Maximum Likelihood Approach Research Articles

Comparative analysis of complete chloroplast genomes of 14 Asteraceae species.

The Asteraceae family, the largest and one of the most diverse families of angiosperms, presents significant challenges in taxonomic classification and systematic research due to its vast species diversity and morphological complexity. A comprehensive understanding of the chloroplast genomes within this family is essential for refining taxonomic classifications and advancing phylogenetic studies. In this study, we sequenced the complete chloroplast genomes of 14 Asteraceae species and conducted a thorough bioinformatic analysis of their characteristics. The chloroplast genomes, ranging from 150,907bp to 152,858bp, exhibit a typical quadripartite structure: a large single-copy (LSC) region (83,044bp to 84,625bp), a small single-copy (SSC) region (18,223bp to 18,673bp), and a pair of inverted repeats (IRs) (24,806bp to 25,201bp). These genomes encode 87 to 89 protein-coding genes (PCGs), 36 to 37 tRNA genes, and 8 rRNA genes, with high conservation in size, structure, gene content, and order. Comparative analysis with other Asteraceae species' chloroplast genomes revealed notable similarities and structural variations, particularly in the IR regions. Nucleotide polymorphism analysis identified four genes-trnY-GUA, trnE-UUC, ycf1, and rrn23-with higher Pi values, suggesting potential hotspots for evolutionary studies. Phylogenetic analysis using maximum likelihood (ML) and Bayesian inference (BI) approaches provided new insights, proposing the reclassification of Himalaiella auriculata and Jacobaea raphanifolia as independent genera, distinct from Saussurea and Senecio. This study presents a comprehensive analysis of the chloroplast genome structures and phylogenetic relationships of 14 Asteraceae species, offering critical data for future molecular identification, evolutionary biology, and population genetics research. The findings hold significant implications for the ongoing refinement of Asteraceae taxonomic classifications and enhance our understanding of the evolutionary dynamics within this complex family.

Equilibrium dynamical models in the inner region of the Large Magellanic Cloud based on Gaia DR3 kinematics

The Large Magellanic Cloud (LMC) contains complex dynamics driven by both internal and external processes. The external forces are due to tidal interactions with the Small Magellanic Cloud and the Milky Way, while internally its dynamics mainly depend on the stellar, gas, and dark matter mass distributions. Despite this complexity, simple physical models often provide valuable insights into the primary driving factors. We used Gaia Data Release 3 (DR3) to explore how well equilibrium dynamical models based on the Jeans equations and the Schwarzschild orbit superposition method are able to describe the LMC's five-dimensional phase-space distribution and line-of-sight (LOS) velocity distribution, respectively. In the Schwarzschild model, we incorporated a triaxial bar component for the first time and derived the LMC's bar pattern speed. We fit comprehensive Jeans dynamical models to all Gaia DR3 stars with proper motion and LOS velocity measurements found in the footprint of the VISTA near-infrared survey of the Magellanic System using a discrete maximum likelihood approach. These models are very efficient at discriminating genuine LMC member stars from Milky Way foreground stars and background galaxies. They constrain the shape, orientation, and enclosed mass of the galaxy under the assumption of axisymmetry. We used the Jeans model results as a stepping stone to more complex two-component Schwarzschild models, which include an axisymmetric disc and a co-centric triaxial bar, which we fit to the LMC Gaia DR3 LOS velocity field using a $ minimisation approach. The Jeans models describe the rotation and velocity dispersion of the LMC disc well, and we find an inclination angle of $ circ circ $, line of nodes orientation of $ circ circ $, and an intrinsic thickness of the disc of $q_0^d = b a (minor to major axis ratio). However, bound to axisymmetry, these models fail to properly describe the kinematics in the central region of the galaxy dominated by the LMC bar. We used the derived disc orientation and the Gaia DR3 density image of the LMC to obtain the intrinsic shape of the bar. Using these two components as input to our Schwarzschild models, we performed orbit integration and weighting in a rotating reference frame fixed to the bar, deriving an independent measurement of the LMC bar pattern speed of $ Both the Jeans and Schwarzschild models predict the same enclosed mass distribution within a radius of $6.2$\,kpc of $ Msun.

Association between brain resting-state functional activities and migraine: a bidirectional mendelian randomization study

Researchers have conducted extensive research on the correlation between brain resting-state functional activities (RSFA) and migraine. However, we still do not fully understand the exact nature of the causal relationship between these RSFA and migraine. We conducted a bidirectional two-sample Mendelian randomization (MR) study to investigate the causal association between migraine and RSFA. We gathered summary statistics from genome-wide association studies for 191 resting-state functional magnetic resonance imaging phenotypes. We employed various analytical methods for bidirectional two-sample MR analyses. This included inverse variance weighted, weighted median, MR Egger, and the constrained maximum likelihood approaches. We also conducted pleiotropy and heterogeneity analyses to evaluate the robustness and reliability. We found the functional connectivity between the default mode and the central executive network (OR = 1.39, p = 4.77 × 10−4, FDR corrected p value = 0.040) and the intensity of spontaneous brain activity in the calcarine or lingual gyrus within the visual network (OR = 0.74, p = 5.94 × 10−4, FDR corrected p value = 0.040) having a causal effect on the risk of migraine. Our MR analysis provided genetic support for these networks, which may play an important role in influencing migraine susceptibility.

Escalation of Human Resource Quality in National Health Resilience Through Estimating Multilevel Model Parameters with the Restricted Maximum Likelihood Approach to The 2019 UTBK Average

Multilevel modeling or Hierarchical Linear Modeling (HLM) is a statistical approach specifically used to analyze data with a two-level structure. This approach allows an understanding of the contribution of factors at both the individual and group levels to the response variable. One method commonly used in HLM is Restricted Maximum Likelihood (REML). REML is a parameter estimation method that is often applied in statistical models, especially linear models that incorporate random components. This allows more efficient parameter assessment compared to conventional estimation methods. In this research, multilevel model parameter estimation analysis was carried out using the limited maximum likelihood approach. The aim is to determine the multilevel linear regression model on the average UTBK score for health cluster study programs in 2019. This involves selecting the optimal node point based on the minimum Generalized Cross Validation (GCV) and identifying the factors that influence it. Predictor variables considered include interest and capacity of study programs at university level (Level-1), as well as the average UNBK and HDI scores at provincial level (Level-2). The findings of this research indicate that the most appropriate multilevel regression model is formed with three nodes with a minimum GCV value at Level-1 of 864.6593 and at Level-2 of 3.1816. At Level-1, the influencing factor is the interest variable and at Level-2 is the average provincial UNBK score in 2019 and the Human Development Index (HDI).

Telescope imaging beyond the Rayleigh limit in extremely low SNR

Abstract The Rayleigh limit and low Signal-to-Noise Ratio (SNR) scenarios pose significant limitations to optical imaging systems used in remote sensing, infrared thermal imaging, and space domain awareness. In this study, we introduce a Stochastic Sub-Rayleigh Imaging (SSRI) algorithm to localize point objects and estimate their positions, brightnesses, and number in low SNR conditions, even below the Rayleigh limit. Our algorithm adopts a maximum likelihood approach and exploits the Poisson distribution of incoming photons to overcome the Rayleigh limit in low SNR conditions. In our experimental validation, which closely mirrors practical scenarios, we focus on conditions with closely spaced sources within the sub-Rayleigh limit (0.49-1.00R) and weak signals (SNR less than 1.2). We use the Jaccard index and Jaccard efficiency as a figure of merit to quantify imaging performance in the sub-Rayleigh region. Our approach consistently outperforms established algorithms such as Richardson-Lucy and CLEAN by 4X in the low SNR, sub-Rayleigh regime. Our SSRI algorithm allows existing telescope-based optical/infrared imaging systems to overcome the extreme limit of sub-Rayleigh, low SNR source distributions, potentially impacting a wide range of fields, including passive thermal imaging, remote sensing, and space domain awareness.

Characteristics and Comparative Analysis of Six Mitogenomes of Genus Kiefferulus Goetghebuer, 1922 (Diptera: Chironomidae).

Chironomidae is a cosmopolitan and species-rich family of insects, with many species serving as useful indicators of aquatic ecosystem health. In this study, we newly sequenced six species of Kiefferulus Goetghebuer, 1922 (Chironomidae: Chironominae) by high-throughput sequencing technology. We analyzed characters of the mitochondrial genome, including the sequence length, nucleotide composition, and evolutionary rates of this genus. The size of the newly obtained sequences ranged from 15,588 to 15,767 bp, and all of them included 22 tRNAs, 13 PCGs, 2 rRNAs, and 1 CR. The CR showed the highest AT content relative to the PCGs, rRNAs, and tRNAs. Relative synonymous codon usage analysis showed that UUA, UUU, and AUU are the preferred codons. The ratio of nonsynonymous (Ka) to synonymous (Ks) substitution rates showed that all Ka/Ks of PCGs were lower than 1, with ATP8 having the highest evolution rate, while COX1 exhibited the lowest evolution rate. We reconstructed the phylogenetic relationship of the genus Kiefferulus based on eight species (six ingroups and two outgroups), using five matrices and employing Maximum likelihood and Bayesian inference approaches. Phylogenetic analysis of the Kiefferulus showed that six species within this genus were classified into a monophyletic clade.

All tangled up: Unraveling phylogenetics and reticulate evolution in the vining ferns, Lygodium (Schizaeales).

Reticulate evolution, often accompanied by polyploidy, is prevalent in plants, and particularly in the ferns. Resolving the resulting non-bifurcating histories remains a major challenge for plant phylogenetics. Here, we present a phylogenomic investigation into the complex evolutionary history of the vining ferns, Lygodium (Lygodiaceae, Schizaeales). Using a targeted enrichment approach with the GoFlag 408 flagellate land plant probe set, we generated large nuclear and plastid sequence datasets for nearly all taxa in the genus and constructed the most comprehensive phylogeny of the family to date using concatenated maximum likelihood and coalescence approaches. We integrated this phylogeny with cytological and spore data to explore karyotype evolution and generate hypotheses about the origins of putative polyploids and hybrids. Our data and analyses support the origins of several putative allopolyploids (e.g., L. cubense, L. heterodoxum) and hybrids (e.g., L. ×fayae) and also highlight the potential prevalence of autopolyploidy in this clade (e.g., L. articulatum, L. flexuosum, and L. longifolium). Our robust phylogenetic framework provides valuable insights into dynamic reticulate evolution in this clade and demonstrates the utility of target-capture data for resolving these complex relationships.

Gamma–lindley regression cure model for corporate credit default prediction

Predicting the firm’s default over time is marked persistently with certain flaws for firms seeking to avoid their exposure to credit risk and losses induced by defaults. From this perspective, a Gamma–lindley cure model, relying on a Gamma–lindley distribution and the survival analysis framework, was introduced to model the default probability and time of corporate credits referring to their inference ability once the firm is likely to default. In addition, it extends the standard mixture cure model allowing more flexibility for modeling lifetime data through relaxing the independence assumption of the probability and the time of default. Furthermore, it handles the missing defaulting labels as a latent variable and identifies three classes of default probability distribution, namely short, medium, and long-term through its potentially accurate classification method. A relevant parameter-learning procedure was described resting on the Maximum Likelihood approach. The results of an empirical analysis on a firms dataset reveal that the advanced Gamma–lindley cure model has a rather effective performance in terms of default time prediction compared to Exponential, Gamma, Weibull, and Cox proportional hazards regression modeling specifications, which yield a meaningful solution for timely credit risk management and cluster firms defaulter in three classes, enabling a deeper analysis of firm’s defaults situation. The numerical experiments were conducted with Python language.

A novel extended Kumaraswamy distribution and its application to COVID‐19 data

AbstractIn the field of biomedical research, data characteristics often exhibit significant variability, challenging the applicability of classical probability distributions for biomedical data modeling. In this research, we introduce a novel four‐parameter distribution called the odd beta prime Kumaraswamy (OBPK) distribution, derived from the odd beta prime generalized family of distributions and the Kumaraswamy distribution. This distribution exhibits greater flexibility compared with the traditional Kumaraswamy distribution. Importantly, the OBPK distribution offers symmetrical, right‐skewed, left‐skewed, bathtub, N‐shaped, J‐shaped, and reversed J‐shaped densities, as well as varied hazard functions, including increasing, decreasing, bathtub, increasing‐decreasing, upside‐down bathtub, and N‐shaped forms. These curvature patterns make it particularly useful for modeling biomedical data. We derive some basic properties of the OBPK distribution. Parameters are estimated using the maximum likelihood approach, and the performance of various estimators is assessed via Monte Carlo simulations. Finally, four applications to real data on COVID‐19 mortality rates from different countries are evaluated to demonstrate the importance of the OBPK model over other extended versions of the Kumaraswamy models. The empirical findings suggest that the OBPK model outperforms other extended versions of the Kumaraswamy models in these applications.

A spectral approach for the dynamic Bradley–Terry model

SummaryThe dynamic ranking, due to its increasing importance in many applications, is becoming crucial, especially with the collection of voluminous time‐dependent data. One such application is sports statistics, where dynamic ranking aids in forecasting the performance of competitive teams, drawing on historical and current data. Despite its usefulness, predicting and inferring rankings pose challenges in environments necessitating time‐dependent modelling. This paper introduces a spectral ranker called Kernel Rank Centrality, designed to rank items based on pairwise comparisons over time. The ranker operates via kernel smoothing in the Bradley–Terry model, utilising a Markov chain model. Unlike the maximum likelihood approach, the spectral ranker is nonparametric, demands fewer model assumptions and computations and allows for real‐time ranking. We establish the asymptotic distribution of the ranker by applying an innovative group inverse technique, resulting in a uniform and precise entrywise expansion. This result allows us to devise a new inferential method for predictive inference, previously unavailable in existing approaches. Our numerical examples showcase the ranker's utility in predictive accuracy and constructing an uncertainty measure for prediction, leveraging data from the National Basketball Association (NBA). The results underscore our method's potential compared with the gold standard in sports, the Arpad Elo rating system.

Single-nanoparticle electrophoretic mobility determination and trapping using active-feedback 3D tracking.

Nanoparticles (NP) are versatile materials with widespread applications across medicine and engineering. Despite rapid incorporation into drug delivery, therapeutics, and many more areas of research and development, there is a lack of robust characterization methods. Light scattering techniques such as dynamic light scattering (DLS) and electrophoretic light scattering (ELS) use an ensemble-averaged approach to the characterization of nanoparticle size and electrophoretic mobility (EM), leading to inaccuracies when applied to polydisperse or heterogeneous populations. To address this lack of single-nanoparticle characterization, this work applies 3D Single-Molecule Active Real-time Tracking (3D-SMART) to simultaneously determine NP size and EM on a per-particle basis. Single-nanoparticle EM is determined by using active feedback to "lock on" to a single particle and apply an oscillating electric field along one axis. A maximum likelihood approach is applied to extract the single-particle EM from the oscillating nanoparticle position along the field-actuated axis, while mean squared displacement is used along the non-actuated axes to determine size. Unfunctionalized and carboxyl-functionalized polystyrene NPs are found to have unique EM based on their individual size and surface characteristics, and it is demonstrated that single-nanoparticle EM is a more precise tool for distinguishing unique NP preparations than diffusion alone, able to determine the charge number of individual NPs to an uncertainty of less than 30. This method also explored individual nanoparticle EM in various ionic strengths (0.25-5 mM) and found decreased EM as a function of increasing ionic strength, in agreement with results determined via bulk characterization methods. Finally, it is demonstrated that the electric field can be manipulated in real time in response to particle position, resulting in one-dimensional electrokinetic trapping. Critically, this new single-nanoparticle EM determination and trapping method does not require microfluidics, opening the possibility for the exploration of single-nanoparticle EM in live tissue and more comprehensive characterization of nanoparticles in biologically relevant environments.

A robust regression model for bounded count health data.

Bounded count response data arise naturally in health applications. In general, the well-known beta-binomial regression model form the basis for analyzing this data, specially when we have overdispersed data. Little attention, however, has been given to the literature on the possibility of having extreme observations and overdispersed data. We propose in this work an extension of the beta-binomial regression model, named the beta-2-binomial regression model, which provides a rather flexible approach for fitting a regression model with a wide spectrum of bounded count response data sets under the presence of overdispersion, outliers, or excess of extreme observations. This distribution possesses more skewness and kurtosis than the beta-binomial model but preserves the same mean and variance form of the beta-binomial model. Additional properties of the beta-2-binomial distribution are derived including its behavior on the limits of its parametric space. A penalized maximum likelihood approach is considered to estimate parameters of this model and a residual analysis is included to assess departures from model assumptions as well as to detect outlier observations. Simulation studies, considering the robustness to outliers, are presented confirming that the beta-2-binomial regression model is a better robust alternative, in comparison with the binomial and beta-binomial regression models. We also found that the beta-2-binomial regression model outperformed the binomial and beta-binomial regression models in our applications of predicting liver cancer development in mice and the number of inappropriate days a patient spent in a hospital.

Statistical inference from partially nominated sets: An application to estimating the prevalence of osteoporosis among adult women

This paper focuses on drawing statistical inference based on a novel variant of maxima or minima nomination sampling (NS) designs. These sampling designs are useful for obtaining more representative sample units from the tails of the population distribution using the available auxiliary ranking information. However, one common difficulty in performing NS in practice is that the researcher cannot obtain a nominated sample unless he/she uniquely determines the sample unit with the highest or the lowest rank in each set. To overcome this problem, a variant of NS, which is called partial nomination sampling, is proposed, in which the researcher is allowed to declare that two or more units are tied in the ranks whenever he/she cannot find the sample unit with the highest or the lowest rank. Based on this sampling design, two asymptotically unbiased estimators are developed for the cumulative distribution function, which is obtained using maximum likelihood and moment-based approaches, and their asymptotic normalities are proved. Several numerical studies have shown that the proposed estimators have higher relative efficiencies than their counterparts in simple random sampling in analyzing either the upper or the lower tail of the parent distribution. The procedures that we developed are then implemented on a real dataset from the Third National Health and Nutrition Examination Survey (NHANES III) to estimate the prevalence of osteoporosis among adult women aged 50 and over. It is shown that in certain circumstances, the techniques that we have developed require only one-third of the sample size needed in SRS to achieve the desired precision. This results in a considerable reduction in time and cost compared to the standard SRS method.

Blouch: Bayesian Linear Ornstein-Uhlenbeck Models for Comparative Hypotheses.

Relationships among species in the tree of life can complicate comparative methods and testing adaptive hypotheses. Models based on the Ornstein-Uhlenbeck process permit hypotheses about adaptation to be tested by allowing traits to either evolve towards fixed adaptive optima (e.g., regimes or niches) or track continuously changing optima that can be influenced by other traits. These models allow estimation of the effects of both adaptation and phylogenetic inertia - resistance to adaptation due to any source - on trait evolution, an approach known as the "adaptation-inertia" framework. However, previous applications of this framework, and most approaches suggested to deal with the issue of species non-independence, are based on a maximum likelihood approach and thus it is difficult to include information based on prior biological knowledge in the analysis, which can affect resulting inferences. Here I present Blouch, (Bayesian Linear Ornstein-Uhlenbeck Models for Comparative Hypotheses), which fits allometric and adaptive models of continuous trait evolution in a Bayesian framework based on fixed or continuous predictors and incorporates measurement error. I first briefly discuss the models implemented in Blouch, and then the new applications for these models provided by a Bayesian framework. This includes the advantages of assigning biologically meaningful priors when compared to non-Bayesian approaches, allowing for varying effects (intercepts and slopes), and multilevel modeling. Validations on simulated data show good performance in recovering the true evolutionary parameters for all models. To demonstrate the workflow of Blouch on an empirical dataset, I test the hypothesis that the relatively larger antlers of larger bodied deer are the result of more intense sexual selection that comes along with their tendency to live in larger breeding groups. While results show that larger bodied deer that live in larger breeding groups have relatively larger antlers, deer living in the smallest groups appear to have a different and steeper scaling pattern of antler size to body size than other groups. These results are contrary to previous findings and may argue that a different type of sexual selection or other selective pressures govern optimum antler size in the smallest breeding groups.

Enhanced positronium lifetime imaging through two-component reconstruction in time-of-flight positron emission tomography

Positronium lifetime imaging (PLI) is a newly demonstrated technique possible with time-of-flight (TOF) positron emission tomography (PET), capable of producing an image reflecting the lifetime of the positron, more precisely ortho-positronium (o-Ps), before annihilation, in addition to the traditional uptake image of the PET tracer. Due to the limited time resolution of TOF-PET systems and the added complexities in physics and statistics, lifetime image reconstruction presents a challenge. Recently, we described a maximum-likelihood approach for PLI by considering only o-Ps. In real-world scenarios, other populations of positrons that exhibit different lifetimes also exist. This paper introduces a novel two-component model aimed at enhancing the accuracy of o-Ps lifetime images. Through simulation studies, we compare this new model with the existing single-component model and demonstrate its superior performance in accurately capturing complex lifetime distributions.

A Probabilistic Approach to Estimate the Temporal Order of Pathway Mutations Accounting for Intra-Tumor Heterogeneity.

The development of cancer involves the accumulation of somatic mutations in several essential biological pathways. Delineating the temporal order of pathway mutations during tumorigenesis is crucial for comprehending the biological mechanisms underlying cancer development and identifying potential targets for therapeutic intervention. Several computational and statistical methods have been introduced for estimating the order of somatic mutations based on mutation profile data from a cohort of patients. However, one major issue of current methods is that they do not take into account intra-tumor heterogeneity (ITH), which limits their ability to accurately discern the order of pathway mutations. To address this problem, we propose PATOPAI, a probabilistic approach to estimate the temporal order of mutations at the pathway level by incorporating ITH information as well as pathway and functional annotation information of mutations. PATOPAI uses a maximum likelihood approach to estimate the probability of pathway mutational events occurring in a specific sequence, wherein it focuses on the orders that are consistent with the phylogenetic structure of the tumors. Applications to whole exome sequencing data from The Cancer Genome Atlas (TCGA) illustrate our method's ability to recover the temporal order of pathway mutations in several cancer types.

Exploring Phylogenetic Signal in Multivariate Phenotypes by Maximizing Blomberg's K.

Due to the hierarchical structure of the tree of life, closely related species often resemble each other more than distantly related species; a pattern termed phylogenetic signal. Numerous univariate statistics have been proposed as measures of phylogenetic signal for single phenotypic traits, but the study of phylogenetic signal for multivariate data, as is common in modern biology, remains challenging. Here we introduce a new method to explore phylogenetic signal in multivariate phenotypes. Our approach decomposes the data into linear combinations with maximal (or minimal) phylogenetic signal, as measured by Blomberg's K. The loading vectors of these phylogenetic components or K-components can be biologically interpreted, and scatterplots of the scores can be used as a low-dimensional ordination of the data that maximally (or minimally) preserves phylogenetic signal. We present algebraic and statistical properties, along with two new summary statistics, KA and KG, of phylogenetic signal in multivariate data. Simulation studies showed that KA and KG have higher statistical power than the previously suggested statistic Kmult, especially if phylogenetic signal is low or concentrated in a few trait dimensions. In two empirical applications to vertebrate cranial shape (crocodyliforms and papionins), we found statistically significant phylogenetic signal concentrated in a few trait dimensions. The finding that phylogenetic signal can be highly variable across the dimensions of multivariate phenotypes has important implications for current maximum likelihood approaches to phylogenetic signal in multivariate data.

Statistical inference of a series reliability system using shock models with Weibull distribution

AbstractIn this study, we define a series system with non‐independent and non‐identical components using a shock model with sources of fatal shocks. Here, it is assumed that the shocks happen randomly and independently, following a Weibull distribution with various scale and shape parameters. A dependability model with unknown parameters is produced by this process. Making statistical conclusions about the model parameters is the main objective of this research. We apply the maximum likelihood and Bayes approaches to determine the model parameters' point and interval estimates. We shall demonstrate that no analytical solutions to the likelihood equations must be solved to obtain the parameters' maximum likelihood estimates. As a result, we will use the R program to approximate the parameter point and interval estimates. Additionally, we will use the bootstrap‐t and bootstrap‐p methods to approximate the confidence intervals. About the Bayesian approach, we presume that each model parameter is independent and follows a gamma prior distribution with a range of attached hyperparameter values. The model parameters' posterior distribution does not take a practical form. We are unable to derive the Bayes estimates in closed forms as a result. To solve this issue, we use the Gibbs sampler from the Metropolis‐Hasting algorithm based on the Markov chain Monte Carlo method to condense the posterior distribution. To demonstrate the relevance of this research, a real data set application is detailed.

Precision Mars Entry Navigation with Atmospheric Density Adaptation via Neural Networks

Spacecraft entering Mars require precise navigation algorithms capable of accurately estimating the vehicle’s position and velocity in dynamic and uncertain atmospheric environments. Discrepancies between the true Martian atmospheric density and the onboard density model can significantly impair the navigation performance. This work introduces a new approach to online filtering for Martian entry using a neural network to estimate atmospheric density and employing a “consider” analysis to account for the uncertainty in the estimate. The network is trained on an exponential atmospheric density model, and its parameters are dynamically adapted in real time to account for any mismatch between the true and estimated densities. The adaptation of the network is formulated as a maximum likelihood problem by leveraging the measurement innovations of the filter to identify optimal network parameters. Within the context of the maximum likelihood approach, incorporating a neural network enables the use of stochastic optimizers known for their efficiency in the machine learning domain. Performance comparisons are conducted against two online adaptive approaches, covariance matching and state augmentation and correction, in various realistic Martian entry navigation scenarios. The results show superior estimation accuracy compared to other approaches and precise alignment of the estimated density with a broad selection of realistic Martian atmospheres sampled from perturbed Mars Global Reference Atmospheric Model data.

Selecting the number of factors in approximate factor models using group variable regularization

. We propose a novel method for the estimation of the number of factors in approximate factor models. The model is based on a penalized maximum likelihood approach incorporating an adaptive hierarchical lasso penalty function that enables setting entire columns of the factor loadings matrix to zero, which corresponds to removing uninformative factors. Additionally, the model is capable of estimating weak factors by allowing for sparsity in the non zero columns. We prove that the proposed estimator consistently estimates the true number of factors. Simulation experiments reveal superior selection accuracies for our method in finite samples over existing approaches, especially for data with cross-sectional and serial correlations. In an empirical application on a large macroeconomic dataset, we show that the mean squared forecast errors of an approximate factor model are lower if the number of included factors is selected by our method.