Likelihood Principle Research Articles

Mixture model for dependent competing risks data and application for diabetic retinopathy treatment

This paper proposes a flexible mixture modeling approach to analyze competing risks data with multiple causes of failure under a progressive first-failure censoring scheme where the causes may not be independent. The failure time distributions corresponding to different causes of failure are assumed to belong to the flexible proportional hazard family of distributions, some important members of which are Weibull, Burr XII and Gompertz distributions. We address the problem here from a classical viewpoint. The point estimates of the parameters can be easily obtained by employing the maximum likelihood principle. For interval estimation purposes, we resort to using the asymptotic confidence intervals. An extensive simulation study is carried out to validate our proposed model. Finally, a diabetic retinopathy treatment dataset is used as an application to study the effectiveness of our proposed model assuming some important members of the proportional hazard family.

Quantitative risk assessment of staphylococcal enterotoxin A (SEA) in pork in metropolitan Bangkok, Thailand

Staphylococcus aureus (SA) food poisoning is caused by the intake of staphylococcal enterotoxin (SE) produced during SA growth in contaminated food. To better evaluate the risk of SA intoxication, the relationship between SE dose and SA intoxication as a dose response (DR) model in the hazard characterization of risk assessment is needed. The objectives of this study were to propose a best-fit DR model based on SE doses in the outbreaks (secondary data) using the principle of maximum likelihood and to assess the risk of SE in pork through probabilistic models. From the goodness-of-fit test, the deviances of exponential, beta-Poisson, and logistic regression model were 5.66, 5.66, and 3.41, respectively. The best-fit DR model was the logistic regression model with the parameters q1 and q2 of 2.90 and 0.97, respectively. The uncertainty of parameters of DR model was represented by 95% confidence contour and the comparison DR curves of the best-fit and 95% likelihood-based confidence limits for the logistic regression model. The mean annual risk estimates of SE intoxication in pork of the Bangkokian population was in the range of 5.7 × 10−2 and 9.0 × 10−1.

Joint estimation of DOA and mutual coupling via imposing an annihilation constraint

The mutual coupling between elements degrades the direction-of-arrival (DOA) estimation performance. This paper considers jointly estimating the DOA and mutual coupling. Firstly, based on the fact that the noiseless array output without mutual coupling consists of complex exponential sums, an annihilation relation is obtained. Then, an optimization problem is proposed by combining a cost function derived from the maximum likelihood principle and a constraint formed by the annihilation relation. The optimization problem is solved by the sequential quadratic programming (SQP) method, where the Jacobian matrix is derived via exploiting the symmetric Toeplitz structure of the mutual coupling matrix. At last, a post-processing method is proposed for further improving the accuracy of mutual coupling estimation. The new method can handle single snapshot estimation, and it is gridless while utilizing the whole aperture. It is also insensitive to overestimation of the degree of mutual coupling. The method has been verified by simulations and compared with representative methods regarding accuracy and efficiency.

Probabilistic forecasting of rainfall response in a Danish stormwater tunnel

• Development of a non-linear SDE-model of rainfall response in a stormwater tunnel. • A modified maximum-likelihood estimation of the non-linear SDE-model. • Probabilistic l -step forecasting with the non-linear SDE-model. • Evaluation of the uncertainty in rainfall response forecasts. Sustainable urban drainage is an economically expensive necessity, partially due to the operation of water pumps. Reliable forecasting of stormwater response following a rainfall event has the potential to reduce those expenses, because it can be used in model predictive control schemes that optimize the energy consumption of pumps significantly better than the commonly applied real-time control systems. Urban drainage systems are traditionally designed around highly complex, deterministic models where an assessment of the uncertainty of the stormwater forecast is either absent or relies on computation–heavy simulations. With offset in a Danish stormwater tunnel, we propose a much faster, but reliable, non-linear continuous-discrete-time state-space model based on stochastic differential equations which can generate probabilistic forecasts that contain complete information about the distribution of uncertainty. We explain step-by-step how the model structure is built from simple physical assumptions, then how the parameters are estimated from maximum likelihood principles and finally we demonstrate the forecasting capabilities of the model. We believe this model would be well-suited for a subsequent model predictive control scheme.

A novel maximum likelihood and moving weighted average based adaptive Kalman filter

For the state estimation with inaccurate noise statistics, the existing adaptive Kalman filters (AKFs) usually have substantial computational complexity or are not easy to estimate online. Inspired by the fact, a new computationally efficient AKF based on maximum likelihood and moving weighted average (MMAKF) is proposed. Firstly, to reduce computational complexity, instead of estimating the noise covariance matrixes, the maximum likelihood principle is introduced to directly estimate the prediction error covariance matrix and innovation covariance matrix. Subsequently, a new moving weighted average algorithm is designed to optimize the estimated results. Then, a computationally efficient AKF is derived, and its convergence performance and application are discussed. Simulation results for the target tracking example illustrate that the proposed AKF can effectively reduce error caused by inaccurate noise statistics and basically keep simplicity and elegance of the classical KF.

Fusion neutron emissivity tomography for ITER Vertical Neutron Camera

ITER Vertical Neutron Camera (VNC) is a diagnostic intended to measure time- and space-resolved neutron emission profile in the poloidal plasma section. It is composed of the two fan-shaped collimating structures: lower (5 collimators) and upper (6 collimators). Every collimator contains 2 fission chambers and 2 diamond detectors.We developed an algorithm of simultaneous reconstruction of DD and DT neutron emissivity profiles from measurements of VNC neutron flux monitors. The algorithm is based on maximum likelihood principle. We consider operation of diamond detectors as threshold counters. By setting deposited energy threshold equal to 3.5 MeV diamond detectors become DT neutron flux monitors. Relying on the different energetic sensitivities of VNC neutron flux monitors (fission chambers and diamond detectors) it is possible to distinguish fluxes of DD and DT neutrons.We evaluated sensitivity of neutron emissivity reconstruction to the statistical errors of measurements, errors of contribution matrix, and errors of magnetic surface shapes. The algorithm has been demonstrated to be robust against errors of the input data.

Morphological and Molecular Identification of Cytotoxic Fungus Species; Hebeloma crustuliniforme and Hebeloma sinapizans

Taxonomic positions and phylogenetic relations of Hebeloma species have not yet been figured out molecularly in Turkey. Most species of the genus are mainly poisonous and a few of which are edible. Hebeloma crustuliniforme and H. sinapizans are two important species that contain deadly toxins so only morphological characters may not be enough for reliable identification. The DNA sequence of the nuclear ribosomal Internal Transcribed spacer (nrITS) region is used in addition to morphological characters in the present study. Phylogenetic analysis is conducted on the sequence dataset by using the Maximum Likelihood (ML) principle to see the taxonomic placement of two poisonous species. Studying morphological traits and molecular markers together is very useful to distinguish these two poisonous species from close relatives. The first sequence data of these species were added to the literature on behalf of our country with this study.

Wavelet-Based Identification for Spinning Projectile with Gasodynamic Control Aerodynamic Coefficients Determination.

Identification of a spinning projectile controlled with gasodynamic engines is shown in this paper. A missile model with a measurement inertial unit was developed from Newton’s law of motion and its aerodynamic coefficients were identified. This was achieved by applying the maximum likelihood principle in the wavelet domain. To assess the results, this was also performed in the time domain. The outcomes were obtained for two cases: when noise was not present and when it was included in the data. In all cases, the identification was performed in the passive mode, i.e., no special system identification experiments were designed. In the noise-free case, aerodynamic coefficients were estimated with high accuracy. When noise was included in the data, the wavelet-based estimates had a drop in their accuracy, but were still very accurate, whereas for the time domain approach the estimates were considered inaccurate.

Improved Cubature Kalman Filtering on Matrix Lie Groups Based on Intrinsic Numerical Integration Error Calibration with Application to Attitude Estimation

This paper investigates the numerical integration error calibration problem in Lie group sigma point filters to obtain more accurate estimation results. On the basis of the theoretical framework of the Bayes–Sard quadrature transformation, we first established a Bayesian estimator on matrix Lie groups for system measurements in Euclidean spaces or Lie groups. The estimator was then employed to develop a generalized Bayes–Sard cubature Kalman filter on matrix Lie groups that considers additional uncertainties brought by integration errors and contains two variants. We also built on the maximum likelihood principle, and an adaptive version of the proposed filter was derived for better algorithm flexibility and more precise filtering results. The proposed filters were applied to the quaternion attitude estimation problem. Monte Carlo numerical simulations supported that the proposed filters achieved better estimation quality than that of other Lie group filters in the mentioned studies.

Variability of \u03b1/\u03b2 ratios for prostate cancer with the fractionation schedule: caution against using the linear-quadratic model for hypofractionated radiotherapy

BackgroundProstate cancer (PCa) is known to be suitable for hypofractionated radiotherapy due to the very low α/β ratio (about 1.5–3 Gy). However, several randomized controlled trials have not shown the superiority of hypofractionated radiotherapy over conventionally fractionated radiotherapy. Besides, in vivo and in vitro experimental results show that the linear-quadratic (LQ) model may not be appropriate for hypofractionated radiotherapy, and we guess it may be due to the influence of fractionation schedules on the α/β ratio. Therefore, this study attempted to estimate the α/β ratio in different fractionation schedules and evaluate the applicability of the LQ model in hypofractionated radiotherapy.MethodsThe maximum likelihood principle in mathematical statistics was used to fit the parameters: α and β values in the tumor control probability (TCP) formula derived from the LQ model. In addition, the fitting results were substituted into the original TCP formula to calculate 5-year biochemical relapse-free survival for further verification.ResultsInformation necessary for fitting could be extracted from a total of 23,281 PCa patients. A total of 16,442 PCa patients were grouped according to fractionation schedules. We found that, for patients who received conventionally fractionated radiotherapy, moderately hypofractionated radiotherapy, and stereotactic body radiotherapy, the average α/β ratios were 1.78 Gy (95% CI 1.59–1.98), 3.46 Gy (95% CI 3.27–3.65), and 4.24 Gy (95% CI 4.10–4.39), respectively. Hence, the calculated α/β ratios for PCa tended to become higher when the dose per fraction increased. Among all PCa patients, 14,641 could be grouped according to the risks of PCa in patients receiving radiotherapy with different fractionation schedules. The results showed that as the risk increased, the k (natural logarithm of an effective target cell number) and α values decreased, indicating that the number of effective target cells decreased and the radioresistance increased.ConclusionsThe LQ model appeared to be inappropriate for high doses per fraction owing to α/β ratios tending to become higher when the dose per fraction increased. Therefore, to convert the conventionally fractionated radiation doses to equivalent high doses per fraction using the standard LQ model, a higher α/β ratio should be used for calculation.

Maximum likelihood speed estimation of moving objects in video signals

Video processing solutions for motion analysis are key tasks in many computer vision applications, ranging from human activity recognition to object detection. In particular, speed estimation algorithms may be relevant in contexts such as street monitoring and environment surveillance. In most realistic scenarios, the projection of a framed object of interest onto the image plane is likely to be affected by dynamic changes mainly related to perspective transformations or periodic behaviours. Therefore, advanced speed estimation techniques need to rely on robust algorithms for object detection that are able to deal with potential geometrical modifications. The proposed method is composed of a sequence of pre-processing operations, that aim to reduce or neglect perspectival effects affecting the objects of interest, followed by the estimation phase based on the Maximum Likelihood (ML) principle, where the speed of the foreground objects is estimated. The ML estimation method represents, indeed, a consolidated statistical tool that may be exploited to obtain reliable results. The performance of the proposed algorithm is evaluated on a set of real video recordings and compared with a block-matching motion estimation algorithm. The obtained results indicate that the proposed method shows good and robust performance.

Algorithm for laboratory diagnostics of parvoviral infection in risk groups.

Parvovirus infection (PVI) is widespread, characterized by airborne, bloodborne and vertical transmission routes. Parvovirus B19 (PVB19) exhibits tropism to erythropoietic cells. According to the increased likelihood principle of PVB19 infection and the severity of the consequences, immunocompromised individuals, especially those with hematological manifestations of diseases, are in increased risk group. Based on the own research results and analysis of the published data, we have proposed specific algorithms for PVI laboratory testing in individual risk groups, taking into account the peculiarities of the development and infection manifestation in each group: in HIV-infected patients, in oncohematological patients with to whom allogeneic hematopoietic stem cell transplantation (allo-HSCT) have been prescribed (blood and bone marrow recipients), as well as in patients with chronic anemia of parasitic etiology. For each group, the main clinical or laboratory marker, treatment procedure, or patient physiological parameters have been determined, based on which it was recommended to test for PVI. For HIV-infected patients, the main criterion for PVI testing is persistent anemia. For oncohematological patients, the basis for PVI testing is allo-HSCT procedure, which is planned or performed for this particular patient. For malaria patients, the patient's age was considered as major criterion, since in malaria and PVI coinfected young children can lead to a fatal outcome. The proposed PVI diagnostics algorithms usein risk groups can help to predict the severe course of underlying disease associated with PVB19 infection, and timely correct the therapy used.

Enhanced profile likelihood method for the nonstationary hydrological frequency analysis

In the nonstationary hydrological frequency analysis (NS-HFA), the profile likelihood (PL) method has shown superiority in uncertainty estimation due to its higher accuracy and realistic asymmetric estimates. However, its wide application has been hindered by two issues, namely the high computational burden and the numerical instability problems arising when dealing with short datasets. This paper aimed to solve or mitigate these two issues. To reduce its computational burden, the classical regula-falsi numerical method was incorporated into the PL method (namely, the RF-PL method) for estimating the bounds of the confidence intervals through an explicit analytical expression of the reparametrized log-likelihood function rather than computing the full profile. The generalized maximum likelihood principle, which constrains the distribution shape parameter to a physically/statistically reasonable range, was extended to the proposed RF-PL method (namely, the RF-GPL method) to handle short datasets. The proposed methods were applied to eight annual maximum series of flow and precipitation from North America, which present temporal trends in the mean and/or the standard deviation, to demonstrate their efficiency. The results showed that the RF-PL method substantially reduced the computational time of the PL method by 94–96% without degrading its estimation accuracy. Moreover, the RF-GPL was proven to be effective in avoiding or substantially mitigating the numerical instability issue of the RF-PL method for small sample sizes in addition to reducing the uncertainty in the estimates. As expected, the superiority of the RF-GPL method decreases with the increase of the sample size, which is beneficial in enhancing the estimation of the shape parameter in the RF-PL method. Therefore, the RF-GPL method is advantageous over the RF-PL method for short datasets, whereas its outperformance would be case-dependent for long datasets. These advancements overcome the common hurdles of the PL method and consequently enable its practical implementation more widely in the NS-HFA.

Probabilistic ultrasound C-scan imaging of barely visible impact damage in CFRP laminates

Ultrasonic pulse-echo C-scan imaging is a widespread method for detecting and characterizing defects in fiber reinforced polymer composites. However, the accurate assessment of a complex distributed damage cluster, like barely visible impact damage, in multi-layer and heterogeneous composites is not straightforward. For reliably estimating the remaining load carrying capacity and/or remaining useful lifetime of a damaged composite, a proper and complete damage assessment is of utmost importance.In this paper, a statistical time-energy gating approach is proposed in view of obtaining improved ultrasonic pulse-echo imaging of impacted composites. The majority of virgin A-scan signals are first clustered by analyzing their back-wall echoes. Next, using the principle of maximum likelihood, a Rice distribution is matched to the instantaneous amplitude in order to estimate the natural variability in the local energy of the virgin response signals. The resulting time-varying reliability interval provides an effective means to identify signals coming from defects or inhomogeneities, and as such to robustly assess defect parameters. The proposed probabilistic imaging procedure is demonstrated on various carbon fiber reinforced polymer laminates with barely visible impact damage. The obtained results are benchmarked by conventional ultrasonic C-scan imaging in through-transmission mode as well as in pulse-echo mode using the classical time gating approach. In contrast to the classical time gate method, the proposed statistical time-energy gating procedure successfully extracts and quantifies the full extent of the complex impact damage cluster. Further, the good noise resistance of the proposed probabilistic imaging method is demonstrated for a wide range of signal-to-noise ratios.

Efficient NOMA Design Without Channel Phase Information Using Amplitude-Coherent Detection

This paper presents the design and bit error rate (BER) analysis of a phase-independent non-orthogonalmultiple access (NOMA) system. The proposed NOMA system can utilize amplitude-coherent detection(ACD) which requires only the channel amplitude for equalization purposes. In what follows, threedifferent designs for realizing the detection of the proposed NOMA are investigated. One is based on themaximum likelihood (ML) principle, while the other two are based on successive interference cancellation(SIC). Closed-form expressions for the BER of all detectors are derived and compared with the BER ofthe coherent ML detector. The obtained results, which are corroborated by simulations, demonstrate that,in most scenarios, the BER is dominated by multiuser interference rather than the absence of the channelphase information. Consequently, the BER using ML and ACD are comparable for various cases ofinterest. The paper also shows that the SIC detector is just an alternative approach to realize the MLdetector, and hence, both detectors provide the same BER performance.

Efficient Approach to Decoupled Localization for Noncircular Sources in the Presence of Doppler Effect

Direction estimation in the presence of the Doppler effect can be carried out according to the maximum likelihood principle, which requires solving a nonlinear multidimensional problem. A complex multidimensional problem can be transformed into simple one-dimensional problems through signal separations. In the existing localization method for noncircular sources that takes into account the Doppler effect based on signal separation, computationally expensive eigen-decomposition of an <inline-formula> <tex-math notation="LaTeX">$N\times N$ </tex-math></inline-formula> matrix is required at each search point where <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> is the number of snapshots. This paper presents an efficient method that requires no eigen-decomposition. The proposed method finds direction estimates by optimization of the same cost function of two variables that the existing method handles. Their estimation performances are thus identical, although the complexity of the former is far less than that of the latter. The optimization of the cost function with respect to one variable is theoretically solved without eigen-decomposition, which leads to lower complexity.

Duplex LCF-VHCF P-S-N design curves: a methodology based on the Maximum Likelihood Principle

Probabilistic-S-N (P-S-N) curves are commonly employed to model the fatigue response of specimens and components and are generally obtained by assuming the statistical distribution of the fatigue life. In industrial applications, starting from the P-S-N curves, the so-called “design curves” or “lower bound S-N curves” are defined for the design of components, in order to ensure a safety margin against fatigue failures. Due to the growing interest in the Very High Cycle Fatigue (VHCF) response of materials, methodologies for the estimation of the design curves should not be limited to the Low Cycle Fatigue (LCF)-High Cycle Fatigue (HCF) life range but should also cover the VHCF region.In this work, the Maximum Likelihood Principle is exploited for the assessment of the design curves of datasets obtained through tests in the LCF-VHCF range, with the P-S-N curves showing a duplex trend. First, the model for the P-S-N curves with duplex trend is defined. Then the proposed methodology for the design curves is described and finally validated with literature datasets.

Using rheological monitoring to determine the gelation kinetics of chitosan-based systems.

The modeling of polymeric reactions is a topic of large interest. The gelation reactions that may result from self-crosslinking or hybrid (agent based-) crosslinking are examples with interest specially in biomaterials applications. The composition of polymer entities during the reaction is hard to follow, and their concentration is not a good measure of the system dynamics. One alternative is monitoring the rheological behavior of the reacting mass, and relate the elastic modulus of the mixture with the rheological degree of conversion. In this paper we use rheological data to fit Malkin and Kulichikin (1996) [1] based models to describe the crosslinking of chitosan. First, the self-crosslinking of chitosan is considered. Then, the agent-based crosslinking reaction promoted by genipin is addressed. We use dynamical rheological data to fit the reaction models. The model fitting problem generated using Maximum Likelihood principle with heteroscedastic prediction error variance is formulated as a Dynamic Optimization problem and subsequently solved with a sequential approach. Parametric confidence regions are computed using the linear approximation of the covariance matrix at the optimum. Further, the parameters correlation matrix is also determined and used to qualitatively infer about the practical identifiability. The reaction order obtained for self-crosslinking kinetics is 1.3375 ± (0.0151) - approximately of first order -, and is 2.2402 ± (0.0373) for hybrid crosslinking (approximately of second order). In both cases we prove the error variance model is heteroskedastic and the model is identifiable. The approach proposed herein can be extended to other polymer systems.

Hierarchical maximum likelihood generalized extended stochastic gradient algorithms for bilinear‐in‐parameter systems

AbstractIn this article, we use the maximum likelihood principle and the multi‐innovation identification theory to study the identification issue of a bilinear‐in‐parameter system with autoregressive moving average noise. A maximum likelihood multi‐innovation stochastic gradient algorithm is derived to estimate the model parameters, which uses not only the current innovation but also the past innovations to improve the parameter estimation accuracy. The maximum likelihood multi‐innovation stochastic gradient algorithm has higher parameter estimation accuracy than the stochastic gradient algorithm. The simulation examples indicate that the proposed methods work well.

Evidence-Based Statistics: An Introduction to the Evidential Approach—from Likelihood Principle to Statistical Practice

Evidence-Based Statistics: An Introduction to the Evidential Approach—from Likelihood Principle to Statistical Practice