# The 35th International Symposium on Lattice Field Theory

18-24 June 2017
Palacio de Congresos
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# Contribution Parallel

Seminarios 8
Software Development

# Improved data covariance estimation techniques applied to lattice QCD

## Speakers

• Dr. james SIMONE

## Content

Quantities in lattice QCD are estimated from statistical fits to lattice correlation functions. For example, a meson mass may be estimated from a fit to a two-point function, $C(t)$, computed at $p$ timeslices, where each measurement is averaged over a sample of $n$, statistically independent gauge configurations. Correlations among $C(t)$ at nearby time slices means that the statistical procedure must includes an estimate of the rank $p$ the covariance matrix. Most often, the desired inverse of the population covariance matrix is simply estimated to be equal to the inverse of the sample covariance matrix. The sample covariance, however, is known to be a poor estimate of the population covariance when $p / n$ is near one. In fact, the sample covariance matrix will have one or more zero eigenvalues when $p / n \ge 1$. Cases where $p / n \sim 1$ are encountered in practice, where the sample covariance matrix is found to have a number "small" eigenvalues. In this talk we discuss the application of linear and nonlinear "shrinkage" techniques to the estimation of population covariance. For the nonlinear shrinkage technique we consider, the estimated covariance matrix approaches the population covariance matrix in the limit $p, n \to \infty$, and $p / n = \mathrm{constant}$.

## Preferred track (if multiple tracks have been selected)

Software Development