# GRID-BASED EXPLORATION OF COSMOLOGICAL PARAMETER SPACE WITH SNAKE

## Abstract

We present a fully parallelized grid-based parameter estimation algorithm for investigating multidimensional likelihoods called Snake, and apply it to cosmological parameter estimation. The basic idea is to map out the likelihood grid-cell by grid-cell according to decreasing likelihood, and stop when a certain threshold has been reached. This approach improves vastly on the 'curse of dimensionality' problem plaguing standard grid-based parameter estimation simply by disregarding grid cells with negligible likelihood. The main advantages of this method compared to standard Metropolis-Hastings Markov Chain Monte Carlo methods include (1) trivial extraction of arbitrary conditional distributions; (2) direct access to Bayesian evidences; (3) better sampling of the tails of the distribution; and (4) nearly perfect parallelization scaling. The main disadvantage is, as in the case of brute-force grid-based evaluation, a dependency on the number of parameters, N{sub par}. One of the main goals of the present paper is to determine how large N{sub par} can be, while still maintaining reasonable computational efficiency; we find that N{sub par} = 12 is well within the capabilities of the method. The performance of the code is tested by comparing cosmological parameters estimated using Snake and the WMAP-7 data with those obtained using CosmoMC, the current standardmore »

- Authors:

- Publication Date:

- OSTI Identifier:
- 22270558

- Resource Type:
- Journal Article

- Journal Name:
- Astrophysical Journal

- Additional Journal Information:
- Journal Volume: 777; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0004-637X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ALGORITHMS; ASTROPHYSICS; BACKGROUND RADIATION; COMPARATIVE EVALUATIONS; COSMOLOGY; MARKOV PROCESS; MONTE CARLO METHOD; PERFORMANCE; SPACE

### Citation Formats

```
Mikkelsen, K., Næss, S. K., and Eriksen, H. K., E-mail: kristin.mikkelsen@astro.uio.no.
```*GRID-BASED EXPLORATION OF COSMOLOGICAL PARAMETER SPACE WITH SNAKE*. United States: N. p., 2013.
Web. doi:10.1088/0004-637X/777/2/172.

```
Mikkelsen, K., Næss, S. K., & Eriksen, H. K., E-mail: kristin.mikkelsen@astro.uio.no.
```*GRID-BASED EXPLORATION OF COSMOLOGICAL PARAMETER SPACE WITH SNAKE*. United States. doi:10.1088/0004-637X/777/2/172.

```
Mikkelsen, K., Næss, S. K., and Eriksen, H. K., E-mail: kristin.mikkelsen@astro.uio.no. Sun .
"GRID-BASED EXPLORATION OF COSMOLOGICAL PARAMETER SPACE WITH SNAKE". United States. doi:10.1088/0004-637X/777/2/172.
```

```
@article{osti_22270558,
```

title = {GRID-BASED EXPLORATION OF COSMOLOGICAL PARAMETER SPACE WITH SNAKE},

author = {Mikkelsen, K. and Næss, S. K. and Eriksen, H. K., E-mail: kristin.mikkelsen@astro.uio.no},

abstractNote = {We present a fully parallelized grid-based parameter estimation algorithm for investigating multidimensional likelihoods called Snake, and apply it to cosmological parameter estimation. The basic idea is to map out the likelihood grid-cell by grid-cell according to decreasing likelihood, and stop when a certain threshold has been reached. This approach improves vastly on the 'curse of dimensionality' problem plaguing standard grid-based parameter estimation simply by disregarding grid cells with negligible likelihood. The main advantages of this method compared to standard Metropolis-Hastings Markov Chain Monte Carlo methods include (1) trivial extraction of arbitrary conditional distributions; (2) direct access to Bayesian evidences; (3) better sampling of the tails of the distribution; and (4) nearly perfect parallelization scaling. The main disadvantage is, as in the case of brute-force grid-based evaluation, a dependency on the number of parameters, N{sub par}. One of the main goals of the present paper is to determine how large N{sub par} can be, while still maintaining reasonable computational efficiency; we find that N{sub par} = 12 is well within the capabilities of the method. The performance of the code is tested by comparing cosmological parameters estimated using Snake and the WMAP-7 data with those obtained using CosmoMC, the current standard code in the field. We find fully consistent results, with similar computational expenses, but shorter wall time due to the perfect parallelization scheme.},

doi = {10.1088/0004-637X/777/2/172},

journal = {Astrophysical Journal},

issn = {0004-637X},

number = 2,

volume = 777,

place = {United States},

year = {2013},

month = {11}

}