The Isis programme is an approach to simulation, forecasting and management of complex systems that accepts models are always imperfect. The Isis programme emphasizes and exploits the dynamical aspects of the model, rather than the statistical. The key concepts and tools are shadowing and indistinguishable states.
For general overview of the Isis programme see Judd and Stemler, 2009b. The basic theory for perfect and imperfect model scenarios was developed in Judd and Smith, 2001 and Judd and Smith, 2004 respectively. Stemler and Judd, 2009 provides a more up-to-date and focussed guide to implementing shadowing filters. For comparisons of shadowing filters with extended Kalman filters see Judd, 2003, and for a comparison with particle filters see Judd and Stemler, 2009a. Comparisons with variational methods are mentioned in Judd, 2008a.
The technical report Judd et al, 2004a is an application of a shadowing filter to the NOGAPS operational weather model. Many of the results in the report also appear in Judd et al, 2008, and the more theoretical papers Judd, 2008a, b also include applications to NOGAPS. Judd et al, 2004b discusses using shadowing filters without an adjoint of the model. Identifying model error in an operational weather model is discussed in Judd et al, 2008.
On more technical and theoretical issues Ridout and Judd, 2002 discusses the behaviour of shadowing filter algorithms in perfect hyperbolic models, and Judd, 2008b considers non-hyperbolic and imperfect models, including operational weather models. Judd, 2008a looks at issues on obtaining optimal shadowing pseudo-orbits. Judd, 2003a, Judd, 2007a and Judd and Stemler, 2009a all provide criticisms of the assumptions of other approaches like sequential Bayesian filters and demonstrate failures of these methods.
Issues of ensemble forecasting are discussed in Weisheimer et al, 2004, Judd et al, 2007 and Teixeira et al, 2007
The most significant work here is the application of information theory to phenomenological modelling of time-series of nonlinear systems. The book chapter Judd, 2003c provides a overview of most of this work. Judd and Mees, 1995 introduces the basic theory and model selection algorithms. Judd and Mees, 1998 introduces the important idea that the embedding of time-series into a state-space should be treated as a modelling problem.
Various applications of the methods are discussed in Judd and Mees, 1996, 1997, Mees and Judd, 1996a, b, Allie et al, 1997a, b. Especially applications to identifying periodicity in infant breathing in Small et al, 1996, 1999 and Small and Judd, 1999. The periodicity work resulted in Rock et al, 2008 that investigates seasonality in suicides, but actually uses only simple methods. See also McSharry et al, 2001 for an application of model selection to boiling.
A number of techniques have been developed as diagnostic tests of timeseries, including Cao et al, 1997a, b, 1998a, b, Small and Judd, 1998a, b. The work on surrogate data tests with Small are based on early work on estimation of dimension Judd, 1989, 1992, Judd and Mees, 1991.
Further extensions and refinements of the modelling methods appear in Pilgram et al, 2002, Small et al, 2002, Nakamura et al, 2003, 2004, 2006, 2007.
Some issues concerning symbolic dynamics are considered in Hirata et al 2004, Hirata and Judd, 2005, with applications in Hirata et al, 2005 and Judd, 2007b.
The book Control of Chaos Eds. Judd et al, 2007 contains a number of authored or co-authored papers.
Despite the large amount of time I have put into developing the CalMæth software, there is only one publication Monson and Judd, 2000.