**Phase Plane Analysis of One- And Two-Dimensional Autonomous ODE Systems** (**phaseR**)

Performs a qualitative analysis of one- and two-dimensional autonomous ordinary differential equation systems, using phase plane methods. Programs are available to identify and classify equilibrium points, plot the direction field, and plot trajectories for multiple initial conditions. In the one-dimensional case, a program is also available to plot the phase portrait. Whilst in the two-dimensional case, programs are additionally available to plot nullclines and stable/unstable manifolds of saddle points. Many example systems are provided for the user. For further details can be found in Grayling (2014) <doi:10.32614/RJ-2014-023>.

**Distributions for Ecological Models in ‘nimble’** (**nimbleEcology**)

Common ecological distributions for ‘nimble’ models in the form of nimbleFunction objects. Includes Cormack-Jolly-Seber, occupancy, dynamic occupancy, hidden Markov, and dynamic hidden Markov models. (Jolly (1965) <doi:10.2307/2333826>, Seber (1965) <10.2307/2333827>, Turek et al. (2016) <doi:10.1007/s10651-016-0353-z>).

**Bayesian Estimation of Bivariate Volatility Model** (**BayesBEKK**)

The Multivariate Generalized Autoregressive Conditional Heteroskedasticity (MGARCH) models are used for modelling the volatile multivariate data sets. In this package a variant of MGARCH called BEKK (Baba, Engle, Kraft, Kroner) proposed by Engle and Kroner (1995) <http://…/3532933> has been used to estimate the bivariate time series data using Bayesian technique.

**Data Transformation or Simulation with Empirical Covariance Matrix** (**simTargetCov**)

Transforms or simulates data with a target empirical covariance matrix supplied by the user. The method to obtain the data with the target empirical covariance matrix is described in Section 5.1 of Christidis, Van Aelst and Zamar (2019) <arXiv:1812.05678>.

**Graphical and Numerical Checks for Mode-Finding Routines** (**optimCheck**)

Tools for checking that the output of an optimization algorithm is indeed at a local mode of the objective function. This is accomplished graphically by calculating all one-dimensional ‘projection plots’ of the objective function, i.e., varying each input variable one at a time with all other elements of the potential solution being fixed. The numerical values in these plots can be readily extracted for the purpose of automated and systematic unit-testing of optimization routines.

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