The power spectrum of a zero-mean stationary Gaussian random process is assumed to be known except for one or more parameters which are to be estimated from an observation of the process during a finite time interval. The approximation is introduced that the coefficients of the Fourier series expansion of a realization of long-time duration are uncorrelated. Based on this approximation maximum ...

Real world does not only provide noisy instead of perfect data. Every experimentalist has now and then to deal with outliers. The situation is simple if isolated points stick out of the general trend by a large amount. Arguments can then usually be found why such a point should be disregarded. The situation becomes critical if the outliers are not that obvious. This is usually the case for para...

SHARMA, SIDDHARTH. Parameter Estimation for System Biology Models on GPU Clusters . (Under the direction of Dr. James Tuck.) In this work, we consider the parallelization of interval based parameter estimation with uncertainty propagation for non-linear ODE models. This approach is especially important in systems biology research as it addresses the uncertainty often present in data recorded fr...

This paper contains a review of the issues surrounding sinusoidal parameter estimation which is a vital part of many audio manipulation algorithms. A number of algorithms which use the phase of the Fourier transform for estimation (e.g. [1]) are explored and shown to be identical. Their performance against a classical interpolation estimator [2] and comparison with the Cramer Rao Bound (CRB) is...

This paper deals with the minimax parameter estimation of nonlinear parametric models from experimental data. Taking advantage of the special structure of the minimax problem, a new e¢cient and reliable algorithm based on interval constraint propagation is proposed. As an illustration, the ill-conditioned problem of estimating the parameters of a two-exponential model is considered.

Using a perturbation matrix, we introduced a hyperplane used to define a generalized null-spectrum, based on both the signal and noise subspaces, while the MUSIC and Min-Norm null-spectra are defined based only on the noise subspace. With the generalized nullspectrum, we derived the upper and lower bounds of a class of the generalized null-spectrum, called the maximum and minimum null-spectra, ...

Ranking of alternatives is a common, difficult and repeatedly addressed problem, especially when it requires negotiation of experts. The celebrated Arrow’s impossibility theorem expresses formally its difficulty. In spite of theprogressmadebyadopting soft ranking, the problem is far from being generically solved. The paper provides a, probably novel, problem formulation by viewing ranking of al...

The problem of estimating the parameters for continuous-time partially observed systems is discussed. New exact lters for obtaining Maximum Likelihood (ML) parameter estimates via the Expectation Maximization algorithm are derived. The methodology exploits relations between incomplete and complete data likelihood and gradient of likelihood functions, which are derived using Girsanov's measure t...

Example 4.1 (Psichokinesis). Imagine controlling things with your mind. For example, skipping a song by just thinking about it. One way to do this is by putting D sensors in your head (in your headphones, for example). These sensors would record small voltages generated by your brain, store them in a vector x ∈ R, and send them to a machine (phone, computer, server, etc.). The machine should in...