Posts Tagged ‘kalman filter’

Estimating Endangered Species Interaction Risk with the Kalman Filter

March 22, 2014

Crossposting from the Reconhub:

AJAETogether with my co-author Stephen Stohs, I recently published an article in the American Journal of Agricultural Economics. The main gist is that with rare events like endangered species interactions, the statistical information in yearly data sets is limited, and that data from several years provide better information for decision making. We provide a method that is based on the Kalman filter and that allow for observations unequally spaced  in time. The method also takes account of spatiotemporal effects. We discuss the particular case of leatherback turtle bycatch in a gillnet fishery in California and Oregon. The leatherback is an endangered species, and in order to reduce bycatch, extensive spatiotemporal closures was imposed on the fishery in 2000. Our analysis shows that the interaction risk likely was smaller than in the scenarios that motivated the closures. To discuss whether the closures were and are warranted, require further analysis, however. As we discuss in the concluding section, closures in California may lead to trade leakages such that the total effect on the leatherback turtle stock is unknown. And the value of the leatherback in the ecosystem, and the value of its mere existence, is unknown.

The abstract:

To address the tradeoff between biodiversity conservation in marine ecosystems and fishing opportunity, it is important to quantify the risk of endangered species interactions in commercial fisheries. We propose a Kalman filter suitable for rare events to estimate the endangered leatherback turtle take risk in the California drift gillnet fishery in the years 1990–2010, conditional on spatiotemporal factors that affect take rates. Results suggest interaction risk has remained stable, but with substantial variation over the spatiotemporal distribution of effort. Our methods might also apply to recreation demand analysis with rare event risk, or to applications involving irregularly spaced observations, like trade-level stock market data.

The Ensemble Kalman Filter

October 27, 2010

The standard Kalman filter and even the Extended Kalman filter (for nonlinear problems) proved inadequate. I’ve now placed my hope in what’s known as the Ensemble Kalman Filter:

Another sequential data assimilation method which has received a lot of attention is named the Ensemble Kalman Filter (EnKF). The method was originally proposed as a stochastic or Monte Carlo alternative to the deterministic [Extended Kalman filter] by Evensen (1994a).  The EnKF was designed to resolve the two major problems related to the use of the [Extended Kalman filter] with nonlinear dynamics in large state spaces, i.e. the use of an approximate closure scheme and the huge computational requirements associated with the storage and forward integration of the error covariance matrix.

The EnKF gained popularity because of its simple conceptual formulation and relative ease of implementation, e.g. it requires no derivation of a tangent linear operator or adjoint equations and no integrations backward in time. Furthermore, the computational requirements are affordable and comparable to other popular sophisticated assimilation methods […].*

* Excerpt from Geir Evensen’s Data Assimilation: The Ensemble Kalman Filter, 2007, p. 38.

What is a Kalman Filter?

September 28, 2010

Theoretically, the Kalman Filter is an estimator for what is called the linear-quadratic problem, which is the problem of estimating the instantaneous “state” […] of a linear system perturbed by white noise by using measurements linearly related to the state but corrupted by white noise. The resulting estimator is statistically optimal with respect to any quadratic function of estimation error.

Practically, it is certainly one of the greater discoveries in the history of statistical estimation theory and possibly the greatest discovery in the twentieth century. It has enabled humankind to do many things that could not have been done without it, and it has become as indispensable as silicon in the makeup of many electronic systems. Its most immediate applications have been for the control of complex dynamic systems such as continuous manufacturing processes, aircraft, ships, or spacecraft. To control a dynamic system, you must first know what it is doing. For these applications, it is not always possible or desirable to measure every variable that you want to control, and the Kalman filter provides a means for inferring the missing information from indirect (and noisy) measurements. The Kalman filter is also used for prediction the likely future courses of dynamic systems that people are not likely to control, such as the flow of rivers during flood, the trajectories of celestial bodies, or the prices of traded commodities.

Yay! The above is the opening paragraphs of Mohinder S. Grewal and Angus P. Andrews Kalman Filtering: Theory and Practice Using MATLAB, Second Edition (2001, John Wiley & Sons, Inc.), which currently is under my scrutiny.

How am I supposed to read this?

October 1, 2008

This quote is from Randall L. Eubank’s very small book ‘A Kalman Filter Primer’, p. 2:

The amount of knowledge one has about this dependence [between the predictors and predictands] then determines the specifics of how the predictors are utilized in constructing a prediction formula or prescription that translate predictors into actual predictions for the predictans.