We solve non linear least squares problems with optional equality and/or inequality constraints. Non linear iterations are globalized with back-tracking method. Linear problems are solved by dense QR decomposition from LAPACK which can limit the size of treated problems. On the other side, we avoid condition number degradation which happens in classical quadratic programming approach. Inequality constraints treatment on each non linear iteration is based on NNLS method (by Lawson and Hanson). We provide an original function lsi_ln for solving linear least squares problem with inequality constraints in least norm sens. Thus if Jacobian of the problem is rank deficient a solution still can be provided. However, truncation errors are probable in this case. Equality constraints are treated by using a basis of Null-space. User defined function calculating residuals must return a list having residual vector (not their squared sum) and Jacobian. If Jacobian is not in the returned list, package numDeriv is used to calculated finite difference version of Jacobian. The NLSIC method was fist published in Sokol et al. (2012) <doi:10.1093/bioinformatics/btr716>.

Compiles functions to trim, bin, visualise, and analyse activity/sleep time-series data collected from the Drosophila Activity Monitor (DAM) system (Trikinetics, USA). The following methods were used to compute periodograms - Chi-square periodogram: Sokolove and Bushell (1978) <doi:10.1016/0022-5193(78)90022-X>, Lomb-Scargle periodogram: Lomb (1976) <doi:10.1007/BF00648343>, Scargle (1982) <doi:10.1086/160554> and Ruf (1999) <doi:10.1076/brhm.30.2.178.1422>, and Autocorrelation: Eijzenbach et al. (1986) <doi:10.1111/j.1440-1681.1986.tb00943.x>. Identification of activity peaks is done after using a Savitzky-Golay filter (Savitzky and Golay (1964) <doi:10.1021/ac60214a047>) to smooth raw activity data. Three methods to estimate anticipation of activity are used based on the following papers - Slope method: Fernandez et al. (2020) <doi:10.1016/j.cub.2020.04.025>, Harrisingh method: Harrisingh et al. (2007) <doi:10.1523/JNEUROSCI.3680-07.2007>, and Stoleru method: Stoleru et al. (2004) <doi:10.1038/nature02926>. Rose plots and circular analysis are based on methods from - Batschelet (1981) <ISBN:0120810506> and Zar (2010) <ISBN:0321656865>.

Hierarchical continuous (and discrete) time state space modelling, for linear and nonlinear systems measured by continuous variables, with limited support for binary data. The subject specific dynamic system is modelled as a stochastic differential equation (SDE) or difference equation, measurement models are typically multivariate normal factor models. Linear mixed effects SDE's estimated via maximum likelihood and optimization are the default. Nonlinearities, (state dependent parameters) and random effects on all parameters are possible, using either max likelihood / max a posteriori optimization (with optional importance sampling) or Stan's Hamiltonian Monte Carlo sampling. See <https://github.com/cdriveraus/ctsem/raw/master/vignettes/hierarchicalmanual.pdf> for details. See <https://osf.io/preprints/psyarxiv/4q9ex_v2> for a detailed tutorial. Priors may be used. For the conceptual overview of the hierarchical Bayesian linear SDE approach, see <https://www.researchgate.net/publication/324093594_Hierarchical_Bayesian_Continuous_Time_Dynamic_Modeling>. Exogenous inputs may also be included, for an overview of such possibilities see <https://www.researchgate.net/publication/328221807_Understanding_the_Time_Course_of_Interventions_with_Continuous_Time_Dynamic_Models> . <https://cdriver.netlify.app/> contains some tutorial blog posts.

This package provides a general-purpose framework for Interpretable Contextual-Accountable and Responsible Machine Learning (ICARM) that works with any clean tabular data across any application domain including healthcare, finance, social science, business, and education. Automatically detects whether a prediction task is binary classification, multi-class classification, or regression from the target variable type. Provides a unified entry point icarm_fit() supporting both interpretable learners (Classification and Regression Trees (CART), logistic regression, linear regression, Generalized Additive Models (GAM)) and extended learners (random forest, XGBoost', Support Vector Machines (SVM)) with consistent interfaces for global and local model explanation including approximate SHapley Additive exPlanations (SHAP) values and Partial Dependence Profiles (PDPs), learning curve diagnostics, group-level fairness auditing across protected attributes, probability calibration, threshold analysis, multi-model comparison, reproducible JavaScript Object Notation (JSON) audit trails, and accountability scorecards. The contextual accountability framing emphasises that algorithmic fairness and interpretability requirements depend on the deployment domain and must be evaluated accordingly. Extends the civic.icarm framework (Awe 2025) <https://cran.r-project.org/package=civic.icarm> to general-purpose applications beyond civic and political education.

Obtains lists of files of remote sensing collections for Southern Ocean surface properties. Commonly used data sources of sea surface temperature, sea ice concentration, and altimetry products such as sea surface height and sea surface currents are cached in object storage on the Pawsey Supercomputing Research Centre facility. Patterns of working to retrieve data from these object storage catalogues are described. The catalogues include complete collections of datasets Reynolds et al. (2008) "NOAA Optimum Interpolation Sea Surface Temperature (OISST) Analysis, Version 2.1" <doi:10.7289/V5SQ8XB5>, Spreen et al. (2008) "Artist Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E) sea ice concentration" <doi:10.1029/2005JC003384>. In future releases helpers will be added to identify particular data collections and target specific dates for earth observation data for reading, as well as helpers to retrieve data set citation and provenance details. This work was supported by resources provided by the Pawsey Supercomputing Research Centre with funding from the Australian Government and the Government of Western Australia. This software was developed by the Integrated Digital East Antarctica program of the Australian Antarctic Division.

In staggered difference-in-differences designs the treatment effect is a vector of cohort-time effects rather than a single number. Estimating each separately is unbiased but imprecise when some are equal, while pooling them all is precise but biased under genuine heterogeneity. This package treats the choice as a partition-selection problem on the cohort-time cells and provides two estimators for it: a Dirichlet process mixture fitted by a collapsed Gibbs sampler, whose posterior marginalises over the unknown partition and reports co-clustering probabilities, and an L0'-penalised estimator that returns a single partition and arises as the fixed-variance maximum a posteriori solution of the same model. Also provides tests for whether the cohort-time effects carry recoverable heterogeneity at all, sampler diagnostics including exact enumeration of the partition posterior for small designs, regularisation paths for both estimators, and a calibrated data-generating process. All estimators accept a vector of first-stage cohort-time effects with their joint covariance, so any heterogeneity-robust first-stage estimator may be used. Methods are described in Arora and Wagle (2026) <doi:10.2139/ssrn.7207083>.

The PBIB designs are important type of incomplete block designs having wide area of their applications for example in agricultural experiments, in plant breeding, in sample surveys etc. This package constructs various series of PBIB designs and assists in checking all the necessary conditions of PBIB designs and the association scheme on which these designs are based on. It also assists in calculating the efficiencies of PBIB designs with any number of associate classes. The package also constructs Youden-m square designs which are Row-Column designs for the two-way elimination of heterogeneity. The incomplete columns of these Youden-m square designs constitute PBIB designs. With the present functionality, the package will be of immense importance for the researchers as it will help them to construct PBIB designs, to check if their PBIB designs and association scheme satisfy various necessary conditions for the existence, to calculate the efficiencies of PBIB designs based on any association scheme and to construct Youden-m square designs for the two-way elimination of heterogeneity. R. C. Bose and K. R. Nair (1939) <http://www.jstor.org/stable/40383923>.

Penalized parametric change-point detection by functional pruning dynamic programming algorithm. The successive means are constrained using a graph structure with edges defining the nature of the changes These changes can be unconstrained (type std), up or down constrained (type up and down) or constrained by a minimal size jump (type abs). The type null means that the graph allows us to stay on the same segment. To each edge we can associate some additional properties: a minimal gap size, a penalty, some robust parameters (K,a) for biweight (K) and Huber losses (K and a). The user can also constrain the inferred means to lie between some minimal and maximal values. Data is modeled by a cost with possible use of a robust loss, biweight and Huber (see edge parameters K and a). These costs should have a quadratic, log-linear or a log-log representation. This includes quadratic Gaussian cost (type = mean'), log-linear cost (type = variance', poisson or exp') and log-log cost (type = negbin'). More details in the paper published in the Journal of Statistical Software: <doi:10.18637/jss.v106.i06>.

Additional nonlinear regression functions using self-start (SS) algorithms. One of the functions is the Beta growth function proposed by Yin et al. (2003) <doi:10.1093/aob/mcg029>. There are several other functions with breakpoints (e.g. linear-plateau, plateau-linear, exponential-plateau, plateau-exponential, quadratic-plateau, plateau-quadratic and bilinear), a non-rectangular hyperbola and a bell-shaped curve. Twenty eight (28) new self-start (SS) functions in total. This package also supports the publication Nonlinear regression Models and applications in agricultural research by Archontoulis and Miguez (2015) <doi:10.2134/agronj2012.0506>, a book chapter with similar material <doi:10.2134/appliedstatistics.2016.0003.c15> and a publication by Oddi et. al. (2019) in Ecology and Evolution <doi:10.1002/ece3.5543>. The function nlsLMList uses nlsLM for fitting, but it is otherwise almost identical to nlme::nlsList'.In addition, this release of the package provides functions for conducting simulations for nlme and gnls objects as well as bootstrapping. These functions are intended to work with the modeling framework of the nlme package. It also provides four vignettes with extended examples.

The Genetic Algorithm (GA) is a type of optimization method of Evolutionary Algorithms. It uses the biologically inspired operators such as mutation, crossover, selection and replacement.Because of their global search and robustness abilities, GAs have been widely utilized in machine learning, expert systems, data science, engineering, life sciences and many other areas of research and business. However, the regular GAs need the techniques to improve their efficiency in computing time and performance in finding global optimum using some adaptation and hybridization strategies. The adaptive GAs (AGA) increase the convergence speed and success of regular GAs by setting the parameters crossover and mutation probabilities dynamically. The hybrid GAs combine the exploration strength of a stochastic GAs with the exact convergence ability of any type of deterministic local search algorithms such as simulated-annealing, in addition to other nature-inspired algorithms such as ant colony optimization, particle swarm optimization etc. The package adana includes a rich working environment with its many functions that make possible to build and work regular GA, adaptive GA, hybrid GA and hybrid adaptive GA for any kind of optimization problems. Cebeci, Z. (2021, ISBN: 9786254397448).

The first major functionality is to compute the bias in regression coefficients of misspecified linear gene-environment interaction models. The most generalized function for this objective is GE_bias(). However GE_bias() requires specification of many higher order moments of covariates in the model. If users are unsure about how to calculate/estimate these higher order moments, it may be easier to use GE_bias_normal_squaredmis(). This function places many more assumptions on the covariates (most notably that they are all jointly generated from a multivariate normal distribution) and is thus able to automatically calculate many of the higher order moments automatically, necessitating only that the user specify some covariances. There are also functions to solve for the bias through simulation and non-linear equation solvers; these can be used to check your work. Second major functionality is to implement the Bootstrap Inference with Correct Sandwich (BICS) testing procedure, which we have found to provide better finite-sample performance than other inference procedures for testing GxE interaction. More details on these functions are available in Sun, Carroll, Christiani, and Lin (2018) <doi:10.1111/biom.12813>.

An implementation of popular screening methods that are commonly employed in ultra-high and high dimensional data. Through this publicly available package, we provide a unified framework to carry out model-free screening procedures including SIS (Fan and Lv (2008) <doi:10.1111/j.1467-9868.2008.00674.x>), SIRS(Zhu et al. (2011)<doi:10.1198/jasa.2011.tm10563>), DC-SIS (Li et al. (2012) <doi:10.1080/01621459.2012.695654>), MDC-SIS(Shao and Zhang (2014) <doi:10.1080/01621459.2014.887012>), Bcor-SIS (Pan et al. (2019) <doi:10.1080/01621459.2018.1462709>), PC-Screen (Liu et al. (2020) <doi:10.1080/01621459.2020.1783274>), WLS (Zhong et al.(2021) <doi:10.1080/01621459.2021.1918554>), Kfilter (Mai and Zou (2015) <doi:10.1214/14-AOS1303>), MVSIS (Cui et al. (2015) <doi:10.1080/01621459.2014.920256>), PSIS (Pan et al. (2016) <doi:10.1080/01621459.2014.998760>), CAS (Xie et al. (2020) <doi:10.1080/01621459.2019.1573734>), CI-SIS (Cheng and Wang. (2023) <doi:10.1016/j.cmpb.2022.107269>), CSIS (Cheng et al. (2024) <doi:10.1007/s00180-023-01399-5>) and Log-rank SIS.

This package provides a typical gait analysis requires the examination of the motion of nine joint angles on the left-hand side and six joint angles on the right-hand side across multiple subjects. Due to the quantity and complexity of the data, it is useful to calculate the amount by which a subjectâ s gait deviates from an average normal profile and to represent this deviation as a single number. Such a measure can quantify the overall severity of a condition affecting walking, monitor progress, or evaluate the outcome of an intervention prescribed to improve the gait pattern. This R package provides tools for computing the Functional Gait Deviation Index, a novel index for quantifying gait pathology using multivariate functional principal component analysis. The package supports analysis at the level of both legs combined, individual legs, and individual joints/planes. It includes functions for functional data preprocessing, multivariate functional principal component decomposition, FGDI computation, and visualisation of gait abnormality scores. Further details can be found in Minhas, S. K., Sangeux, M., Polak, J., & Carey, M. (2025). The Functional Gait Deviation Index. Journal of Applied Statistics <doi:10.1080/02664763.2025.2514150>.

We provide two algorithms for monitoring change points with online matrix-valued time series, under the assumption of a two-way factor structure. The algorithms are based on different calculations of the second moment matrices. One is based on stacking the columns of matrix observations, while another is by a more delicate projected approach. A well-known fact is that, in the presence of a change point, a factor model can be rewritten as a model with a larger number of common factors. In turn, this entails that, in the presence of a change point, the number of spiked eigenvalues in the second moment matrix of the data increases. Based on this, we propose two families of procedures - one based on the fluctuations of partial sums, and one based on extreme value theory - to monitor whether the first non-spiked eigenvalue diverges after a point in time in the monitoring horizon, thereby indicating the presence of a change point. This package also provides some simple functions for detecting and removing outliers, imputing missing entries and testing moments. See more details in He et al. (2021)<doi:10.48550/arXiv.2112.13479>.

This package provides a set of tools for relational and event analysis, including two- and one-mode network brokerage and structural measures, and helper functions optimized for relational event analysis with large datasets, including creating relational risk sets, computing network statistics, estimating relational event models, and simulating relational event sequences. For more information on relational event models, see Butts (2008) <doi:10.1111/j.1467-9531.2008.00203.x>, Lerner and Lomi (2020) <doi:10.1017/nws.2019.57>, Bianchi et al. (2024) <doi:10.1146/annurev-statistics-040722-060248>, and Butts et al. (2023) <doi:10.1017/nws.2023.9>. In terms of the structural measures in this package, see Leal (2025) <doi:10.1177/00491241251322517>, Burchard and Cornwell (2018) <doi:10.1016/j.socnet.2018.04.001>, and Fujimoto et al. (2018) <doi:10.1017/nws.2018.11>. This package was developed with support from the National Science Foundationâ s (NSF) Human Networks and Data Science Program (HNDS) under award number 2241536 (PI: Diego F. Leal). Any opinions, findings, and conclusions, or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the NSF.

An implementation for high-dimensional time series analysis methods, including factor model for vector time series proposed by Lam and Yao (2012) <doi:10.1214/12-AOS970> and Chang, Guo and Yao (2015) <doi:10.1016/j.jeconom.2015.03.024>, martingale difference test proposed by Chang, Jiang and Shao (2023) <doi:10.1016/j.jeconom.2022.09.001>, principal component analysis for vector time series proposed by Chang, Guo and Yao (2018) <doi:10.1214/17-AOS1613>, cointegration analysis proposed by Zhang, Robinson and Yao (2019) <doi:10.1080/01621459.2018.1458620>, unit root test proposed by Chang, Cheng and Yao (2022) <doi:10.1093/biomet/asab034>, white noise tests proposed by Chang, Yao and Zhou (2017) <doi:10.1093/biomet/asw066> and Chang et al. (2026+), CP-decomposition for matrix time series proposed by Chang et al. (2023) <doi:10.1093/jrsssb/qkac011> and Chang et al. (2026+) <doi:10.48550/arXiv.2410.05634>, CP-decomposition for tensor time series proposed by Chang et al. (2026+) <doi:10.48550/arXiv.2606.08560>, and statistical inference for spectral density matrix proposed by Chang et al. (2025) <doi:10.1080/01621459.2025.2468013>.

Construction and analysis of multivalued zero-sum matrix games over the abstract space of probability distributions, which describe the losses in each scenario of defense vs. attack action. The distributions can be compiled directly from expert opinions or other empirical data (insofar available). The package implements the methods put forth in the EU project HyRiM (Hybrid Risk Management for Utility Networks), FP7 EU Project Number 608090. The method has been published in Rass, S., König, S., Schauer, S., 2016. Decisions with Uncertain Consequences-A Total Ordering on Loss-Distributions. PLoS ONE 11, e0168583. <doi:10.1371/journal.pone.0168583>, and applied for advanced persistent thread modeling in Rass, S., König, S., Schauer, S., 2017. Defending Against Advanced Persistent Threats Using Game-Theory. PLoS ONE 12, e0168675. <doi:10.1371/journal.pone.0168675>. A volume covering the wider range of aspects of risk management, partially based on the theory implemented in the package is the book edited by S. Rass and S. Schauer, 2018. Game Theory for Security and Risk Management: From Theory to Practice. Springer, <doi:10.1007/978-3-319-75268-6>, ISBN 978-3-319-75267-9.

To implement a general framework to quantitatively infer Community Assembly Mechanisms by Phylogenetic-bin-based null model analysis, abbreviated as iCAMP (Ning et al 2020) <doi:10.1038/s41467-020-18560-z>. It can quantitatively assess the relative importance of different community assembly processes, such as selection, dispersal, and drift, for both communities and each phylogenetic group ('bin'). Each bin usually consists of different taxa from a family or an order. The package also provides functions to implement some other published methods, including neutral taxa percentage (Burns et al 2016) <doi:10.1038/ismej.2015.142> based on neutral theory model and quantifying assembly processes based on entire-community null models ('QPEN', Stegen et al 2013) <doi:10.1038/ismej.2013.93>. It also includes some handy functions, particularly for big datasets, such as phylogenetic and taxonomic null model analysis at both community and bin levels, between-taxa niche difference and phylogenetic distance calculation, phylogenetic signal test within phylogenetic groups, midpoint root of big trees, etc. Version 1.3.x mainly improved the function for QPEN and added function icamp.cate() to summarize iCAMP results for different categories of taxa (e.g. core versus rare taxa).

Builds a joint probabilistic forecast across series and horizons using adaptive copulas (Gaussian/t) with shrinkage-repaired correlations. At the low level it calls a probabilistic mixer per series and horizon, which backtests several simple predictors, predicts next-window Continuous Ranked Probability Score (CRPS), and converts those scores into softmax weights to form a calibrated mixture (r/q/p/dfun). The mixer blends eight simple predictors: a naive predictor that wraps the last move in a PERT distribution; an arima predictor using auto.arima for one-step forecasts; an Exponentially Weighted Moving Average (EWMA) gaussian predictor with mean/variance under a Gaussian; a historical bootstrap predictor that resamples past horizon-aligned moves; a drift residual bootstrap predictor combining linear trend with bootstrapped residuals; a volatility-scaled naive predictor centering on the last move and scaling by recent volatility; a robust median mad predictor using median/MAD with Laplace or Normal shape; and a shrunk quantile predictor that fits a few quantile regressions over time and interpolates to a full predictive. The function then couples the per-series mixtures on a common transform (additive/multiplicative/log-multiplicative), simulates coherent draws, and returns both transformed- and level-scale samplers and summaries.

While some non-coding RNAs (ncRNAs) are assigned critical regulatory roles, most remain functionally uncharacterized. This presents a challenge whenever an interesting set of ncRNAs needs to be analyzed in a functional context. Transcripts located close-by on the genome are often regulated together. This genomic proximity on the sequence can hint to a functional association. We present a tool, NoRCE, that performs cis enrichment analysis for a given set of ncRNAs. Enrichment is carried out using the functional annotations of the coding genes located proximal to the input ncRNAs. Other biologically relevant information such as topologically associating domain (TAD) boundaries, co-expression patterns, and miRNA target prediction information can be incorporated to conduct a richer enrichment analysis. To this end, NoRCE includes several relevant datasets as part of its data repository, including cell-line specific TAD boundaries, functional gene sets, and expression data for coding & ncRNAs specific to cancer. Additionally, the users can utilize custom data files in their investigation. Enrichment results can be retrieved in a tabular format or visualized in several different ways. NoRCE is currently available for the following species: human, mouse, rat, zebrafish, fruit fly, worm, and yeast.

Pooling, backward and forward selection of linear, logistic and Cox regression models in multiply imputed datasets. Backward and forward selection can be done from the pooled model using Rubin's Rules (RR), the D1, D2, D3, D4 and the median p-values method. This is also possible for Mixed models. The models can contain continuous, dichotomous, categorical and restricted cubic spline predictors and interaction terms between all these type of predictors. The stability of the models can be evaluated using (cluster) bootstrapping. The package further contains functions to pool model performance measures as ROC/AUC, Reclassification, R-squared, scaled Brier score, H&L test and calibration plots for logistic regression models. Internal validation can be done across multiply imputed datasets with cross-validation or bootstrapping. The adjusted intercept after shrinkage of pooled regression coefficients can be obtained. Backward and forward selection as part of internal validation is possible. A function to externally validate logistic prediction models in multiple imputed datasets is available and a function to compare models. For Cox models a strata variable can be included. Eekhout (2017) <doi:10.1186/s12874-017-0404-7>. Wiel (2009) <doi:10.1093/biostatistics/kxp011>. Marshall (2009) <doi:10.1186/1471-2288-9-57>.

This package provides a framework of interoperable R6 classes (Chang, 2020, <https://CRAN.R-project.org/package=R6>) for building ensembles of viable models via the pattern-oriented modeling (POM) approach (Grimm et al.,2005, <doi:10.1126/science.1116681>). The package includes classes for encapsulating and generating model parameters, and managing the POM workflow. The workflow includes: model setup; generating model parameters via Latin hyper-cube sampling (Iman & Conover, 1980, <doi:10.1080/03610928008827996>); running multiple sampled model simulations; collating summary results; and validating and selecting an ensemble of models that best match known patterns. By default, model validation and selection utilizes an approximate Bayesian computation (ABC) approach (Beaumont et al., 2002, <doi:10.1093/genetics/162.4.2025>), although alternative user-defined functionality could be employed. The package includes a spatially explicit demographic population model simulation engine, which incorporates default functionality for density dependence, correlated environmental stochasticity, stage-based transitions, and distance-based dispersal. The user may customize the simulator by defining functionality for translocations, harvesting, mortality, and other processes, as well as defining the sequence order for the simulator processes. The framework could also be adapted for use with other model simulators by utilizing its extendable (inheritable) base classes.

This package provides functions are provided that facilitate the import and analysis of SNP (single nucleotide polymorphism) and silicodart (presence/absence) data. The main focus is on data generated by DarT (Diversity Arrays Technology), however, data from other sequencing platforms can be used once SNP or related fragment presence/absence data from any source is imported. Genetic datasets are stored in a derived genlight format (package adegenet'), that allows for a very compact storage of data and metadata. Functions are available for importing and exporting of SNP and silicodart data, for reporting on and filtering on various criteria (e.g. CallRate', heterozygosity, reproducibility, maximum allele frequency). Additional functions are available for visualization (e.g. Principle Coordinate Analysis) and creating a spatial representation using maps. dartR supports also the analysis of 3rd party software package such as newhybrid', structure', NeEstimator and blast'. Since version 2.0.3 we also implemented simulation functions, that allow to forward simulate SNP dynamics under different population and evolutionary dynamics. Comprehensive tutorials and support can be found at our github repository: github.com/green-striped-gecko/dartR/. If you want to cite dartR', you find the information by typing citation('dartR') in the console.

Develops algorithms for fitting, prediction, simulation and initialization of the following models (1)- hidden hybrid Markov/semi-Markov model, introduced by Guedon (2005) <doi:10.1016/j.csda.2004.05.033>, (2)- nonparametric mixture of B-splines emissions (Langrock et al., 2015 <doi:10.1111/biom.12282>), (3)- regime switching regression model (Kim et al., 2008 <doi:10.1016/j.jeconom.2007.10.002>) and auto-regressive hidden hybrid Markov/semi-Markov model, (4)- spline-based nonparametric estimation of additive state-switching models (Langrock et al., 2018 <doi:10.1111/stan.12133>) (5)- robust emission model proposed by Qin et al, 2024 <doi:10.1007/s10479-024-05989-4> (6)- several emission distributions, including mixture of multivariate normal (which can also handle missing data using EM algorithm) and multi-nomial emission (for modeling polymer or DNA sequences) (7)- tools for prediction of future state sequence, computing the score of a new sequence, splitting the samples and sequences to train and test sets, computing the information measures of the models, computing the residual useful lifetime (reliability) and many other useful tools ... (read for more description: Amini et al., 2022 <doi:10.1007/s00180-022-01248-x> and its arxiv version: <doi:10.48550/arXiv.2109.12489>).