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In 1999, Judi Romijn compared two model checkers (CADP and SPIN) on the HAVi interoperability audio-video protocol for consumer electronics. [3] In 2003, Yifei Dong, Xiaoqun Du, Gerard J. Holzmann, and Scott A. Smolka published a comparison of four model checkers (namely: Cospan, Murphi, SPIN, and XMC) on a communication protocol, the GNU i ...
a "semi-parametric" model contains finite-dimensional parameters of interest and infinite-dimensional nuisance parameters; a "semi-nonparametric" model has both finite-dimensional and infinite-dimensional unknown parameters of interest. Some statisticians believe that the concepts "parametric", "non-parametric", and "semi-parametric" are ...
Model checking is also studied in the field of computational complexity theory. Specifically, a first-order logical formula is fixed without free variables and the following decision problem is considered: Given a finite interpretation, for instance, one described as a relational database, decide whether the interpretation is a model of the ...
To estimate the parameters of a model, the model must be properly identified. That is, the number of estimated (unknown) parameters (q) must be less than or equal to the number of unique variances and covariances among the measured variables; p(p + 1)/2. This equation is known as the "t rule".
In the mathematical theory of stochastic processes, variable-order Markov (VOM) models are an important class of models that extend the well known Markov chain models. In contrast to the Markov chain models, where each random variable in a sequence with a Markov property depends on a fixed number of random variables, in VOM models this number of conditioning random variables may vary based on ...
Pathological behavior, however, occurs when we have many small strata because the number of parameters grow with the amount of data. For example, if each stratum contains two datapoints, then the number of parameters in a model with N {\displaystyle N} datapoints is N / 2 + p {\displaystyle N/2+p} , so the number of parameters is of the same ...
For this model, there are three parameters: c, φ, and the variance of the ε i. More generally, a pth-order autoregressive model has p + 2 parameters. (If, however, c is not estimated from the data, but instead given in advance, then there are only p + 1 parameters.)
Identifiability of the model in the sense of invertibility of the map is equivalent to being able to learn the model's true parameter if the model can be observed indefinitely long. Indeed, if {X t} ⊆ S is the sequence of observations from the model, then by the strong law of large numbers,