Maximum Likelihood Calibration Research Articles

Time delay calibration techniques for receiving arrays in SNSPD-based optical communication systems

Superconducting nanowire single photon detectors (SNSPDs) have attracted considerable attention in the field of free-space optical communications, especially for ultra-long-distance communications. Calibrating the inherent time delay in the optoelectronic circuit of SNSPD arrays is critical to enabling photon detection with high time accuracy. In this paper, we propose two methods for estimating the inherent timing error: Gaussian fitting calibration (GFC) and maximum-likelihood calibration (MLC). In particular, MLC estimates the timing error by taking into account the deadtime and jitter characteristics of SNSPD. Experimental results demonstrate the effectiveness of the proposed methods.

A Maximum Likelihood Calibration of the Tip of the Red Giant Branch Luminosity from High Latitude Field Giants Using Gaia Early Data Release 3 Parallaxes

The calibration of the tip of the red giant branch (TRGB) in the I band has a direct role in determinations of the Hubble constant, a subject of recent interest due to the discrepancy between direct and indirect estimates of its value. We present a maximum likelihood method designed to obtain an independent calibration of the brightness of TRGB using Gaia parallaxes from the Early Data Release 3 (EDR3) of Milky Way field giants at high Galactic latitude. We adopt simple parameterizations for the Milky Way stellar luminosity function and density law and optimize the likelihood of the observed sample as a function of those parameters. Using parameters to partially constrain the luminosity function from other galaxies similar to the Milky Way for which high-quality TRGB data are available, we find values of the TRGB magnitude of (stat) ± 0.09 (sys) mag, where the systematic uncertainty covers the range of shape parameters found in our Milky Way sample and in reference galaxies. While APASS Data Release 9 all-sky photometry is insufficient to provide a reliable constraint on the shape of the Milky Way luminosity function, we estimate that the photometry from Gaia Data Release 3 (mid-2022) will allow better constraints on the shape, and lower statistical uncertainties on the tip by a factor of 3. With the expected releases of improved parallax measurements from Gaia, the method of calibrating the TRGB luminosity from field giants is expected to reach ∼0.01 mag uncertainty, which is an important step toward a precise TRGB-based determination of the Hubble constant.

Modeling dominant height using stand and water balance variables for loblolly pine in the Western Gulf, US

Site-index models based on dominant height and age are commonly accepted measures of site productivity in forest plantations. Therefore, reliable estimates of dominant height over time are critical, as they provide the foundations for site productivity estimates used in growth and yield models. Forest site productivity depends on the combination of many environmental factors, whereas tree height is only a general proxy indicator of these factors interacting over time, and as such, subject to large errors. Hence, selection of appropriate environmental variables along with field-based data is expected to result in more consistent estimates. Although previous studies have incorporated climatic variables into site-index models, there is still a lack of understanding among the forest research community with respect to the selection of suitable climatic variables. Models including climatic water balance components such as water-deficit and excess-water are scarce. These components are especially important to address the influence of drought on plant growth. The main objective of this study is to evaluate the change in dominant height estimates of forest stands with respect to changes in water balance components. High-resolution actual evapotranspiration (AET) and potential evapotranspiration (PET) were combined to determine water excess/deficit of sites. These were incorporated into a loblolly pine polymorphic site index model using a generalized algebraic difference approach and maximum likelihood calibration methods that accounted for long-term uncertainty in the results. Our model further improves the precision in dominant height estimates for loblolly pine in the southeast US.

Correction to Maximum Likelihood Calibration of the UNRES Force Field for Simulation of Protein Structure and Dynamics.

ADVERTISEMENT RETURN TO ISSUEPREVErratumNEXTORIGINAL ARTICLEThis notice is a correctionCorrection to Maximum Likelihood Calibration of the UNRES Force Field for Simulation of Protein Structure and DynamicsPaweł Krupa, Anna Hałabis, Wioletta Żmudzińska, Stanisław Ołdziej, Harold A. Scheraga, and Adam Liwo*Cite this: J. Chem. Inf. Model. 2018, 58, 1, 206Publication Date (Web):December 28, 2017Publication History Published online28 December 2017Published inissue 22 January 2018https://doi.org/10.1021/acs.jcim.7b00716Copyright © 2017 American Chemical SocietyRIGHTS & PERMISSIONSArticle Views801Altmetric-Citations-LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (225 KB) Get e-Alerts Get e-Alerts

Maximum Likelihood Calibration of the UNRES Force Field for Simulation of Protein Structure and Dynamics.

By using the maximum likelihood method for force-field calibration recently developed in our laboratory, which is aimed at achieving the agreement between the simulated conformational ensembles of selected training proteins and the corresponding ensembles determined experimentally at various temperatures, the physics-based coarse-grained UNRES force field for simulations of protein structure and dynamics was optimized with seven small training proteins exhibiting a variety of secondary and tertiary structures. Four runs of optimization, in which the number of optimized force-field parameters was gradually increased, were carried out, and the resulting force fields were subsequently tested with a set of 22 α-, 12 β-, and 12 α + β-proteins not used in optimization. The variant in which energy-term weights, local, and correlation potentials, side-chain radii, and anisotropies were optimized turned out to be the most transferable and outperformed all previous versions of UNRES on the test set.

A Method and On-Line Tool for Maximum Likelihood Calibration of Immunoblots and Other Measurements That Are Quantified in Batches.

Experimental measurements require calibration to transform measured signals into physically meaningful values. The conventional approach has two steps: the experimenter deduces a conversion function using measurements on standards and then calibrates (or normalizes) measurements on unknown samples with this function. The deduction of the conversion function from only the standard measurements causes the results to be quite sensitive to experimental noise. It also implies that any data collected without reliable standards must be discarded. Here we show that a “1-step calibration method” reduces these problems for the common situation in which samples are measured in batches, where a batch could be an immunoblot (Western blot), an enzyme-linked immunosorbent assay (ELISA), a sequence of spectra, or a microarray, provided that some sample measurements are replicated across multiple batches. The 1-step method computes all calibration results iteratively from all measurements. It returns the most probable values for the sample compositions under the assumptions of a statistical model, making them the maximum likelihood predictors. It is less sensitive to measurement error on standards and enables use of some batches that do not include standards. In direct comparison of both real and simulated immunoblot data, the 1-step method consistently exhibited smaller errors than the conventional “2-step” method. These results suggest that the 1-step method is likely to be most useful for cases where experimenters want to analyze existing data that are missing some standard measurements and where experimenters want to extract the best results possible from their data. Open source software for both methods is available for download or on-line use.

On Calibration of Three-Axis Magnetometer

Magnetometer has received wide applications in attitude determination and scientific measurements. Calibration is an important step for any practical magnetometer use. The most popular three-axis magnetometer calibration methods are attitude-independent and have been founded on an approximate maximum likelihood (ML) estimation with a quartic subjective function, derived from the fact that the magnitude of the calibrated measurements should be constant in a homogeneous magnetic field. This paper highlights the shortcomings of those popular methods and proposes to use the quadratic optimal ML estimation instead for magnetometer calibration. Simulation and test results show that the optimal ML calibration is superior to the approximate ML methods for magnetometer calibration in both accuracy and stability, especially for those situations without sufficient attitude excitation. The significant benefits deserve the moderately increased computation burden. The main conclusion obtained in the context of magnetometer in this paper is potentially applicable to various kinds of three-axis sensors.

Taxon selection using statistical learning techniques to improve transfer function prediction

Transfer functions are widely used in palaeoecology to provide quantitative environmental reconstructions using biological proxies. Most models use all but the rarest taxa present in the training set, even though many may be unrelated to the environmental variable of interest. We hypothesise that retaining such non-informative taxa will reduce model robustness and present a method for variable selection motivated by the statistical learning algorithm in random forests. We apply our species-pruning algorithm into weighted averaging (WA) and maximum likelihood calibration of response curves (MLRCs), and compare results of boosted regression trees (BRTs) using artificial and real datasets. Results from the artificial data show that WA is particularly sensitive to the influence of both non-informative taxa and secondary environmental variables in the training set or fossil assemblage, and that BRTs are relatively immune to these effects. Furthermore, species-pruned WA and MLRCs offer substantial improvements over all-species models when the training set includes non-informative taxa but does not guard against confounding effects when species have bi- or multivariate responses to the primary and one or more secondary variables. Tests with a limited set of examples of real data indicate that BRTs, MLRCs or species-pruned models have no apparent advantage over WA. We discuss possible reasons for this contradiction and suggest that more tests are needed to properly evaluate BRTs and species-pruned models.

A Received Signal Strength-based Primary User Localization Scheme for Cognitive Radio Sensor Networks Using Underlay Model-based Spectrum Access

For cognitive radio sensor networks (CRSNs) that use underlay-based spectrum access, the location of the primary user (PU) plays an important role in the power control of the secondary users (SUs), because the SUs must keep the minimum interference level required by the PU. Received signal strength (RSS)-based localization schemes provide low-cost implementation and low complexity, thus it is suitable for the PU localization in CRSNs. However, the RSS-based localization schemes have a high localization error because they use an inexact path loss exponent (PLE). Thus, applying a RSS-based localization scheme into the PU localization would cause a high interference to the PU. In order to reduce the localization error and improve the channel reuse rate, we propose a RSS-based PU localization scheme that uses distance calibration for CRSNs using underlay model-based spectrum access. Through the simulation results, it is shown that the proposed scheme can provide less localization error as well as more spectrum utilization than the RSS-based PU localization using the mean and the maximum likelihood calibration.

Maximum likelihood calibration of a magnetometer using inertial sensors

Magnetometers and inertial sensors (accelerometers and gyroscopes) are widely used to estimate 3D orientation. For the orientation estimates to be accurate, the sensor axes need to be aligned and the magnetometer needs to be calibrated for sensor errors and for the presence of magnetic disturbances. In this work we use a grey-box system identification approach to compute maximum likelihood estimates of the calibration parameters. An experiment where the magnetometer data is highly disturbed shows that the algorithm works well on real data, providing good calibration results and improved heading estimates. We also provide an identifiability analysis to understand how much rotation is needed to be able to solve the calibration problem.

Maximum-Likelihood Calibration of an X-ray Computed Tomography System.

We present a maximum-likelihood (ML) method for calibrating the geometrical parameters of an x-ray computed tomography (CT) system. This method makes use of the full image data and not a reduced set of data. This algorithm is particularly useful for CT systems that change their geometry during the CT acquisition, such as an adaptive CT scan. Our ML search method uses a contracting-grid algorithm that does not require initial starting values to perform its estimate, thus avoiding problems associated with choosing initialization values.

Inference models for tidal flat elevation and sediment grain size: A Preliminary approach on tidal flat macrobenthic community

A vertical transect with 4 km length was established for the macrofaunal survey on the Chokchon macrotidal flat in Kyeonggi Bay, Incheon, Korea, 1994. Tidal elevation (m) and sediment mean grain size (φ) were inversely predicted by the transfer functions from the faunal assemblages. Three methods: weighted average using optimum value (WA), tolerance weighted version of the weighted average (WAT ) and maximum likelihood calibration (MLC) were employed. Estimates of tidal elevation and mean grain size obtained by using the three different methods showed positively corresponding trends with the observations. The estimates of MLC were found to have the minimum value of sum of squares due to errors (SSE). When applied to the previous data (1990~1992), each of three inference models exhibited high predictive power. This result implied there are visible relationships between species composition and faunas’ critical environmental factors. Although a potential significance of the two major abiotic factors was re-affirmed, a weak tendency of biological interaction was detected from faunal distribution patterns across the flat. In comparison to the spatial and temporal patterns of the estimates, it was suggested that sediment characteristics were the primary factors regulating the distribution of macrofaunal assemblages, rather than tidal elevation, and the species composition may be sensitively determined by minute changes in substratum properties on a tidal flat.

Inverse stochastic moment analysis of steady state flow in randomly heterogeneous media

Nonlocal stochastic moment equations have been used successfully to analyze steady state and transient flow in randomly heterogeneous media conditional on measured values of medium properties. We present a nonlinear geostatistical inverse algorithm for steady state flow that makes it possible to further condition such analyses on measured values of state variables. Our approach accounts for all scales of spatial variability resolvable by the computational grid. It is based on recursive finite element approximations of exact nonlocal first and second conditional moment equations. Hydraulic conductivity is parameterized geostatistically on the basis of measured values at discrete locations and unknown values at discrete “pilot points.” Prior estimates of pilot point values are obtained (optionally) by generalized kriging. Posterior estimates at pilot points and (optionally) at measurement points are obtained by calibrating mean flow against measured values of head. The parameters are projected onto a computational grid via kriging. Maximum likelihood calibration allows estimating not only hydraulic but also (optionally) unknown variogram parameters with or without prior information about the former. The approach yields covariance matrices for parameter estimation as well as head and flux prediction errors, the latter being obtained a posteriori. We implement our inverse approach on highly and mildly heterogeneous media under superimposed mean uniform and convergent flows in a bounded two‐dimensional domain. Our examples illustrate how conductivity and head data act separately and jointly to reduce parameter estimation errors and to model predictive uncertainty. We also evaluate the functional form of the log conductivity variogram and its parameters using likelihood‐based model discrimination criteria.

Active array sensor localization

Sensor array processing algorithms for source localization often require precise knowledge of the sensor locations, which is often not available in practice. Errors in the sensor locations are known to degrade severely the performance of these algorithms. This paper proposes iterative damped Gauss-Newton maximum likelihood array sensor localization algorithms using known calibration source signals. Cramér-Rao bound (CRB) expressions for the sensor location parameters are found for this problem. Two calibration source signal models are considered. One assumes that each signal waveform is known up to a scaling constant and phase, while the other requires complete knowledge of the signal waveform. For uncorrelated, completely known calibration signals, a necessary and sufficient condition for the optimal choice of the source bearings that minimizes the sensor position CRB variances is presented. Numerical results illustrate that the maximum likelihood calibration algorithms attain the CRB asymptotically.

Dissolved organic carbon reconstructions from diatom assemblages in PIRLA project lakes, North America

Diatom-based palaeolimnological reconstructions of dissolved organic carbon (DOC) are presented for four regional data sets of the North American ‘Paleoecological Investigation of Recent Lake Acidification (PIRLA)’ project, and for a combined, three-region set. Species optima and tolerances along the DOC gradient were estimated by using maximum likelihood and weighted-averaging regression. Weighted-averaging regression appears to be the most robust and tractable technique for estimating optima, and the apparent error (mean standard error of the relation) was as good for weighted-averaging calibration as for maximum likelihood calibration. Calculated species optima are not entirely consistent among regions and the best ‘indicators’ for DOC in the PIRLA data-sets are not in good agreement with those found in the literature. Example reconstructions demonstrate that DOC changes are often less than 100 µmol l-1, and that the DOC declines in some recently acidified lakes parallel reconstructed pH declines.

Inferring pH from diatoms: a comparison of old and new calibration methods

Two new methods for inferring pH from diatoms are presented. Both are based on the observation that the relationships between diatom taxa and pH are often unimodal. The first method is maximum likelihood calibration based on Gaussian logit response curves of taxa against pH. The second is weighted averaging. In a lake with a particular pH, taxa with an optimum close to the lake pH will be most abundant, so an intuitively reasonable estimate of the lake pH is to take a weighted average of the pH optima of the species present. Optima and tolerances of diatom taxa were estimated from contemporary pH and proportional diatom counts in littoral zone samples from 97 pristine soft water lakes and pools in Western Europe. The optima showed a strong relation with Hustedt's pH preference groups. The two new methods were then compared with existing calibration methods on the basis of differences between inferred and observed pH in a test set of 62 additional samples taken between 1918 and 1983. The methods were ranked in order of performance as follows (between brackets the standard error of inferred pH in pH units); maximum likelihood (0.63) > weighted averaging (0.71) = multiple regression using pH groups (0.71) = the Gasse & Tekaia method (0.71) > Renberg & Hellberg's Index B (0.83) » multiple regression using taxa (2.2). The standard errors are larger than those usually obtained from surface sediment samples. The relatively large standard may be due to seasonal variation and to the effects of other factors such as humus content. The maximum likelihood method is statistically rigorous and can in principle be extended to allow for additional environmental factors. It is computer intensive however. The weighted averaging approach is a good approximation to the maximum likelihood method and is recommended as a practical and robust alternative.

Note on the maximum likelihood calibration on Dial's assignment method

This note demonstrates that it is possible to obtain a maximum likelihood estimation of the ø parameter in Dial's assignment method without repeated application of the assignment algorithm implicit in the procedure introduced recently by Robillard (1974). While the two methods produce comparable results, that outlined here greatly reduces sample requirements, and seems to reduce computation time, based on comparison with Robillard's example.