# Towards optimal extraction of cosmological information from nonlinear data

## Abstract

One of the main unsolved problems of cosmology is how to maximize the extraction of information from nonlinear data. If the data are nonlinear the usual approach is to employ a sequence of statistics (N-point statistics, counting statistics of clusters, density peaks or voids etc.), along with the corresponding covariance matrices. However, this approach is computationally prohibitive and has not been shown to be exhaustive in terms of information content. Here we instead develop a hierarchical Bayesian approach, expanding the likelihood around the maximum posterior of linear modes, which we solve for using optimization methods. By integrating out the modes using perturbative expansion of the likelihood we construct an initial power spectrum estimator, which for a fixed forward model contains all the cosmological information if the initial modes are gaussian distributed. We develop a method to construct the window and covariance matrix such that the estimator is explicitly unbiased and nearly optimal. We then generalize the method to include the forward model parameters, including cosmological and nuisance parameters, and primordial non-gaussianity. We apply the method in the simplified context of nonlinear structure formation, using either simplified 2-LPT dynamics or N-body simulations as the nonlinear mapping between linear and nonlinear density,more »

- Authors:

- Univ. of California, Berkeley, CA (United States). Berkeley Center for Cosmological Physics and Dept. of Physics; Univ. of California, Berkeley, CA (United States). Dept. of Astronomy; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Physics Dept.
- Univ. of California, Berkeley, CA (United States). Berkeley Center for Cosmological Physics and Dept. of Physics

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1523502

- Grant/Contract Number:
- AC02-05CH11231

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Cosmology and Astroparticle Physics

- Additional Journal Information:
- Journal Volume: 2017; Journal Issue: 12; Journal ID: ISSN 1475-7516

- Publisher:
- Institute of Physics (IOP)

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

```
Seljak, Uroš, Aslanyan, Grigor, Feng, Yu, and Modi, Chirag. Towards optimal extraction of cosmological information from nonlinear data. United States: N. p., 2017.
Web. doi:10.1088/1475-7516/2017/12/009.
```

```
Seljak, Uroš, Aslanyan, Grigor, Feng, Yu, & Modi, Chirag. Towards optimal extraction of cosmological information from nonlinear data. United States. doi:10.1088/1475-7516/2017/12/009.
```

```
Seljak, Uroš, Aslanyan, Grigor, Feng, Yu, and Modi, Chirag. Tue .
"Towards optimal extraction of cosmological information from nonlinear data". United States. doi:10.1088/1475-7516/2017/12/009. https://www.osti.gov/servlets/purl/1523502.
```

```
@article{osti_1523502,
```

title = {Towards optimal extraction of cosmological information from nonlinear data},

author = {Seljak, Uroš and Aslanyan, Grigor and Feng, Yu and Modi, Chirag},

abstractNote = {One of the main unsolved problems of cosmology is how to maximize the extraction of information from nonlinear data. If the data are nonlinear the usual approach is to employ a sequence of statistics (N-point statistics, counting statistics of clusters, density peaks or voids etc.), along with the corresponding covariance matrices. However, this approach is computationally prohibitive and has not been shown to be exhaustive in terms of information content. Here we instead develop a hierarchical Bayesian approach, expanding the likelihood around the maximum posterior of linear modes, which we solve for using optimization methods. By integrating out the modes using perturbative expansion of the likelihood we construct an initial power spectrum estimator, which for a fixed forward model contains all the cosmological information if the initial modes are gaussian distributed. We develop a method to construct the window and covariance matrix such that the estimator is explicitly unbiased and nearly optimal. We then generalize the method to include the forward model parameters, including cosmological and nuisance parameters, and primordial non-gaussianity. We apply the method in the simplified context of nonlinear structure formation, using either simplified 2-LPT dynamics or N-body simulations as the nonlinear mapping between linear and nonlinear density, and 2-LPT dynamics in the optimization steps used to reconstruct the initial density modes. We demonstrate that the method gives an unbiased estimator of the initial power spectrum, providing among other a near optimal reconstruction of linear baryonic acoustic oscillations.},

doi = {10.1088/1475-7516/2017/12/009},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 12,

volume = 2017,

place = {United States},

year = {2017},

month = {12}

}

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