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Real Name
Elizabeth Eli Holmes


I am an applied population biologist. I work mainly on methods for population viability analysis and on analysis of multivariate autoregressive state-space models in ecological applications. Main projects:

  • LAMBDA: MAR-1 analysis of community data vis-a-vis Ives et al 2003. (developers Steve Viscido and Eli Holmes)
  • Kalman-EM: Estimation of constrained and unconstrained multivariate autoregressive state-space models via a Kalman filter and smoother plus EM algorithm. (developers Eli Holmes and Eric Ward)
  • MARSS: Our R package that replaces Kalman-EM.  Fully documented with help files and has a manual.  Version 3.0 (in 2011) will provide Bayesian and data-cloning methods. (developed by Eli Holmes, Eric Ward, and Kellie Wills)
  • DARTER: Diffusion Approximation Tools for Extinction Risk Estimation.  An Excel program that computes a Bayesian posterior for some PVA metrics using a Kalman filter + SIR search (developed by Brice Semmens and Eli Holmes)
  • Data-cloning: Data-cloning (vis-a-vis Lele et al., 2007, Ecology Letters) for ML estimation for MARSS models.  Uses OpenBugs (developed by Eric Ward). Simpler code for univariate case is here: Data-cloning I.

My papers can be found on my website:


  • Bayesian MAR(1) model

    This set of Matlab scripts conducts a first order MAR(1) model to estimate interactive effects, and covariate effects, on a time series of data from a community.

    It uses a Gibbs sampler to estimate parameters, and currently is set up with diffuse priors on all parameters for the model. It is pretty basic at this point, but it works.

    Note on the Gamma distribution:

    Going back and forth between Matlab/R/WinBUGS can be confusing, because of the different parameterizations of the gamma pdf. Here's the Matlab/BUGS forms and the R equivalents:

    Matlab: X ~ g(a,b) E[X] = ab

    R equivalent: X ~ g(shape=a,scale=b)

    BUGS: X ~ g(a,b) E[X] = a/b

    R equivalent: X ~ g(shape=a,rate=b) OR

    X ~ g(shape=a,scale=1/b)

  • DARTER (Diffusion Approximation Tools for Extinction Risk Estimation)

    This program allows one to walk through the steps required to conduct a population viability analysis, or PVA, using a population time time series. The model outputs probabilities of extinction as a function of time steps into the future, and importantly, gives confidence intervals for these probabilities.

    This tool has two major advantages over traditional PVA techniques:

    1) It uses a state-space Kalman filter that allows for both process and non-process error.

    So what's the big deal? --Functionally it filters the data, and allows a more accurate fit for population parameters of interest.2) It uses a Bayesian sampling-importance-resampling algorithm to fully address uncertainty in the parameter estimates given the data.Rather than developing a single function that describes the probability of population extinction through time, we can use the uncertainty in parameter estimates to develop 'probabilities of probabilities', or, the uncertainty surrounding the probability of extinction through time.

  • Data Cloning I: univariate

    by eric.ward, last updated 5/26/08, sharing set to Public
    This script writes and runs the data cloning procedure described by Lele et al. (2007, Ecology Letters). The routine is in R, and requires the user to install OpenBUGS before running. The number of clones can (and should) be modified. For this simple example, 100 clones takes ~ 2 minutes on my 2.5 year old laptop (1.66Ghz, 1GB RAM). More details and diagnostics can be found in the multivariate cloning project.
  • DM

    by e2holmes, last updated 7/4/13, sharing set to Public
    Development site for DM package
  • Generate stochastic population processes

    by e2holmes, last updated 6/13/07, sharing set to Public
    These are function for generating various standard types of stochastic population processes: random walks, Ornstein-Uhlenbeck, discrete Gompertz, etc. Also some random number generators needed by these are here. These matlab files need the Matlat Statistics Toolbox.
  • Gibbs sampler for multiple linear regression

    by brice.semmens, last updated 7/5/08, sharing set to Public

    The point of this code is to show how to do it with a conjugate distribution such that the method can easily be plugged into LAMBDA.

    The function assumes that:

    1)the B coefficients are normally distributed ~N(prior_mean,prior_s2)and thus have a normal distribution prior. Large prior variances produce suitably "diffuse" priors

    2) the model variance is gamma distributed Ga(alpha, beta), with an associated prior. Small values of alpha and beta (<.001) produce a suitably "diffuse" prior. Note that Matlab's parameterization of their gamma function is a bit wonky compared to the standard. Basically, Matlab uses Ga(alpha,1/beta)-- ie. inverse of the standard scale parameter.

    The R code contains 2 versions of Bayesian linear regression. The first (univariate.all) uses the multivariate normal distribution to sample regression coefficients; the second (univariate.vat) does variable at a time sampling. Both R versions are nearly identical, allow a flexible range of priors for B, and allow the prior variance to be specified either as the shape-scale (e.g. gamma, scaled inv chi sq) or in terms of the mean-variance. Output includes saved parameter draws, which can be fed into CODA, and the calculation of the log(Bayes Factor) to be used for model selection.

    by e2holmes, last updated 9/11/07, sharing set to Public
    LAMBDA is a MatLab toolkit designed to do MAR-1 based data analysis on long-term datasets and is based on the methods described in Ives et al. 2003, Ecological Monographs 73:301-330. LAMBDA is designed to allow the user to step through the entire modeling process, from importing the data, to obtaining descriptive statistics of the dataset, to, finally, performing a MAR-1 regression model and obtaining output parameters. A MAR-1 process is a Multivariate, Auto-Regressive first (1st) order process. Essentially, it is a means of estimating interactions between multiple variates from time series data, using matrix algebra. A MAR-1 model is a stochastic, non-mechanistic model that uses time series data on species numbers and co-variates to deduce inter-population interactions and the effects of covariates (e.g., physical variables) on populations.

    Where does it come from?

    LAMBDA is a product of the Mathematical Biology program at the Northwest Fisheries Science Center in Seattle, WA, and was developed with support by NOAA/NMFS and the National Research Council. It is open-source software released under the GNU GPL license, meaning you are free to use and modify it in (almost) any way you see fit. LAMBDA was developed by Steven Viscido while on a National Research Council postdoctoral associateship with Elizabeth Holmes.


    LAMBDA is based on the techniques outlined in the paper Ives et al. 2003, Ecological Monographs 73:301-330. The code for the actual MAR-1 regression was based on the "MARbasic.m" MatLab script written by Tony Ives (available at the Ecological Archives). The parameter search code was based on an unpublished script written by Tony Ives. All other code was written by Steven Viscido.

    Executable version

    Download the LAMBDA executable along the installation instructions from the links below.

    LAMBDA_MCR_pkg.exe 0.9.2 Warning: This is a 138 MB file!

    Installation Instructions

    The executable version of LAMBDA does not require MatLab. Its system requirements are Windows XP/2000, 256 MB of RAM, and 150 MB of Hard Drive Space.

    If Installation hangs

    This is a bug on MatLab's side. To work around it, you will need to install vcredist_x86.exe (32 bit systems) or vcredist_x64.exe (64 bit system) first and then repeat the LAMBDA installation. But read the If_Installation_Hangs.txt readme file if this happens to you. This bug affects about 20% of computers, randomly it would seem.

    Matlab Source Code

    This is not needed if you are using the executable version. Current source code version is The source code can be downloaded below. Requirements for running LAMBDA from the source code are
    • MatLab version 7.0.1 (R14) w/service Pack 1, or later
    • MatLab's Statistics and Optimization toolboxes
    • At least 256 MB of RAM on your system
    • 5 MB of Hard Drive space for the LAMBDA installation
  • MARSS Dev Site

    This is the DEVELOPMENT site for the MARSS.  For the current MARSS  release go to CRAN or download straight from the R GUI using "Install Packages" menu.

    MARSS fits mulitvariate autoregressive state-space (MARSS) models with Gaussian errors to multivariate time series data.  A MARSS model is:

    x(t) = B(t) x(t-1) + u(t) + C(t)c(t) + v(t), v(t)~MVN(0,Q)

    y(t) = Z(t) x(t) + a(t) + D(t)d(t) + w(t), w(t)~MVN(0,R)

    Project news (Feb 26, 2013): MARSS 3.4 uploaded to CRAN.  I fixed MARSSkfas to work with the new KFAS package in order to use the Koopman/Durbin filter/smoother algorithms. I also coded up a lag-one covariance smoother using an augmented state-space model that you can then run through the smoother to get the lag-one covariances.  I added a coef() and residuals() method to improve output.

    Developers: Eli Holmes, Eric Ward, Mark Scheuerell and Kellie Wills

    Current known issues:

    • When variance is "unconstrained", the covariances can be set to 0 in the degen.test() and this leads to not pos-def matrix and error.  Need to block setting to 0 when this happens, or block covariances set to zero?  Currently, deal with this by setting allow.degen=FALSE when covariances are estimated.
    • demean.states=TRUE is causing the EM algorithm to give drops in logLik. This is not really a bug but perhaps a property of demean.states.  Removed the demean.states option in vrs 3.3.

    MARSS 4.0 in progress:

    • 4.0 involves a substantial change in the model object structure---however the user should not notice the difference.  The change allows the developers to more easily code up new model structures. 
    • Progress continues on writing functions for standard output, e.g. predict function added. 
    • Integration with LateX begun so that output can be sent to a tex or pdf file instead of just the console.


  • Plotting routines

    by e2holmes, last updated 6/13/07, sharing set to Public
    Miscellaneous matlab plotting functions that come in handy.
  • PVA estimation code

    A series of modules for estimation of PVA parameters from time series data. Uses kalman filters, REML, and slope methods.
  • Searchers and samplers

    by e2holmes, last updated 6/13/07, sharing set to Public
    This is a collection of routines for numerical sampling and searching of multivariate surfaces. It contains things like gibbs samplers, metropolis algorithms, mcmc and simulated annealing algorithms.
  • Teaching code for State-space models

    This is some matlab labs for teaching basic concepts about stochastic population trajectories and estimation for those trajectories.


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