Bayesian Interval Research Articles

On Estimation of Three-Component Mixture of Distributions via Bayesian and Classical Approaches

In this study, we model a heterogeneous population assuming the three-component mixture of the Pareto distributions assuming type I censored data. In particular, we study some statistical properties (such as various entropies, different inequality indices, and order statistics) of the three-component mixture distribution. The ML estimation and the Bayesian estimation of the mixture parameters have been performed in this study. For the ML estimation, we used the Newton Raphson method. To derive the posterior distributions, different noninformative priors are assumed to derive the Bayes estimators. Furthermore, we also discussed the Bayesian predictive intervals. We presented a detailed simulation study to compare the ML estimates and Bayes estimates. Moreover, we evaluated the performance of different estimates assuming various sample sizes, mixing weights and test termination times (a fixed point of time after which all other tests are dismissed). The real-life data application is also a part of this study.

Abstract CT207: Phase 1 first-in-human study of ABBV-151 as monotherapy or in combination with budigalimab in patients with locally advanced or metastatic solid tumors

Abstract Background Glycoprotein-A repetitions predominant (GARP) regulates membrane-bound transforming growth factor β1 (TGFβ1), an immunosuppressive cytokine. ABBV-151 is a first-in-class monoclonal antibody (mAb) that binds to the GARP-TGFβ1 complex and blocks TGFβ1 release. Preclinical data demonstrated that targeting both GARP-TGFβ1 and programmed cell death protein 1 (PD-1) improved antitumor effects compared with anti-PD-1 alone. Combining ABBV-151 with the anti-PD-1 mAb budigalimab (ABBV-181) may enable a more effective antitumor immune response by reducing the immunosuppressive effect of TGFβ1. Trial design This is a multicenter phase 1, dose escalation and dose expansion study (NCT03821935) in patients (pts; ≥18 yr, Eastern Cooperative Oncology Group performance status 0-1) with locally advanced or metastatic solid tumors. The primary objective of dose escalation is to determine the recommended phase 2 dose (RP2D) of ABBV-151 as monotherapy or with budigalimab; dose expansion will assess the objective response rate of ABBV-151 ± budigalimab. Secondary/exploratory objectives include assessing preliminary efficacy, safety, tolerability, pharmacokinetics (PK), and evaluating potential pharmacodynamic and predictive biomarkers. Dose escalation of ABBV-151, guided by a Bayesian optimal interval design, will assess dose-limiting toxicities during the first 28-day cycle and will be utilized until the RP2D is defined. ABBV-151 + budigalimab (fixed dose) will start ≥2 dose levels below that proven safe for ABBV-151. Adverse events will be evaluated per National Cancer Institute Common Terminology Criteria v5.0. Response will be assessed using Response Evaluation Criteria In Solid Tumors (RECIST) v1.1 and iRECIST every 8 weeks. PK of ABBV-151 will be characterized. Saturation of GARP-TGFβ1 on platelets and PD-1 on CD4 T cells will be determined. Modulation of cytokines, chemokines, lymphocyte activity, and gene expression will be assessed in blood, while gene signatures and protein markers will be explored in tumor tissues. Baseline tumor characteristics will be retrospectively related to response. Enrollment initiated Mar 2019, with 37 pts enrolled as of May 2020. Citation Format: John Powderly, Toshio Shimizu, Patricia LoRusso, Albiruni Razak, Kathy Miller, Arjun Balar, Jordi Bruix, Loren Michel, Martha Blaney, Xiaowen Guan, Susan Lacy, Satwant Lally, Stacie Lambert, Rachel Leibman, Gregory Vosganian, Talia Golan, Anthony Tolcher. Phase 1 first-in-human study of ABBV-151 as monotherapy or in combination with budigalimab in patients with locally advanced or metastatic solid tumors [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2021; 2021 Apr 10-15 and May 17-21. Philadelphia (PA): AACR; Cancer Res 2021;81(13_Suppl):Abstract nr CT207.

Improved constraints on neutrino mixing from the T2K experiment with3.13×1021protons on target

The T2K experiment reports updated measurements of neutrino and antineutrino oscillations using both appearance and disappearance channels. This result comes from an exposure of $14.9~(16.4) \times 10^{20}$ protons on target in neutrino (antineutrino) mode. Significant improvements have been made to the neutrino interaction model and far detector reconstruction. An extensive set of simulated data studies have also been performed to quantify the effect interaction model uncertainties have on the T2K oscillation parameter sensitivity. T2K performs multiple oscillation analyses that present both frequentist and Bayesian intervals for the PMNS parameters. For fits including a constraint on \ssqthonethree from reactor data and assuming normal mass ordering T2K measures $\sin^2\theta_{23} = 0.53^{+0.03}_{-0.04}$ and $\Delta{}m^2_{32} = (2.45 \pm 0.07) \times 10^{-3}$ eV$^{2}$c$^{-4}$. The Bayesian analyses show a weak preference for normal mass ordering (89% posterior probability) and the upper $\sin^2\theta_{23}$ octant (80% posterior probability), with a uniform prior probability assumed in both cases. The T2K data exclude CP conservation in neutrino oscillations at the $2\sigma$ level.

Comparison of some interval estimation methods for the parameters of the gamma distribution

Several methods of finding interval estimators of the parameters of the gamma distribution are considered in the literature. In this work we compare the following methods: Wald confidence intervals; profile likelihood intervals; Bayesian intervals using the Jeffreys prior, the reference prior when α is the parameter of interest and β the nuisance parameter, the reference prior when β is the parameter of interest and α the nuisance parameter; and three fiducial methods. The comparison is done using Montecarlo simulations, in terms of the coverage probabilities and the expected lengths of the intervals, considering small, medium and large sample sizes. As an important result of the simulations we found that the fiducial methods are the best when the sample size is very small, and as the sample size increases all the methods, except the Wald confidence intervals, have a similar behavior. An example of application is shown considering earthquake data of Mexico.

Inference on stress-strength reliability for the two-parameter exponential distribution based on generalized order statistics

ABSTRACT Stress-strength reliability is a measure to compare the lifetimes of two systems. It is inferred for the two-parameter exponential distribution using generalized order statistics first without constraint on the location and scale parameters, second when the scale parameters are equal. A generalized confidence interval, bootstrap confidence intervals, a Bayesian interval, and a highest posterior density interval are computed for the stress-strength parameter. A Monte Carlo simulation shows that generalized confidence intervals provide more accurate average lengths of confidence intervals and higher probabilities to contain the true value of the parameter. Application: Confidence intervals for the time to remission of 20 leukemic patients treated with one of two drugs are approximately the same in most generalized statistical models. In addition, the time to remission for patients with the first drug is tested to be shorter than for patients with the second drug.

Abstract OT-28-04: Neratinib and tepotinib combination in advanced breast cancer and inflammatory breast cancer patients with abnormal HER2 and c-Met pathway activity as measured by the CELsignia signaling pathway activity test

Abstract Background: While HER2 targeted therapeutics have significantly improved outcomes of patients with HER2 overexpressed advanced breast cancer (ABC), c-Met pathway activation serves as a resistance mechanism in about 60% of patients. Neratinib is an irreversible tyrosine kinase inhibitor of the ErbB family of receptors (EGFR, HER2, and HER4) and tepotinib is a tyrosine kinase inhibitor of c-Met. From live extracted cells from patient biopsies, the CELsignia Pathway Activity Test measures in real-time ErbB and c-Met signaling activity and the dynamic response to pathway inhibition by targeted therapy ex vivo. The CELsignia test may identify patients with ABC who would benefit from the combination of neratinib and tepotinib regardless of the molecular breast cancer subtype. Trial Design: We designed a phase Ib/II multi-center, non-randomized, open-label study of combination of neratinib with tepotinib in patients with advanced breast cancer including those with inflammatory breast cancer. The study sites include UT MD Anderson Cancer Center, City of Hope, and The Ohio State University Cancer Center. Four dose levels of neratinib, and two dose levels of tepotinib will be studied in phase Ib to determine the maximum tolerated dose (MTD). Phase II portion of the study will test the early efficacy of neratinib and tepotinib combination in patients with HER2-/HR+ ABC with abnormal HER2 and c-Met signaling activity determined by the CELsignia test. Eligibility: All patients with IBC/ABC will be eligible for the phase Ib. Eligible patients must have measurable metastatic disease per RECIST v1.1 or unresectable disease amenable for biopsy and have had at >1 line of systemic therapy for advanced disease. Patients will have an Eastern Cooperative Oncology Group performance status of 0 to 2. For the phase II component, patients must have hyperactive HER2 and c-Met signaling determined by CELsignia test. Aims: The primary objective of the phase Ib component is to determine the MTD of the combination in previously treated IBC/ABC of any molecular subtype. The primary objective of the phase II component is to determine the overall response rate (ORR) in patients with HER2-/HR+ ABC who have a positive CELsignia test result (described in the Eligibility). Secondary objectives include progression free and overall survival, clinical benefit rate, duration of response, and safety and tolerability. Exploratory objectives will be to assess HER2 and c-Met driven signaling pathways as either hyperactive or abnormally active by CELsignia test. Statistical Methods: The phase I study will be conducted using a Bayesian optimal interval (BOIN) design to establish the MTD and the recommended phase II dose and assess early efficacy of the combination with a maximum of 21 patients. Two dose levels of tepotinib, and four dose levels of neratinib will be studied. The phase II study will assess the ORR using Bayesian optimal phase 2 (BOP2) design to rule out a 10% ORR in favor of a 30% target ORR, with a power of 80% and two-sided 5% significance level. Accrual: Once MTD is determined, up to 29 evaluable CELsignia test positive subjects will be enrolled to the phase II component of the study and an interim analysis will be performed when the total number of enrolled patients reaches 15. We hope to complete the accrual of patients by July 2022 and to schedule the last patient visit by July 2023. Contact information: For more information or to refer a patient, email blim@mdanderson.org, eahobbs@mdanderson.org Citation Format: Evthokia Hobbs, Eric Lindquist, Brian Sullivan, Esther Yoon, Ying Yuan, Angela Marx, Jie Willey, Huiming Sun, Rachel Layman, Daniel Stover, Yuan Yuan, Bora Lim. Neratinib and tepotinib combination in advanced breast cancer and inflammatory breast cancer patients with abnormal HER2 and c-Met pathway activity as measured by the CELsignia signaling pathway activity test [abstract]. In: Proceedings of the 2020 San Antonio Breast Cancer Virtual Symposium; 2020 Dec 8-11; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2021;81(4 Suppl):Abstract nr OT-28-04.

Bayesian prediction interval for a constant-stress partially accelerated life test model under censored data

The present communication develops the tools for Bayesian prediction of the Gompertz distribution based on CSPALT. The Metropolis-Hastings algorithm is applied to evaluate the BPIs for a censored sample based on unified hybrid censoring scheme. In order to investigate the impact of methodologies adopted, two numerical examples are performed. The simulated results show that reducing the censoring percentages causes smaller BPIs. The flexibility of the UHCS in evaluating the BPIs can be helped to overcome many difficulties in engineering problems.

Interval estimation of the overall treatment effect in random-effects meta-analyses: Recommendations from a simulation study comparing frequentist, Bayesian, and bootstrap methods.

There exists a variety of interval estimators for the overall treatment effect in a random-effects meta-analysis. A recent literature review summarizing existing methods suggested that in most situations, the Hartung-Knapp/Sidik-Jonkman (HKSJ) method was preferable. However, a quantitative comparison of those methods in a common simulation study is still lacking. Thus, we conduct such a simulation study for continuous and binary outcomes, focusing on the medical field for application. Based on the literature review and some new theoretical considerations, a practicable number of interval estimators is selected for this comparison: the classical normal-approximation interval using the DerSimonian-Laird heterogeneity estimator, the HKSJ interval using either the Paule-Mandel or the Sidik-Jonkman heterogeneity estimator, the Skovgaard higher-order profile likelihood interval, a parametric bootstrap interval, and a Bayesian interval using different priors. We evaluate the performance measures (coverage and interval length) at specific points in the parameter space, that is, not averaging over a prior distribution. In this sense, our study is conducted from a frequentist point of view. We confirm the main finding of the literature review, the general recommendation of the HKSJ method (here with the Sidik-Jonkman heterogeneity estimator). For meta-analyses including only two studies, the high length of the HKSJ interval limits its practical usage. In this case, the Bayesian interval using a weakly informative prior for the heterogeneity may help. Our recommendations are illustrated using a real-world meta-analysis dealing with the efficacy of an intramyocardial bone marrow stem cell transplantation during coronary artery bypass grafting.

Bayesian Stochastic Neural Network Model for Turbomachinery Damage Prediction

Turbomachinery often suffers various defects such as impeller cracking, resulting in forced outage, increased maintenance costs, and reduced productivity. Condition monitoring and damage prognostics has been widely used as an increasingly important and powerful tool to improve the system availability, reliability, performance, and maintainability, but still very challenging due to multiple sources of data uncertainties and the complexity of analytics modeling. This paper presents an intelligent probabilistic methodology for anomaly prediction of high-fidelity turbomachine, considering multiple data imperfections and multivariate correlation. The proposed method adeptly integrates several advanced state-of-the-art signal processing and artificial intelligence techniques: wavelet multi-resolution decomposition, Bayesian hypothesis testing, probabilistic principal component analysis, and fuzzy stochastic neural network modeling. The advanced signal processing is employed to reduce dimensionality and to address multivariate correlation and data uncertainty for damage prediction. Instead of conventionally using raw time series data, principal components are utilized in the establishment of stochastic neural network model and anomaly prediction. Bayesian interval hypothesis testing metric is then presented to quantitatively compare the predicted and measured data for model validation and anomaly evaluation, thus providing a confidence indicator to judge the model quality and evaluate the equipment status. Bayesian method is developed in this study for denoising the raw data with multiresolution wavelet decomposition, quantifying the model accuracy, and assessing the equipment status. The dynamic stochastic neural network model is established via the nonlinear autoregressive moving average with exogenous inputs approach. It seamlessly integrates the fuzzy clustering and independent Bernoulli random function into radial basis function neural network. A natural gradient method based on Kullback-Leibler distance criterion is employed to maximize the log-likelihood loss function. The effectiveness of the proposed methodology and procedure is demonstrated with the 11-variable time series data and the forced outage event of a real-world centrifugal compressor.

Statistical Inference for Gompertz Distribution Using the Adaptive-General Progressive Type-II Censored Samples

In this article, we combine the adaptive progressive Type-II censoring model with the general progressive model, to obtain the estimates for the parameters of Gompertz distribution, and the Bayesian prediction intervals. Estimation is executed using the maximum likelihood method (MLE) and the Bayesian method. Bayesian estimates are constructed depending on four types of loss functions. The credible intervals and the asymptotic confidence intervals are determined for the parameters of Gompertz distribution based on the Bayesian estimates and the MLEs, respectively. Finally, a real data example and the simulation study are discussed to compare the proposed methods.

Empirical weighted Bayesian tolerance intervals

ABSTRACT Bayesian statistics has been widely utilized as an approach that can incorporate prior knowledge into statistical inference. Tolerance intervals (TI) are the most commonly used statistical methods for product quality assurance. There are two main Bayesian approaches for calculating statistical tolerance intervals: Hamada and Wolfinger. A simulation-based approach was implemented to compare two-sided Wolfinger, Hamada, and frequentist tolerance intervals which control the probability content at a specified level of confidence. As sample sizes increase, compared to frequentist, Hamada TI become more conservative while Wolfinger TI are more liberal. To address this issue, we propose an empirical weighted Bayesian TI approach that is a compromise between Hamada and Wolfinger approaches. The proposed Bayesian TI result in narrower limits in certain scenarios while ensuring the confidence content coverage remains comparable to frequentist.

Checkerboard: a Bayesian efficacy and toxicity interval design for phase I/II dose-finding trials

ABSTRACT The rise of targeted therapy and immunotherapy has challenged the conventional more-is-better phase I trial design paradigm that focuses on finding the MTD. In this article, we propose a novel model-assisted phase I/II design, called checkerboard design, that considers both toxicity and efficacy. As an extension of the keyboard design, the checkerboard design models the joint distribution of toxicity and efficacy, and divides toxicity and efficacy domain into a series of equal-width intervals or keys. In light of interim data, the checkerboard design continuously updates the posterior distribution of toxicity and efficacy, and adaptively determine the optimal dose for treating the next cohort of patients based on the posterior probability of toxicity and efficacy keys. As a model-assisted design, one important advantage of the checkerboard design is that its decision rule can be pretabulated, greatly simplifying its implementation. We also extend the checkerboard design to handle continuous efficacy endpoint. Simulations study shows that the checkerboard design yields competitive performance comparable to existing model-based phase I/II designs, but is simpler and easier to implement in real applications.

On adaptive progressive hybrid censored Burr type III distribution: application to the nano droplet dispersion data

ABSTRACT In the current paper, the maximum likelihood and Bayes estimators for the two shape parameters of the Burr Type III distribution are investigated based on adaptive Type II progressive hybrid censored data. The maximum likelihood estimators are provided for estimating the unknown parameters. The existence and uniqueness of the maximum likelihood estimation are shown using the graphical method. The Bayes estimates are obtained under two loss functions using the Lindley’s method and Metropolis-Hastings sampling procedure. Further, approximate and Bayesian intervals are constructed. Monte Carlo simulation study is performed to check the accuracy of the estimates and compare the performance of the proposed confidence intervals. Also, the nano droplet data is analyzed to illustrate the application and development of the inference methods.

Improving Dose-Finding for New Agents as Monotherapy and Add-On Therapy

ABSTRACT With the recent advancement in immuno-oncology, next-stage early oncology development is focusing on identifying the best combinations of established immunotherapies with new agents to either overcome drug resistance or achieve synergic effects. Although the combination is the focus, safety profile of the new agent alone must be explored. Therefore, many trials have both monotherapy and add-on combination therapy arms. Finding the maximum tolerable dose (MTD) for the new agent in both arms is critical. Traditional oncology dose-finding methods and MTD estimation algorithm do not handle the correlation and interplay between the two arms and the selected MTDs may contradict with each other. To overcome these issues, we applied a two-dimensional pool-adjacent-violators algorithm to MTD estimation and modified the standard Bayesian optimal interval design (BOIN) to allow for information flow between arms during dose-finding. We also showed that a naïve adaptation of standard BOIN that is much simpler to implement demonstrated empirically similar performance. These new approaches were assessed with simulations and demonstrated improvement for trials with both monotherapy and add-on combination therapy arms. Albeit proposed in the context with immunotherapy as the backbone drug, our approaches can be applied to any new agent in combination with a fixed dose of another drug. Supplementary materials for this article are available online.

Abstract A21: Time-to-event Bayesian optimal interval design to accelerate phase I pediatric oncology trials

Abstract Late-onset toxicity is common for novel molecularly targeted agents and immunotherapy. It causes major logistic difficulty for existing adaptive phase I trial designs, which require the observance of toxicity early enough to apply dose escalation rules for new patients. The same logistic difficulty arises when the accrual is rapid. We propose the time-to-event Bayesian optimal interval (TITE-BOIN) design to accelerate phase I trials by allowing for real-time dose assignment decisions for new patients while some enrolled patients’ toxicity data are still pending. Similar to the rolling six design, the TITE-BOIN dose escalation/de-escalation rule can be tabulated before the trial begins, making it transparent and simple to implement, but is more flexible in choosing the target DLT rate and has higher accuracy to identify the MTD. Compared to the more complicated model-based time-to-event continuous reassessment method (TITE-CRM), the TITE-BOIN has comparable accuracy to identify the MTD but is simpler to implement with substantially better overdose control. A numerical study shows that the TITE-BOIN design supports continuous accrual, without sacrificing patient safety or the accuracy of identifying the MTD, and therefore has great potential to accelerate early-phase drug development. Note: This abstract was not presented at the conference. Citation Format: Ying Yuan, Ruitao Lin, Daniel Li, Lei Nie, Katherine Warren. Time-to-event Bayesian optimal interval design to accelerate phase I pediatric oncology trials [abstract]. In: Proceedings of the AACR Special Conference on the Advances in Pediatric Cancer Research; 2019 Sep 17-20; Montreal, QC, Canada. Philadelphia (PA): AACR; Cancer Res 2020;80(14 Suppl):Abstract nr A21.

Phase I study of the Bcl-2 inhibitor venetoclax with DA-EPOCH-R as initial therapy for aggressive B-cell lymphomas.

8003 Background: Dose-adjusted (DA) EPOCH-R is a frontline treatment for aggressive B-cell lymphomas. Bcl-2 is associated with chemoresistance due to BCL2 gene rearrangement or protein overexpression in lymphomas and is antagonized by BH3 mimetic venetoclax (ven). We conducted a phase I study combining ven with DA-EPOCH-R in aggressive B-cell lymphomas. Methods: This phase 1 study used Bayesian optimal interval design with dose expansion. Eligible patients (pts) were 18 years with newly diagnosed diffuse large B-cell (DLBCL), primary mediastinal, and high grade B-cell lymphoma (HGBCL) with double hit (DHL) or not otherwise specified (NOS). Ven was dosed at 400 mg (DL1), 600 mg (DL2), and 800 mg (DL3) daily for 10 days with 6 cycles of DA-EPOCH-R. A subsequent cohort received ven 600 mg daily for 5 days (DL2B). Toxicities were graded by CTCAE v4.0 and response assessed by Lugano criteria. Dose limiting toxicity (DLT) period was cycle 1 and primarily included grade (gr) ≥3 neutropenia on cycle 2 day 1, gr ≥4 febrile neutropenia/thrombocytopenia, and gr ≥3 nausea, vomiting, diarrhea despite supportive care. Results: 30 pts enrolled with median age 64 (24-79), and 50% female. Ann Arbor stage was III-IV in 23. IPI was high risk in > 50%. Diagnosis was DHL (15), DLBCL NOS (13), and HGBCL NOS (2). 18 had MYC and 14 had BCL2 rearrangements. Bcl-2 was expressed ≥50% by IHC in 21/26 with data. There were no DLTs in DL1 (3 pts) or DL2 (9 pts). 1/6 had DLT in DL3 (gr 4 thrombocytopenia). Ven dose reductions occurred in subsequent cycles in 4 (2 in DL2; 2 in DL3). Of 18 in DL1-3, EPOCH was escalated above level 1 in 1 and de-escalated below level 1 in 7. Because of delays and ven dose reductions in DL2-3 due in part to cytopenias, infections and GI toxicities, we accrued DL2B. In DL2B, 0/12 pts had DLTs or ven dose reductions. EPOCH was escalated above level 1 in 4 and de-escalated below level 1 in 3. 1 died of sepsis during cycle 3. Most common gr 3-4 toxicities across all dose levels were cytopenias; febrile neutropenia occurred in 57%. Most common non-hematologic toxicities of all grades were hypocalcemia, nausea, diarrhea, hypokalemia and fatigue. ORR (N = 30) ITT was 97% with 27 (90%) complete and 2 (7%) partial responses; 1 was not evaluable. Follow up is ongoing. Of 15 DHL, ORR and CRR were 93% and 80%. Conclusions: We identified ven 600 mg for 5 days per cycle as RP2D with DA-EPOCH-R. DL2B was well tolerated and required no ven dose reductions. Further efficacy and safety is being evaluated in Alliance 51701, DA-EPOCH-R/R-CHOP in DH/double expressor lymphomas, using the dosing regimen defined by this study. Clinical trial information: NCT03036904 .

Bayesian interval mapping of count trait loci based on zero-inflated generalized Poisson regression model.

Count phenotypes with excessive zeros are often observed in the biological world. Researchers have studied many statistical methods for mapping the quantitative trait loci (QTLs) of zero-inflated count phenotypes. However, most of the existing methods consist of finding the approximate positions of the QTLs on the chromosome by genome-wide scanning. Additionally, most of the existing methods use the EM algorithm for parameter estimation. In this paper, we propose a Bayesian interval mapping scheme of QTLs for zero-inflated count data. The method takes advantage of a zero-inflated generalized Poisson (ZIGP) regression model to study the influence of QTLs on the zero-inflated count phenotype. The MCMC algorithm is used to estimate the effects and position parameters of QTLs. We use the Haldane map function to realize the conversion between recombination rate and map distance. Monte Carlo simulations are conducted to test the applicability and advantage of the proposed method. The effects of QTLs on the formation of mouse cholesterol gallstones were demonstrated by analyzing an mouse dataset.

The Support Interval

A frequentist confidence interval can be constructed by inverting a hypothesis test, such that the interval contains only parameter values that would not have been rejected by the test. We show how a similar definition can be employed to construct a Bayesian support interval. Consistent with Carnap’s theory of corroboration, the support interval contains only parameter values that receive at least some minimum amount of support from the data. The support interval is not subject to Lindley’s paradox and provides an evidence-based perspective on inference that differs from the belief-based perspective that forms the basis of the standard Bayesian credible interval.

Estimation and prediction based on type-I hybrid censored data from the Poisson-Exponential distribution

This paper considers the problems of estimation and prediction when lifetime data following Poisson-exponential distribution are observed under type-I hybrid censoring. For both the problems, we compute point and associated interval estimates under classical and Bayesian approaches. For point estimates in the problem of estimation, we compute maximum likelihood estimates using Newton–Raphson, Expectation-Maximization and Stochastic Expectation-Maximization algorithms under classical approach, and under Bayesian approach we compute Bayes estimates with the help of Lindley and importance sampling technique under informative and non-informative priors using symmetric and asymmetric loss functions. The associated interval estimates are obtained using the Fisher information matrix and Chen and Shao method respectively under classical and Bayesian approaches. Further, the predictive point estimates and associated predictive interval estimates are computed by making use of best unbiased and conditional median predictors under classical approach, and Bayesian predictive and associated Bayesian predictive interval estimates in the problem of prediction. We analysis real data set, and conduct Monte Carlo simulation study for the comparison of various proposed methods of estimation and prediction. Finally, a conclusion is given.

Stress–Strength Parameter Estimation Based on Type-II Hybrid Progressive Censored Samples for a Kumaraswamy Distribution

In this paper, when the stress and strength are two independent Kumaraswamy random variables, we derive the point and interval estimate of the stress-strength parameter, from both frequentist and Bayesian viewpoints, under the Type-II hybrid progressive censoring scheme. In fact, the problem is solved in two cases. First, with the assumption that the stress and strength have different first shape parameters and the common second shape parameter, we attain maximum likelihood estimate (MLE), approximation MLE, and two Bayesian approximation estimates, Lindley's approximation and the Markov chain Monte Carlo (MCMC) method, due to lack of closed forms. Also, the asymptotic confidence interval of R is constructed by asymptotic distribution of it. Moreover, by using the MCMC method, we achieve the highest posterior density credible intervals. Second, with the assumption that the common shape parameter is known, we attain the MLE, the exact Bayes estimate, and the uniformly minimum-variance unbiased estimate of R. Also, we construct the asymptotic and Bayesian intervals for the stress-strength parameter. Furthermore, to compare the performance of various methods, we apply the Monte Carlo simulation. Finally, one real dataset is analyzed for demonstrative aims.