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In this paper, the performance of the repeat-accumulate codes with (ML) decoding are analyzed and compared to random codes by very tight bounds. Some simple codes are shown that perform very close to Shannon limit with maximum likelihood decoding.
This paper describes an extended-image tracking technique based on the maximum likelihood estimation.
Studies in condition monitoring literature often aim to detect rolling element bearing faults because they have one of the biggest shares among defects in turbo machinery. Accordingly, several prognosis and diagnosis methods have been devised to identify fault signatures from vibration signals. The underlying idea behind traditional indicators often revolves around tracking both cyclostationarity and abnormal impulses in the vibration signals without distinguishing the two. A recently proposed method to capture the rolling element bearing degradation lays out the groundwork for new indicator families utilizing generalized likelihood ratio test. This novel approach exploits the cyclostationarity and the impulsiveness of vibration signals independently in order to estimate the most suitable indicators for a given fault. However, the method has yet to be tested on complex experimental vibration signals such as those of a wind turbine gearbox. In this study, the approach is applied to the NREL Wind Turbine Gearbox Condition Monitoring Round Robin Study data set for bearing fault detection purposes. The data set is measured on an experimental test rig of a wind turbine gearbox, hence the complexity of the vibration signals is similar to a real case. Furthermore, the new indicators are also tested with signals that carry multiple fault signatures. The outcome demonstrates that the proposed method is capable of distinguishing between healthy and damaged vibration signals measured on a complex wind turbine gearbox.
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 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.
Here, we propose improvements to the Dynamic Likelihood Filter (DLF), a Bayesian data assimilation filtering approach, specifically tailored to wave problems. The DLF approach was developed to address the common challenge in the application of data assimilation to hyperbolic problems in the geosciences and in engineering, where observation systems are sparse in space and time. When these observations have low uncertainties, as compared to model uncertainties, the DLF exploits the inherent nature of information and uncertainties to propagate along characteristics to produce estimates that are phase aware as well as amplitude aware, as would be the case in the traditional data assimilation approach. Along characteristics, the stochastic partial differential equations underlying the linear or nonlinear stochastic dynamics are differential equations. This study focuses on developing the explicit challenges of relating dynamics and uncertainties in the Eulerian and Lagrangian frames via dynamic Gaussian processes. It also implements the approach using the ensemble Kalman filter (EnKF) and compares the DLF approach to the conventional one with respect to wave amplitude and phase estimates in linear and nonlinear wave problems. Numerical comparisons show that the DLF/EnKF outperforms the EnKF estimates, when applied to linear and nonlinear wave problems. This advantage is particularly noticeable when sparse, low uncertainty observations are used.
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 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.
ABSTRACT Obtaining accurately calibrated redshift distributions of photometric samples is one of the great challenges in photometric surveys like LSST, Euclid, HSC, KiDS, and DES. We present an inference methodology that combines the redshift information from the galaxy photometry with constraints from two-point functions, utilizing cross-correlations with spatially overlapping spectroscopic samples, and illustrate the approach on CosmoDC2 simulations. Our likelihood framework is designed to integrate directly into a typical large-scale structure and weak lensing analysis based on two-point functions. We discuss efficient and accurate inference techniques that allow us to scale the method to the large samples of galaxies to be expected in LSST. We consider statistical challenges like the parametrization of redshift systematics, discuss and evaluate techniques to regularize the sample redshift distributions, and investigate techniques that can help to detect and calibrate sources of systematic error using posterior predictive checks. We evaluate and forecast photometric redshift performance using data from the CosmoDC2 simulations, within which we mimic a DESI-like spectroscopic calibration sample for cross-correlations. Using a combination of spatial cross-correlations and photometry, we show that we can provide calibration of the mean of the sample redshift distribution to an accuracy of at least 0.002(1 + z), consistent with the LSST-Y1 science requirements for weak lensing and large-scale structure probes.
ABSTRACT We present a new approach to measure the power-law temperature density relationship $T=T_0 (\rho/ \bar{\rho })^{\gamma -1}$ and the UV background photoionization rate $\Gamma _{{{{\rm H\, {\small I}}}}{}}$ of the intergalactic medium (IGM) based on the Voigt profile decomposition of the Ly α forest into a set of discrete absorption lines with Doppler parameter b and the neutral hydrogen column density $N_{\rm H\, {\small I}}$. Previous work demonstrated that the shape of the $b-N_{{{{\rm H\, {\small I}}}}{}}$ distribution is sensitive to the IGM thermal parameters T0 and γ, whereas our new inference algorithm also takes into account the normalization of the distribution, i.e. the line-density dN/dz, and we demonstrate that precise constraints can also be obtained on $\Gamma _{{{{\rm H\, {\small I}}}}{}}$. We use density-estimation likelihood-free inference (DELFI) to emulate the dependence of the $b-N_{{{{\rm H\, {\small I}}}}{}}$ distribution on IGM parameters trained on an ensemble of 624 nyx hydrodynamical simulations at z = 0.1, which we combine with a Gaussian process emulator of the normalization. To demonstrate the efficacy of this approach, we generate hundreds of realizations of realistic mock HST/COS data sets, each comprising 34 quasar sightlines, and forward model the noise and resolution to match the real data. We use this large ensemble of mocks to extensively test our inference and empirically demonstrate that our posterior distributions are robust. Our analysis shows that by applying our new approach to existing Ly α forest spectra at z ≃ 0.1, one can measure the thermal and ionization state of the IGM with very high precision ($\sigma _{\log T_0} \sim 0.08$ dex, σγ ∼ 0.06, and $\sigma _{\log \Gamma _{{{{\rm H\, {\small I}}}}{}}} \sim 0.07$ dex).
We present simulation-based cosmological wcold dark matter (wCDM) inference using dark energy survey year 3 weak-lensing maps, via neural data compression of weak-lensing map summary statistics: power spectra, peak counts, and direct map-level compression/inference with convolutional neural networks (CNN). Using simulation-based inference, also known as likelihood-free or implicit inference, we use forward-modelled mock data to estimate posterior probability distributions of unknown parameters. This approach allows all statistical assumptions and uncertainties to be propagated through the forward-modelled mock data; these include sky masks, non-Gaussian shape noise, shape measurement bias, source galaxy clustering, photometric redshift uncertainty, intrinsic galaxy alignments, non-Gaussian density fields, neutrinos, and non-linear summary statistics. We include a series of tests to validate our inference results. This paper also describes the Gower Street simulation suite: 791 full-sky pkdgrav3 dark matter simulations, with cosmological model parameters sampled with a mixed active-learning strategy, from which we construct over 3000 mock dark energy survey lensing data sets. For wCDM inference, for which we allow –1 < w < –$\frac{1}{3}$, our most constraining result uses power spectra combined with map-level (CNN) inference. Using gravitational lensing data only, this map-level combination gives Ω m = 0.283$^{+0.020}_{–0.027}$, S 8 = 0.804$^{+0.025}_{–0.017}$, and w < –0.80 (with a 68 per cent credible interval); compared to the power spectrum inference, this is more than a factor of two improvement in dark energy parameter (Ω DE , w) precision.
Abstract This paper shows how to use conditional generative models in two-dimensional (2D) airfoil optimization to probabilistically predict good initialization points within the vicinity of the optima given the input boundary conditions, thus warm starting and accelerating further optimization. We accommodate the possibility of multiple optimal designs corresponding to the same input boundary condition and take this inversion ambiguity into account when designing our prediction framework. To this end, we first employ the conditional formulation of our previous work BézierGAN–Conditional BézierGAN (CBGAN)—as a baseline, then introduce its sibling conditional entropic BézierGAN (CEBGAN), which is based on optimal transport regularized with entropy. Compared with CBGAN, CEBGAN overcomes mode collapse plaguing conventional GANs, improves the average lift-drag (Cl/Cd) efficiency of airfoil predictions from 80.8% of the optimal value to 95.8%, and meanwhile accelerates the training process by 30.7%. Furthermore, we investigate the unique ability of CEBGAN to produce a log-likelihood lower bound that may help select generated samples of higher performance (e.g., aerodynamic performance). In addition, we provide insights into the performance differences between these two models with low-dimensional toy problems and visualizations. These results and the probabilistic formulation of this inverse problem justify the extension of our GAN-based inverse design paradigm to other inverse design problems or broader inverse problems.
The mass of the top quark is measured in 36.3 fb -1 of LHC proton–proton collision data collected with the CMS detector at $\sqrt{s}=13\,\text {Te}\hspace{-.08em}\text {V}$. The measurement uses a sample of top quark pair candidate events containing one isolated electron or muon and at least four jets in the final state. For each event, the mass is reconstructed from a kinematic fit of the decay products to a top quark pair hypothesis. A profile likelihood method is applied using up to four observables per event to extract the top quark mass. The top quark mass is measured to be 171.77 ± 0.37 GeV. This approach significantly improves the precision over previous measurements.
Cross-correlation techniques have played a long-standing and pivotal role in seismic event monitoring. However, the performance of correlation-based detectors is challenged by nuisance seismicity, or nontarget signals. Such detections are a problem when the mission is to automatically map events to the correct source region. Using aftershocks of the 2014 $M_w$ 6.0 South Napa, California, earthquake, we demonstrate the effectiveness of utilizing a dynamic correlation processor framework in a generalized likelihood ratio test (GLRT) detector configuration to minimize nontarget detections. A GLRT maximizes a detection statistic with respect to one or more unknown parameters. In this case, the detection statistic is a template signal match against the waveform in a window sliding over a data stream, and the unknown parameter is an index variable indicating group membership of the template event or events. Detected events are assigned to the event group that yields the largest detection statistic. In this work, our results show that a GLRT detector will outperform a suite of independently operating correlation and subspace detectors in terms of having a lower nontarget detection rate at a given missed detection rate. We also show that a GLRT detector composed of a few high-rank subspace detectors has a slightly higher nontarget detection rate, but a significantly lower missed detection rate, than a GLRT detector composed of many low-rank subspace detectors. The high-rank GLRT configuration produced impressive results even with marginal data (single channel, single station, and very low time bandwidth product), which bodes well for the utility of building efficient aftershock classification systems and global monitoring systems at larger scales. However, future work is required to assess performance at the regional scale and to assess the performance of the system at detecting target events not used in the detector template creation.
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.
Accurate particle identification is crucial in any high-energy physics experiment, allowing scientists to understand the unique interactions and mechanisms at play in a detector. In this project, I develop and study a likelihood-based particle identification (PID) algorithm for the Short-Baseline Near Detector, which offers a more physically motivated strategy for PID.
Astronomers who search for periodic signals using Lomb–Scargle periodograms rely on false alarm level (FAL) estimates to identify statistically significant peaks. Although FALs are often calculated from white noise models, many astronomical time series suffer from red noise. Prewhitening is a statistical technique in which a continuum model is subtracted from the log power spectrum estimate, after which the observer can proceed with a white-noise treatment. Here we present a prewhitening-based method of calculating frequency-dependent FALs. We fit power laws and autoregressive models of order 1 to each Lomb–Scargle periodogram by minimizing the Whittle approximation to the negative log-likelihood (NLL), then calculate FALs based on the best-fit model power spectrum. Our technique is a novel extension of the Whittle NLL to datasets with uneven time sampling. We demonstrate FAL calculations using observations of α Cen B, GJ 581, HD 192310, synthetic data from the radial velocity (RV) fitting challenge, and Kepler observations of a differential rotator. The Kepler data analysis shows that only true rotation signals are detected by red noise FALs, while white noise FALs suggest all spurious peaks in the low-frequency range are significant. A high-frequency sinusoid injected into α Cen B logR$'$ HK observations exceeds the 1% red noise FAL despite having only 8.9% of the power of the dominant rotation signal. In a periodogram of HD 192310 RVs, peaks associated with differential rotation and planets are detected against the 5% red noise FAL without iterative model fitting or subtraction. The software for calculating red noise–based FALs is available on GitHub.
Maximum likelihood estimation of vector parameter in finite stationary ergodic markov chains