Likelihood-based Methods Research Articles

A Likelihood-Based Triangulation Method for Uncertainties in Through-Water Depth Mapping

Coastal environments, which are crucial for economic and strategic reasons, heavily rely on accurate bathymetry for safe navigation and resource monitoring. Recent advancements in through-water photogrammetry have shown promise in mapping shallow waters efficiently. However, robust uncertainty modeling methods for these techniques, especially in challenging coastal environments, are lacking. This study introduces a novel likelihood-based approach for through-water photogrammetry, focusing on uncertainties associated with camera pose—a key factor affecting depth mapping accuracy. Our methodology incorporates probabilistic modeling and stereo-photogrammetric triangulation to provide realistic estimates of uncertainty in Water Column Depth (WCD) and Water–Air Interface (WAI) height. Using simulated scenarios for both drone and airborne surveys, we demonstrate that viewing geometry and camera pose quality significantly influence resulting uncertainties, often overshadowing the impact of depth itself. Our results reveal the superior performance of the likelihood ratio statistic in scenarios involving high attitude noise, high flight altitude, and complex viewing geometries. Notably, drone-based applications show particular promise, achieving decimeter-level WCD precision and WAI height estimations comparable to high-quality GNSS measurements when using large samples. These findings highlight the potential of drone-based surveys in producing more accurate bathymetric charts for shallow coastal waters. This research contributes to the refinement of uncertainty quantification in bathymetric charting and sets a foundation for future advancements in through-water surveying methodologies.

Crossover evaluation of time-of-flight-based attenuation correction in brain 18F-FDG and 18F-flutemetamol PET.

Brain-dedicated positron emission tomography (PET) systems offer high spatial resolution and sensitivity for accurate clinical assessments. Attenuation correction (AC) is important in PET imaging, particularly in brain studies. This study assessed the reproducibility of attenuation maps (µ-maps) generated by a specialized time-of-flight (TOF) brain-dedicated PET system for imaging using different PET tracers. Twelve subjects underwent both 18F-fluorodeoxyglucose (FDG)-PET and 18F-flutemetamol (FMM) amyloid-PET scans. Images were reconstructed with µ-maps obtained by a maximum likelihood-based AC method. Voxel-based and region-based analyses were used to compare µ-maps obtained with FDG-PET versus FMM-PET; FDG-PET images reconstructed using an FDG-PET µ-map (FDG × FDG) versus those reconstructed with an FMM-PET µ-map (FDG × FMM); and FMM-PET images reconstructed using an FDG-PET µ-map (FMM × FDG) versus those reconstructed with an FMM-PET µ-map (FMM × FMM). Small but significant differences in µ-maps were observed between tracers, primarily in bone regions. In the comparison between the µ-maps obtained with FDG-PET and FMM-PET, the µ-maps obtained with FDG-PET had higher µ-values than those obtained with FMM-PET in the parietal regions of the head and skull, in a portion of the cerebellar dentate nucleus and on the surface of the frontal lobe. The comparison between FDG and FDG × FMM values in different regions yielded findings similar to those of the µ-maps comparison. FDG × FMM values were significantly higher than FDG values in the bilateral temporal bones and a small part of the temporal lobe. Similarly, FMM values were significantly higher than FMM × FDG values in the bilateral temporal bones. FMM × FDG values were significantly higher than FMM values in a small area of the right cerebellar hemisphere. However, the relative errors in these µ-maps were within ± 4%, suggesting that they are clinically insignificant. In PET images reconstructed with the original and swapped µ-maps, the relative errors were within ± 7% and the quality was nearly equivalent. These findings suggest the clinical reliability of the AC method without an external radiation source in TOF brain-dedicated PET systems.

A likelihood-based monitoring method for social networks with auto-correlated labeled Poisson model

Social network monitoring aims to detect any significant change in the structure of communications from the normal condition. The normal condition can be a set of networks considered as a reference set. This set is represented in dynamic cases by a probability model. Statistical process control methods can be applied to signal changes in the reference set. These signals can be useful for decision-makers in various applications, from marketing analysis to criminal investigations. In most of the developed models, the networks are assumed independent over time. However, this assumption may be questioned in real-world applications. Accordingly, this article formulates the social network as an auto-correlated labeled Poisson model and monitors it using a control method based on likelihood statistics. A simulation study is performed to evaluate the performance of the proposed methods in terms of the average run length criterion. The obtained results revealed that the proposed methods can reliably detect significant changes.

Scalable CNN-based classification of selective sweeps using derived allele frequencies.

Selective sweeps can successfully be distinguished from neutral genetic data using summary statistics and likelihood-based methods that analyze single nucleotide polymorphisms (SNPs). However, these methods are sensitive to confounding factors, such as severe population bottlenecks and old migration. By virtue of machine learning, and specifically convolutional neural networks (CNNs), new accurate classification models that are robust to confounding factors have been recently proposed. However, such methods are more computationally expensive than summary-statistic-based ones, yielding them impractical for processing large-scale genomic data. Moreover, SNP data are frequently preprocessed to improve classification accuracy, further exacerbating the long analysis times. To this end, we propose a 1D CNN-based model, dubbed FAST-NN, that does not require any preprocessing while using only derived allele frequencies instead of summary statistics or raw SNP data, thereby yielding a sample-size-invariant, scalable solution. We evaluated several data fusion approaches to account for the variance of the density of genetic diversity across genomic regions (a selective sweep signature), and performed an extensive neural architecture search based on a state-of-the-art reference network architecture (SweepNet). The resulting model, FAST-NN, outperforms the reference architecture by up to 12% inference accuracy over all challenging evolutionary scenarios with confounding factors that were evaluated. Moreover, FAST-NN is between 30× and 259× faster on a single CPU core, and between 2.0× and 6.2× faster on a GPU, when processing sample sizes between 128 and 1000 samples. Our work paves the way for the practical use of CNNs in large-scale selective sweep detection. https://github.com/SjoerdvandenBelt/FAST-NN.

Kilonova Spectral Inverse Modelling with Simulation-based Inference: An Amortized Neural Posterior Estimation Analysis

Kilonovae represent a category of astrophysical transients, identifiable as the electromagnetic (EM) counterparts associated with the coalescence events of binary systems comprising neutron stars and neutron star–black hole pairs. They act as probes for heavy-element nucleosynthesis in astrophysical environments. These studies rely on an inference of the physical parameters (e.g., ejecta mass, velocity, composition) that describe kilonovae-based on EM observations. This is a complex inverse problem typically addressed with sampling-based methods such as Markov Chain Monte Carlo or nested sampling algorithms. However, repeated inferences can be computationally expensive, due to the sequential nature of these methods. This poses a significant challenge to ensuring the reliability and statistical validity of the posterior approximations and, thus, the inferred kilonova parameters themselves. We present a novel approach: simulation-based inference using simulations produced by KilonovaNet. Our method employs an ensemble of amortized neural posterior estimation (ANPE) with an embedding network to directly predict posterior distributions from simulated spectral energy distributions. We take advantage of the quasi-instantaneous inference time of ANPE to demonstrate the reliability of our posterior approximations using diagnostics tools, including coverage diagnostic and posterior predictive checks. We further test our model with real observations from AT 2017gfo, the only kilonova with multimessenger data, demonstrating agreement with previous likelihood-based methods while reducing inference time down to a few seconds. The inference results produced by ANPE appear to be conservative and reliable, paving the way for testable and more efficient kilonova parameter inference.

Structured methods for parameter inference and uncertainty quantification for mechanistic models in the life sciences.

Parameter inference and uncertainty quantification are important steps when relating mathematical models to real-world observations and when estimating uncertainty in model predictions. However, methods for doing this can be computationally expensive, particularly when the number of unknown model parameters is large. The aim of this study is to develop and test an efficient profile likelihood-based method, which takes advantage of the structure of the mathematical model being used. We do this by identifying specific parameters that affect model output in a known way, such as a linear scaling. We illustrate the method by applying it to three toy models from different areas of the life sciences: (i) a predator-prey model from ecology; (ii) a compartment-based epidemic model from health sciences; and (iii) an advection-diffusion reaction model describing the transport of dissolved solutes from environmental science. We show that the new method produces results of comparable accuracy to existing profile likelihood methods but with substantially fewer evaluations of the forward model. We conclude that our method could provide a much more efficient approach to parameter inference for models where a structured approach is feasible. Computer code to apply the new method to user-supplied models and data is provided via a publicly accessible repository.

Polygenic hazard score models for the prediction of Alzheimer's free survival using the lasso for Cox's proportional hazards model.

The prediction of the susceptibility of an individual to a certain disease is an important and timely research area. An established technique is to estimate the risk of an individual with the help of an integrated risk model, that is, a polygenic risk score with added epidemiological covariates. However, integrated risk models do not capture any time dependence, and may provide a point estimate of the relative risk with respect to a reference population. The aim of this work is twofold. First, we explore and advocate the idea of predicting the time-dependent hazard and survival (defined as disease-free time) of an individual for the onset of a disease. This provides a practitioner with a much more differentiated view of absolute survival as a function of time. Second, to compute the time-dependent risk of an individual, we use published methodology to fit a Cox's proportional hazard model to data from a genetic SNP study of time to Alzheimer's disease (AD) onset, using the lasso to incorporate further epidemiological variables such as sex, APOE (apolipoprotein E, a genetic risk factor for AD) status, 10 leading principal components, and selected genomic loci. We apply the lasso for Cox's proportional hazards to a data set of 6792 AD patients (composed of 4102 cases and 2690 controls) and 87 covariates. We demonstrate that fitting a lasso model for Cox's proportional hazards allows one to obtain more accurate survival curves than with state-of-the-art (likelihood-based) methods. Moreover, the methodology allows one to obtain personalized survival curves for a patient, thus giving a much more differentiated view of the expected progression of a disease than the view offered by integrated risk models. The runtime to compute personalized survival curves is under a minute for the entire data set of AD patients, thus enabling it to handle datasets with 60,000-100,000 subjects in less than 1 h.

MSR94 A Flexible, Likelihood-Based Method for Estimating Underlying Distributions, Mean and SD-Based on Reported Quantiles Such as Median and Inter-Quartile Range

MSR94 A Flexible, Likelihood-Based Method for Estimating Underlying Distributions, Mean and SD-Based on Reported Quantiles Such as Median and Inter-Quartile Range

Likelihood-based instrumental variable methods for Cox proportional hazards model

Likelihood-based instrumental variable methods for Cox proportional hazards model

Adaptive Robust Control of Uncertain Euler-Lagrange Systems Using Gaussian Processes.

This article proposes a novel adaptive robust control approach based on Gaussian processes (GPs) for the high-precision tracking problem of uncertain Euler-Lagrange (EL) systems with time-varying external disturbances. Given a prior dynamic model, the GP regression (GPR) technique is employed to obtain a nonparametric data-based uncertainty model, including its probabilistic confidence intervals. Based on the adaptive sliding mode control (ASMC) framework, the posterior means of GPs are utilized for dynamic compensation, whereas the posterior variances are applied to adjust the feedback gains. This proposed control strategy is robust against significant system uncertainty with low feedback gains. A novel adaptive law for updating hyperparameters based on tracking error feedback is presented, thereby improving the performance of both tracking control and GP modeling simultaneously. Compared to existing likelihood-based optimization methods, this hyperparameter adaptive law enables data-efficient and fast uncertainty learning for control applications. The proposed control strategy guarantees the semiglobal asymptotic convergence to zero tracking error with a specified probability. Simulations using an underwater robot model demonstrate that the utilization of GPs and hyperparameter adaptive law significantly improves the performance of tracking control and uncertainty learning.

Artificial neural networks for model identification and parameter estimation in computational cognitive models.

Computational cognitive models have been used extensively to formalize cognitive processes. Model parameters offer a simple way to quantify individual differences in how humans process information. Similarly, model comparison allows researchers to identify which theories, embedded in different models, provide the best accounts of the data. Cognitive modeling uses statistical tools to quantitatively relate models to data that often rely on computing/estimating the likelihood of the data under the model. However, this likelihood is computationally intractable for a substantial number of models. These relevant models may embody reasonable theories of cognition, but are often under-explored due to the limited range of tools available to relate them to data. We contribute to filling this gap in a simple way using artificial neural networks (ANNs) to map data directly onto model identity and parameters, bypassing the likelihood estimation. We test our instantiation of an ANN as a cognitive model fitting tool on classes of cognitive models with strong inter-trial dependencies (such as reinforcement learning models), which offer unique challenges to most methods. We show that we can adequately perform both parameter estimation and model identification using our ANN approach, including for models that cannot be fit using traditional likelihood-based methods. We further discuss our work in the context of the ongoing research leveraging simulation-based approaches to parameter estimation and model identification, and how these approaches broaden the class of cognitive models researchers can quantitatively investigate.

Spectral neural approximations for models of transcriptional dynamics

The advent of high-throughput transcriptomics provides an opportunity to advance mechanistic understanding of transcriptional processes and their connections to cellular function at an unprecedented, genome-wide scale. These transcriptional systems, which involve discrete stochastic events, are naturally modeled using chemical master equations (CMEs), which can be solved for probability distributions to fit biophysical rates that govern system dynamics. While CME models have been used as standards in fluorescence transcriptomics for decades to analyze single-species RNA distributions, there are often no closed-form solutions to CMEs that model multiple species, such as nascent and mature RNA transcript counts. This has prevented the application of standard likelihood-based statistical methods for analyzing high-throughput, multi-species transcriptomic datasets using biophysical models. Inspired by recent work in machine learning to learn solutions to complex dynamical systems, we leverage neural networks and statistical understanding of system distributions to produce accurate approximations to a steady-state bivariate distribution for a model of the RNA life cycle that includes nascent and mature molecules. The steady-state distribution to this simple model has no closed-form solution and requires intensive numerical solving techniques: our approach reduces likelihood evaluation time by several orders of magnitude. We demonstrate two approaches, whereby solutions are approximated by 1) learning the weights of kernel distributions with constrained parameters or 2) learning both weights and scaling factors for parameters of kernel distributions. We show that our strategies, denoted by kernel weight regression and parameter-scaled kernel weight regression, respectively, enable broad exploration of parameter space and can be used in existing likelihood frameworks to infer transcriptional burst sizes, RNA splicing rates, and mRNA degradation rates from experimental transcriptomic data.

Does Sample Size, Sampling Strategy, or Handling of Concentrations Below the Lower Limit of Quantification Matter When Externally Evaluating Population Pharmacokinetic Models?

Precision dosing requires selecting the appropriate population pharmacokinetic model, which can be assessed through external evaluations (EEs). The lack of understanding of how different study design factors influence EE study outcomes makes it challenging to select the most suitable model for clinical use. This study aimed to evaluate the impact of sample size, sampling strategy, and handling of concentrations below thelowerlimit of quantification (BLQ) on the outcomes of EE for four population pharmacokinetic models using vancomycin and tobramycin as examples. Three virtual patient populations undergoing vancomycin or tobramycin therapy were simulated with varying sample size and sampling scenarios. The three approaches used to handle BLQ data were to (1) discard them, (2) impute them as LLOQ/2, or (3) use a likelihood-based approach. EEs were performed with NONMEM and R. Sample size did not have an important impact on the EE results for a given scenario. Increasing the number of samples per patient did not improve predictive performance for two out of the three evaluated models. Evaluating a model developed with rich sampling did not result in better performance than those developed with regular therapeutic drug monitoring. A likelihood-based method to handle BLQ samples impacted the outcomes of the EE with lower bias for predicted troughs. This study suggests that a large sample size may not be necessary for an EE study, and models selected based on TDM may be more generalizable. The study highlights the need for guidelines for EE of population pharmacokinetic models for clinical use.

Leveraging new methods for comprehensive characterization of mitochondrial DNA in esophageal squamous cell carcinoma

BackgroundMitochondria play essential roles in tumorigenesis; however, little is known about the contribution of mitochondrial DNA (mtDNA) to esophageal squamous cell carcinoma (ESCC). Whole-genome sequencing (WGS) is by far the most efficient technology to fully characterize the molecular features of mtDNA; however, due to the high redundancy and heterogeneity of mtDNA in regular WGS data, methods for mtDNA analysis are far from satisfactory.MethodsHere, we developed a likelihood-based method dMTLV to identify low-heteroplasmic mtDNA variants. In addition, we described fNUMT, which can simultaneously detect non-reference nuclear sequences of mitochondrial origin (non-ref NUMTs) and their derived artifacts. Using these new methods, we explored the contribution of mtDNA to ESCC utilizing the multi-omics data of 663 paired tumor-normal samples.ResultsdMTLV outperformed the existing methods in sensitivity without sacrificing specificity. The verification using Nanopore long-read sequencing data showed that fNUMT has superior specificity and more accurate breakpoint identification than the current methods.Leveraging the new method, we identified a significant association between the ESCC overall survival and the ratio of mtDNA copy number of paired tumor-normal samples, which could be potentially explained by the differential expression of genes enriched in pathways related to metabolism, DNA damage repair, and cell cycle checkpoint. Additionally, we observed that the expression of CBWD1 was downregulated by the non-ref NUMTs inserted into its intron region, which might provide precursor conditions for the tumor cells to adapt to a hypoxic environment. Moreover, we identified a strong positive relationship between the number of mtDNA truncating mutations and the contribution of signatures linked to tumorigenesis and treatment response.ConclusionsOur new frameworks promote the characterization of mtDNA features, which enables the elucidation of the landscapes and roles of mtDNA in ESCC essential for extending the current understanding of ESCC etiology. dMTLV and fNUMT are freely available from https://github.com/sunnyzxh/dMTLV and https://github.com/sunnyzxh/fNUMT, respectively.

Effect of instrumental polarization with a half-wave plate on the B-mode signal: prediction and correction

We study the effect of incident unpolarized signal converted to polarized light produced by a realistic half-wave plate (HWP) and evaluate the impact of the effect in the measurement of Cosmic Microwave Background (CMB) B-mode polarization signal targeting to probe the tensor-to-scalar ratio r. The HWP is modeled with the Mueller formalism, and coefficients are decomposed for any incident angle into harmonics of the HWP rotation frequency due to azimuthal angle dependence. Although we use a general formalism, band-averaged matrix coefficients are calculated as an example for a 9-layer sapphire HWP using EM propagation simulations. We perform simulations of multi-detector observations in a band centered at 140 GHz using LiteBIRD instrumental configuration. We show both theoretically and with the simulations that most of the artefacts on Stokes parameter maps are produced by the dipole leakage on B-modes induced by the fourth harmonics MQI (4f) and MUI (4f). The resulting effect is strongly linked to the spin-2 focal plane scanning cross linking parameters. We develop a maximum likelihood-based method to correct the IP leakage by joint fitting of the Mueller matrix coefficients as well as the Stokes parameter maps. We show that the residual leakage after correction leads to an additional noise limited uncertainty on r of the order of 10-7, independently of the value of the Mueller matrix coefficients. We discuss the impact of the monopole signal and the potential coupling with other systematic effects such as gain variations and detector nonlinearities.

A Spectral Method for Identifiable Grade of Membership Analysis with Binary Responses.

Grade of membership (GoM) models are popular individual-level mixture models for multivariate categorical data. GoM allows each subject to have mixed memberships in multiple extreme latent profiles. Therefore, GoM models have a richer modeling capacity than latent class models that restrict each subject to belong to a single profile. The flexibility of GoM comes at the cost of more challenging identifiability and estimation problems. In this work, we propose a singular value decomposition (SVD)-based spectral approach to GoM analysis with multivariate binary responses. Our approach hinges on the observation that the expectation of the data matrix has a low-rank decomposition under a GoM model. For identifiability, we develop sufficient and almost necessary conditions for a notion of expectation identifiability. For estimation, we extract only a few leading singular vectors of the observed data matrix and exploit the simplex geometry of these vectors to estimate the mixed membership scores and other parameters. We also establish the consistency of our estimator in the double-asymptotic regime where both the number of subjects and the number of items grow to infinity. Our spectral method has a huge computational advantage over Bayesian or likelihood-based methods and is scalable to large-scale and high-dimensional data. Extensive simulation studies demonstrate the superior efficiency and accuracy of our method. We also illustrate our method by applying it to a personality test dataset.

Robust expansion of phylogeny for fast-growing genome sequence data.

Massive sequencing of SARS-CoV-2 genomes has urged novel methods that employ existing phylogenies to add new samples efficiently instead of de novo inference. 'TIPars' was developed for such challenge integrating parsimony analysis with pre-computed ancestral sequences. It took about 21 seconds to insert 100 SARS-CoV-2 genomes into a 100k-taxa reference tree using 1.4 gigabytes. Benchmarking on four datasets, TIPars achieved the highest accuracy for phylogenies of moderately similar sequences. For highly similar and divergent scenarios, fully parsimony-based and likelihood-based phylogenetic placement methods performed the best respectively while TIPars was the second best. TIPars accomplished efficient and accurate expansion of phylogenies of both similar and divergent sequences, which would have broad biological applications beyond SARS-CoV-2. TIPars is accessible from https://tipars.hku.hk/ and source codes are available at https://github.com/id-bioinfo/TIPars.

Genetic correlation and causal associations between circulating C-reactive protein levels and lung cancer risk.

We aimed to characterize genetic correlations and causal associations between circulating C-reactive protein (CRP) levels and the risk of lung cancer (LC). Leveraging summary statistics from genome-wide association studies of circulating CRP levels among 575,531 individuals of European ancestry, and LC risk among 29,266 cases and 56,450 controls, we investigated genetic associations of circulating CRP levels with the risk of overall lung cancer and its histological subtypes, by using linkage disequilibrium score (LDSC) regression and Mendelian randomization (MR) analyses. Significant positive genetic correlations between circulating CRP levels and the risk of LC and its histological subtypes were identified from LDSC regression, with correlation coefficients ranging from 0.12 to 0.26, and all false discovery adjusted p < 0.05. Univariable MR demonstrated a nominal association between CRP levels and an increased risk of lung squamous cell carcinoma (SCC) (inverse variance-weighted OR = 1.15, 95% CI 1.01-1.30). However, this association disappeared when multivariable MR included cigarettes per day and/or body mass index. By using our recently developed constrained maximum likelihood-based MR method, we identified significant associations of CRP levels with the risk of overall LC (OR 1.06, 95% CI 1.03-1.09), SCC (OR 1.06, 95% CI 1.02-1.09), and small cell lung cancer (SCLC, OR 1.09, 95% CI 1.03-1.15). Moreover, most univariable and multivariable MR analyses also revealed consistent CRP-SCLC associations. There may be a genetic and causal association between circulating CRP levels and the risk of SCLC, which is in line with previous population-based observational studies.

Bayesian Phylogenetic Analysis on Multi-Core Compute Architectures: Implementation and Evaluation of BEAGLE in RevBayes With MPI.

Phylogenies are central to many research areas in biology and commonly estimated using likelihood-based methods. Unfortunately, any likelihood-based method, including Bayesian inference, can be restrictively slow for large datasets-with many taxa and/or many sites in the sequence alignment-or complex substitutions models. The primary limiting factor when using large datasets and/or complex models in probabilistic phylogenetic analyses is the likelihood calculation, which dominates the total computation time. To address this bottleneck, we incorporated the high-performance phylogenetic library BEAGLE into RevBayes, which enables multi-threading on multi-core CPUs and GPUs, as well as hardware specific vectorized instructions for faster likelihood calculations. Our new implementation of RevBayes+BEAGLE retains the flexibility and dynamic nature that users expect from vanilla RevBayes. In addition, we implemented native parallelization within RevBayes without an external library using the message passing interface (MPI); RevBayes+MPI. We evaluated our new implementation of RevBayes+BEAGLE using multi-threading on CPUs and 2 different powerful GPUs (NVidia Titan V and NVIDIA A100) against our native implementation of RevBayes+MPI. We found good improvements in speedup when multiple cores were used, with up to 20-fold speedup when using multiple CPU cores and over 90-fold speedup when using multiple GPU cores. The improvement depended on the data type used, DNA or amino acids, and the size of the alignment, but less on the size of the tree. We additionally investigated the cost of rescaling partial likelihoods to avoid numerical underflow and showed that unnecessarily frequent and inefficient rescaling can increase runtimes up to 4-fold. Finally, we presented and compared a new approach to store partial likelihoods on branches instead of nodes that can speed up computations up to 1.7 times but comes at twice the memory requirements.

Performance of tree-building methods using a morphological dataset and a well-supported Hexapoda phylogeny.

Recently, many studies have addressed the performance of phylogenetic tree-building methods (maximum parsimony, maximum likelihood, and Bayesian inference), focusing primarily on simulated data. However, for discrete morphological data, there is no consensus yet on which methods recover the phylogeny with better performance. To address this lack of consensus, we investigate the performance of different methods using an empirical dataset for hexapods as a model. As an empirical test of performance, we applied normalized indices to effectively measure accuracy (normalized Robinson-Foulds metric, nRF) and precision, which are measured via resolution, one minus Colless' consensus fork index (1-CFI). Additionally, to further explore phylogenetic accuracy and support measures, we calculated other statistics, such as the true positive rate (statistical power) and the false positive rate (type I error), and constructed receiver operating characteristic plots to visualize the relationship between these statistics. We applied the normalized indices to the reconstructed trees from the reanalyses of an empirical discrete morphological dataset from extant Hexapoda using a well-supported phylogenomic tree as a reference. Maximum likelihood and Bayesian inference applying the k-state Markov (Mk) model (without or with a discrete gamma distribution) performed better, showing higher precision (resolution). Additionally, our results suggest that most available tree topology tests are reliable estimators of the performance measures applied in this study. Thus, we suggest that likelihood-based methods and tree topology tests should be used more often in phylogenetic tree studies based on discrete morphological characters. Our study provides a fair indication that morphological datasets have robust phylogenetic signal.