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**Chapter 4** 

© 2012 Üstündag and Cevri, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

*y*( ) ( ; ), *t ft* **θ** (1)

. On the other hand,

**Bayesian Recovery of** 

Dursun Üstündag and Mehmet Cevri

http://dx.doi.org/10.5772/50449

**1. Introduction** 

1 2 ( , ,..., )*<sup>T</sup> <sup>N</sup> tt t* :

Additional information is available at the end of the chapter

**Sinusoids with Simulated Annealing** 

Therefore, our general interest is to subtract this information from data.

mean Gaussian probability distribution with a standard deviation of

1 Static refers to that the amplitudes of the sinusoids do not change with time.

this chapter, we restrict our attention to the static1 sinusoidal model given by

system is described by a vector function *f* in the form:

The ultimate goal of collecting data is to gain meaningful information about a physical system. However, in many situations, the quantities that we would like to determine are different from the ones which we are able to have measured. If the data we measured depends on the quantities we want, it contains at least some information about them.

Let the vector **θ** contain the parameters to be estimated from the (measurements) vector **D**, which is the output of the physical system that one wants to be modeled. The physical

where *t* represents time. In many experiments, the recorded data 1 2 { , ,..., } *<sup>N</sup>* **D** *dd d* are sampled from an unknown function *y*( )*t* together with errors *e t*( ) at discrete times

( ) ( ), ( 1,..., ). *ii i d yt et i N* (2)

The measurement errors *e t*( ) are generally assumed to be drawn independently from a zero

different signal models correspond to different choices of signal model function *f t*(, ) **θ** . In

and reproduction in any medium, provided the original work is properly cited.

## **Chapter 4**
