Profiled Estimation of Differential Equations/<title> </head> <body text="#000000" bgcolor="#FFFFFF" link="#0000FF" vlink="#551A8B" alink="#0000FF"> <center> <p><font size=+8>Profiling Papers and Code</font> <p><img SRC="fhn_linforce.png" BORDER=20 height=200 width=225 align=CENTER> </center> This page provides code and documentation for spline-based estimation of parameters in differential equations via a <i>profiled penalty estimation</i>. <p>The main paper describing the methodology is <p>James Ramsay, Giles Hooker David Campbell and Jiguo Cao, 2007. "<a href="ODE_Estimation.pdf">"Estimating Differential Equations</a>", Journal of the Royal Statistical Society, Series B, Vol 69, No 5. <p>Some proofs from the paper above are given in <p> Giles Hooker, 2007, "<a href="ode_techrep.pdf">Theorems and Calculations for Smoothing-based Profiled Estimation of Differential Equations</a>", Technical Report BU-1671-M, Department of Biological Statistics and Computational Biology, Cornell University. <p>There is a <a href="profiling.zip">Matlab software bundle</a> available for use with the <a href="http://www.psych.mcgill.ca/misc/fda">FDA</a> package. <p>A <a href="Profile_Users_Manual.pdf">users manual</a> for the software bundle is also available. <p> Webpage demonstrations of the software in action using the <a href="FhN_example/FhNEx.html">FitzHugh-Nagumo equations</a> and the <a href="Rossler_example/RosslerEx.html">Rossler equations</a> may be useful to go through. <p> The software supports replicated experiments; this is demonstrated on the <a href="FhN_example/FhNEx_rep.html">FitzHugh-Nagumo equations</a> and the <a href="Rossler_example/RosslerEx_rep.html">Rossler equations</a>. <p> As a useful special case, there is a set of functions for estimating <a href="genlin_example/genlinEx.html">forced, linear, systems</a>, also given as a webpage demonstration. <p> Finally, there is a webpage demonstration for some <a href ="FhN_example/FhN_model_building.html">diagnostic tools</a> for the mis-specification of linear differential equations. A demonstration on <a href="Forcing_example/ForcingFhNEx.html">estimating forcing functions for nonlinear systems</a> is also available. <p> The code currently only allows systems that are observed directly, plus (approximately) Gaussian noise. If you have observations of some transform of a system or want to use some likelihood other than squared error, please feel free to bug us about updating the code. <p> For inquiries, comments, more code, or suggestions, please contact <a href="http://www.psych.mcgill.ca/perpg/pstdc/giles">Giles Hooker</a> at <b>giles[dot]hooker[at]cornel[dot]edu</b>. </body> </html>