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The maximum likelihood estimation is a general estimation procedure. It is often compared to estimation procedures like the ordinary least squares regression or generalized method of moments, to name a few. We discuss some basics about the maximum likelihood estimation, its advantages and disadvantages, and provide an example application to a gamma distribution function.
The maximum likelihood estimation is a general estimation procedure. It is often compared to estimation procedures like the ordinary least squares regression or generalized method of moments, to name a few. We discuss some basics about the maximum likelihood estimation, its advantages and disadvantages, and provide an example application to a gamma distribution function.
Maximum likelihood (ML) phylogenetic inference is widely used in phylogenomics. As heuristic searches most likely find suboptimal trees, it is recommended to conduct multiple (e.g., 10) tree searches in phylogenetic analyses. However, beyond its positive role, how and to what extent multiple tree searches aid ML phylogenetic inference remains poorly explored. Here, we found that a random starting tree was not as effective as the BioNJ and parsimony starting trees in inferring the ML gene tree and that RAxML-NG and PhyML were less sensitive to different starting trees than IQ-TREE. We then examined the effect of the number of tree searches on ML tree inference with IQ-TREE and RAxML-NG, by running 100 tree searches on 19,414 gene alignments from 15 animal, plant, and fungal phylogenomic datasets. We found that the number of tree searches substantially impacted the recovery of the best-of-100 ML gene tree topology among 100 searches for a given ML program. In addition, all of the concatenation-based trees were topologically identical if the number of tree searches was ≥10. Quartet-based ASTRAL trees inferred from 1 to 80 tree searches differed topologically from those inferred from 100 tree searches for 6/15 phylogenomic datasets. Lastly, our simulations showed that gene alignments with lower difficulty scores had a higher chance of finding the best-of-100 gene tree topology and were more likely to yield the correct trees.
Abstract We introduce maximum-likelihood fragment tomography (MLFT) as an improved circuit cutting technique for running clustered quantum circuits on quantum devices with a limited number of qubits. In addition to minimizing the classical computing overhead of circuit cutting methods, MLFT finds the most likely probability distribution for the output of a quantum circuit, given the measurement data obtained from the circuit’s fragments. We demonstrate the benefits of MLFT for accurately estimating the output of a fragmented quantum circuit with numerical experiments on random unitary circuits. Finally, we show that circuit cutting can estimate the output of a clustered circuit with higher fidelity than full circuit execution, thereby motivating the use of circuit cutting as a standard tool for running clustered circuits on quantum hardware.
We present a realization of the maximum-likelihood technique, which is one of the latest modifications of the Baade–Becker–Wesselink method. Our approach is based on nonlinear calibrations of the effective temperature and bolometric correction, which take into account metallicity and surface gravity. It allows one to estimate the key Cepheid parameters, the distance modulus, and the interstellar reddening, combining photometric and spectroscopic data (including the effective temperature data). This method is applied to a sample of 44 Galactic Cepheids for which multiphase temperature measurements are available. The additional data correction is performed to subtract the impact of the component in binary/multiple systems. We also study the effect of shock waves, whose presence in the stellar atmosphere distorts the observational data and leads to systematic errors in the obtained parameters. We determine the optimal restriction on the input data to eliminate this effect. This restriction provides accurate period–radius and period–luminosity relations that are consistent with the results in previous studies. We found the following relations: log R = (0.68 ± 0.03) · log P + (1.14 ± 0.03), M {sub v} = − (2.67 ± 0.16) · (log P − 1) − (4.14 ± 0.05).
Maximum likelihood estimation (MLE) has been used to produce perceptual scales from binary judgments of triads and quadruples. This method relies on Thurstone’s theory of a stochastic perceptual process where the perceived difference of two stimuli is the difference in their perceived strengths. It is possible that the perception of a suprathreshold difference is overestimated when adding smaller differences, a phenomenon referred to as diminishing returns. The current approach to construct a perceptual scale using MLE does not account for this phenomenon. We present a way to model the perception of differences using MLE and Thurstone’s theory, adapted to allow the possibility of diminishing returns. This method is validated using Monte Carlo simulated responses to experimental triads and can correctly model diminishing returns, the absence of diminishing returns, and the opposite of diminishing returns both in the cases when a perceptual scale is known and when the true perceived strengths of the stimuli are unknown. Additionally, this method was applied to empirical data sets to determine its feasibility in investigations of perception. Ultimately, it was found that this analysis allows for more accurate modeling of suprathreshold difference judgments, a more complete understanding of the perceptual processes underlying comparisons, and the evaluation of Thurstone’s theory of difference judgments.
A readily parallelized Maximum Likelihood Estimation (MLE) algorithm with linear computational complexity is demonstrated in real time using only measurements from an extreme ultraviolet (EUV) diagnostic to control the horizontal position of a tokamak plasma. A set of trial emissivity profiles are parameterized by the control quantity of interest (R m ), and the MLE is identified from the profile which minimizes the signal reconstruction residual. The algorithm depends on an empirically determined likelihood function with exponential form. EUV emission (λ ≈ 15eV-1keV) is captured in a poloidal plane by four 16-channel AXUV diodes mounted at different poloidal angles with radial and angular resolution sufficient to discern plasma equilibrium evolution in HBT-EP. Calculations of the plasma major radius by the system are consistent within diagnostic uncertainty for the majority of the discharge with those of: a weighted average of vertical soft X-ray or EUV chords, magnetic sensors, and an equilibrium reconstruction. The feedback system corrects for a horizontal displacement of the major radius equal to 20% of the plasma minor radius by adjusting the vertical field produced from 40 in-vessel control coils in real time. The MLE calculation is performed on a GPU in a 15 μs cycle, with similar performance in this application to a simple weighted average of vertical chords. Finally, results demonstrate horizontal position control using magnetic actuators and an optical observer.
We explore the possibility of evaluating flow harmonics by employing the maximum likelihood estimator (MLE). For a given finite multiplicity, the MLE simultaneously furnishes estimations for all the parameters of the underlying distribution function while efficiently suppressing the variance of measures. Also, the method provides a means to assess a specific class of mixed harmonics, which is not straightforwardly feasible by the approaches primarily based on particle correlations. The results are analyzed using the Wald, likelihood ratio, and score tests of hypotheses. Besides, the resultant flow harmonics obtained using MLE are compared with those derived using particle correlations and event plane methods. Here, the dependencies of extracted flow harmonics on the multiplicity of individual events and the total number of events are analyzed. It is shown that the proposed approach works efficiently to deal with the deficiency in detector acceptability. Moreover, we elaborate on a fictitious scenario where the event plane is not a well-defined quantity in the distribution function. For the latter case, the MLE is shown to largely perform better than the two-particle correlation estimator. In this regard, one concludes that the MLE furnishes a meaningful alternative to the existing approaches for flow analysis.
The three-parameter generalized extreme value distribution arises from classical univariate extreme value theory and is in common use for analysing the far tail of observed phenomena, yet important asymptotic properties of likelihood-based estimation under this standard model have not been established. In this paper, we prove that the maximum likelihood estimator is global and unique. An interesting secondary result entails the uniform consistency of a class of limit relations in a tight neighbourhood of the true shape parameter.
We present the constraint on the growth rate of structure from the combination of DESI DR1 BGS sample, Fundamental Plane, and Tully-Fisher peculiar velocity catalogues using the maximum likelihood fields method. The combined catalogue contains 415,523 galaxy redshifts and 76,616 peculiar velocity measurements. To handle the large amount of data in the DESI DR1 peculiar velocity catalogue, we significantly improve the computational efficiency by rewriting the algorithm with JAX. After removing outliers and Tully-Fisher galaxies that are affected by systematics, we find fσ 8 = 0.483 -0.043 +0.080 (stat) ± 0.018(sys), consistent within 1σ with the power spectrum and correlation function analysis using the same dataset. Combining all three measurements with appropriate correlations, the consensus measurement is fσ 8 (z eff = 0.07) = 0.450±0.055, consistent with Planck +ΛCDM cosmology (fσ 8 = 0.449±0.008). Combining with the high redshift growth rate of structure measurements from DESI ShapeFit, the constraint on the growth index is γ = 0.58±0.11, consistent with GR.
Phylogenetic trees are essential for studying biology, but their reproducibility under identical parameter settings remains unexplored. Here, we find that 3515 (18.11%) IQ-TREE-inferred and 1813 (9.34%) RAxML-NG-inferred maximum likelihood (ML) gene trees are topologically irreproducible when executing two replicates (Run1 and Run2) for each of 19,414 gene alignments in 15 animal, plant, and fungal phylogenomic datasets. Notably, coalescent-based ASTRAL species phylogenies inferred from Run1 and Run2 sets of individual gene trees are topologically irreproducible for 9/15 phylogenomic datasets, whereas concatenation-based phylogenies inferred twice from the same supermatrix are reproducible. Our simulations further show that irreproducible phylogenies are more likely to be incorrect than reproducible phylogenies. These results suggest that a considerable fraction of single-gene ML trees may be irreproducible. Increasing reproducibility in ML inference will benefit from providing analyses’ log files, which contain typically reported parameters (e.g., program, substitution model, number of tree searches) but also typically unreported ones (e.g., random starting seed number, number of threads, processor type).
Abstract In this study, we considered the fluctuation properties of some energy levels of even and odd mass radionuclides, which are used in complex phenomena. Different sequences are prepared by using all the available experimental data and analyzed by using the maximum likelihood estimation technique to get the chaoticity parameter of Abul-magd distribution. The dependence of chaoticity degrees of different radionuclides to their mass regions, their decay modes, and also their physical half-lives are studied. Our results show more chaotic behavior of odd-mass radionuclides in comparison with even–even mass and also the most Poisson-like behavior for even–even mass in the A > 150 mass region. The results offer the most regular behavior for long-lived, even mass radionuclides in comparison to other categories of half-lives. Also, we got an obvious difference between the chaoticity degrees for nuclei which undergo β + decay in comparison with radionuclides which show electron capture mode.
We establish parameter inference for the Poisson canonical polyadic (PCP) tensor model through a latent-variable formulation. Our approach exploits the observation that any random PCP tensor can be derived by marginalizing an unobservable random tensor of one dimension larger. The loglikelihood of this larger dimensional tensor, referred to as the “complete” loglikelihood, is comprised of multiple rank one PCP loglikelihoods. Using this methodology, we first derive maximum likelihood estimators for the PCP model and demonstrate that several existing algorithms for fitting non-negative matrix and tensor factorizations are Expectation-Maximization algorithms. Next, we derive the observed and expected Fisher information matrices for the PCP model. The Fisher information provides us crucial insights into the well-posedness of the tensor model, such as the role that tensor rank plays in identifiability and indeterminacy. For the special case of rank one PCP models, we demonstrate that these results are greatly simplified.
Abstract Correcting spatial orientations of groups of high-dimensional data sets such that they are all in a consistent coordinate system is often a time-consuming and error-prone process. Automation of this process can be accomplished by using Generalized Procrustes Analysis to estimate the relative orientations among a population of high-dimensional data sets. A least squares Procrustes solution is applied through a maximum likelihood estimation and random sample consensus framework for robustness. The likelihood model is comprised of a mixture distribution where inliers are modeled using t -distribution and outliers from a uniform distribution. Applications will focus on a synthetic data set that emulates triaxial acceleration data and also real shock data from a population of triaxial accelerometers. Outliers represent either non-rigid body responses, environmental noise, and/or sensor and data acquisition issues. The intended application for the methodology is to robustly automate the rotation of populations of experimentally collected triaxial accelerometer data sets to a single global coordinate system.
This repository contains 19,414 multiple sequence alignments from 15 phylogenomic studies, all gene trees, and 20,000 simulated genes and trees.
A spectral decomposition method has been implemented to identify and quantify isotopic source terms in high-resolution gamma-ray spectroscopy in static geometry and shielding scenarios. Monte Carlo simulations were used to build the response matrix of a shielded high-purity germanium detector monitoring an effluent stream with a Marinelli configuration. The decomposition technique was applied to a series of calibration spectra taken with the detector using a multi-nuclide standard. These results are compared with decay-corrected values from the calibration certificate. For most nuclei in the standard ( 241 Am, 109 Cd, 137 Cs, and 60 Co), the deviations from the certificate values were generally no more than 6% with a few outliers as high as 10%. Furthermore, for 57 Co, the radionuclide with the lowest activity, the deviations from the standard reached as high as 25%, driven by the meager statistics in the calibration spectra. In addition, a complete treatment of error propagation for the technique is presented.
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