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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. So what's the big deal? -- 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.

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.

KalmanEM.R fits mulitvariate state space models to multivariate time series data.

X(t) = B X(t-1) + U + E(t), E~N(0,Q)

Y(t) = Z X(t) + A + eta(t), eta~N(0,R)

What you need to use this code: Download KalmanEM.R (or scroll down to download all the files).  Open R and source("KalmanEM.R").  That's it.  For basic analyses, all the packages you need are included in the base R distribution.

About this code: This code is used to estimate maximum likelihood parameters for multivariate state space time series models via an EM algorithm using the Kalman filter+smoother. We assume that there are N observation time series over T years, and that there may be shared parameters (growth rates, process error, observation error) across sites. Further, the errors may be correlated between sites and the N sites may be clustered into groups. We have a number of online workshops on multivariate state-space models available with case studies and examples for estimating trends, evaluating population structure, estimating interactions, and analyzing movement data: MSSM workshop  The base EM algorithm is from Shumway and Stoffer (2006). EM is a hill-climbing algorithm and many times the likelihood surface is multi-model. Use KalmanEM(...,MonteCarloInit = TRUE) to turn on searching of the initial condition space. This will deal with the vanilla multi-model problems. The "help files.pdf" file has the R help files for the main functions.

Learning how to use the code: Case Studies.pdf is effectively the current manual. Scripts and data for all the case studies are in the zip file Case studies scripts.zip. The easiest way to learn this code to read case studies 1 and 2 in the Case Studies.pdf. That will walk you through four applications. I have removed Case Study 4 which is on estimation of interactions. Currently we are researching the robustness of estimating interaction terms using MARSS models when the R matrix is free (estimated). One approach is to use a fixed R matrix, but that option is not in the current code. So use caution (meaning test, test, test) if you are using the option B.constraint="unconstrained".

Project news (Nov 2009):  See the file update_info.txt for changes in the code since 8/6/08 and the original release. We are in active development of MARSS 3.0, which is a complete reorganization of the code to make it into an R package.  MARSS 3.0 uses a general EM algorithm to allow you to fit any models of the MSSM form above with fixed values arbitrarily distributed through the matrices.  On Nov 6th, we completed our beta package and are in the final testing phase.  We are also actively working on Bayesian versions and non-Normal versions.  See our personal websites for group news on papers and code coming out of this work: EE Holmes website, Eric Ward website, Brice Semmens website, and Mark Scheuerell website.