidaceae, exhibits a diverse morphology in both reproductive and vegetative characters. While trait diversity and evolution has been extensively studied in Malagasy species and within the Cirrhopetalum alliance clade, the evolution of reproductive and vegetative characters at the whole level of the Asian clade remains largely unexplored. Material and methods – We reconstructed the phylogeny of approximately 11% of all Asian Bulbophyllum species using Bayesian inference and maximum likelihood estimation based on nuclear (ITS) and chloroplast (matK, psbA-trnH) DNA sequence data. This phylogenetic framework allowed us to examine the evolution of two vegetative and four floral characters through ancestral state reconstruction. Key results and conclusion – The ancestral character states of the Asian clade of Bulbophyllum include a single leaf, distinct pseudobulbs, multiple-flowered inflorescences, and lateral and dorsal sepals similar in length. One-leaved pseudobulbs evolved into two-leaved pseudobulbs multiple times. Distinct pseudobulbs gave rise to indistinct pseudobulbs twice. Multiple-flowered inflorescences shifted to solitary flowers and 2–3-flowered inflorescences multiple times, with some instances of evolutionary reversal. Lateral sepal elongation also presents a convergent evolutionary scenario.