# UNSUPERVISED TRANSIENT LIGHT CURVE ANALYSIS VIA HIERARCHICAL BAYESIAN INFERENCE

## Abstract

Historically, light curve studies of supernovae (SNe) and other transient classes have focused on individual objects with copious and high signal-to-noise observations. In the nascent era of wide field transient searches, objects with detailed observations are decreasing as a fraction of the overall known SN population, and this strategy sacrifices the majority of the information contained in the data about the underlying population of transients. A population level modeling approach, simultaneously fitting all available observations of objects in a transient sub-class of interest, fully mines the data to infer the properties of the population and avoids certain systematic biases. We present a novel hierarchical Bayesian statistical model for population level modeling of transient light curves, and discuss its implementation using an efficient Hamiltonian Monte Carlo technique. As a test case, we apply this model to the Type IIP SN sample from the Pan-STARRS1 Medium Deep Survey, consisting of 18,837 photometric observations of 76 SNe, corresponding to a joint posterior distribution with 9176 parameters under our model. Our hierarchical model fits provide improved constraints on light curve parameters relevant to the physical properties of their progenitor stars relative to modeling individual light curves alone. Moreover, we directly evaluate the probability formore »

- Authors:

- Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States)
- Department of Statistics, University of Warwick, Coventry CV4 7AL (United Kingdom)

- Publication Date:

- OSTI Identifier:
- 22364253

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Astrophysical Journal; Journal Volume: 800; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; COMPUTERIZED SIMULATION; DIAGRAMS; HAMILTONIANS; LIMITING VALUES; MONTE CARLO METHOD; NOISE; PROBABILITY; STATISTICAL MODELS; SUPERNOVAE; TRANSIENTS; VISIBLE RADIATION

### Citation Formats

```
Sanders, N. E., Soderberg, A. M., and Betancourt, M., E-mail: nsanders@cfa.harvard.edu.
```*UNSUPERVISED TRANSIENT LIGHT CURVE ANALYSIS VIA HIERARCHICAL BAYESIAN INFERENCE*. United States: N. p., 2015.
Web. doi:10.1088/0004-637X/800/1/36.

```
Sanders, N. E., Soderberg, A. M., & Betancourt, M., E-mail: nsanders@cfa.harvard.edu.
```*UNSUPERVISED TRANSIENT LIGHT CURVE ANALYSIS VIA HIERARCHICAL BAYESIAN INFERENCE*. United States. doi:10.1088/0004-637X/800/1/36.

```
Sanders, N. E., Soderberg, A. M., and Betancourt, M., E-mail: nsanders@cfa.harvard.edu. Tue .
"UNSUPERVISED TRANSIENT LIGHT CURVE ANALYSIS VIA HIERARCHICAL BAYESIAN INFERENCE". United States.
doi:10.1088/0004-637X/800/1/36.
```

```
@article{osti_22364253,
```

title = {UNSUPERVISED TRANSIENT LIGHT CURVE ANALYSIS VIA HIERARCHICAL BAYESIAN INFERENCE},

author = {Sanders, N. E. and Soderberg, A. M. and Betancourt, M., E-mail: nsanders@cfa.harvard.edu},

abstractNote = {Historically, light curve studies of supernovae (SNe) and other transient classes have focused on individual objects with copious and high signal-to-noise observations. In the nascent era of wide field transient searches, objects with detailed observations are decreasing as a fraction of the overall known SN population, and this strategy sacrifices the majority of the information contained in the data about the underlying population of transients. A population level modeling approach, simultaneously fitting all available observations of objects in a transient sub-class of interest, fully mines the data to infer the properties of the population and avoids certain systematic biases. We present a novel hierarchical Bayesian statistical model for population level modeling of transient light curves, and discuss its implementation using an efficient Hamiltonian Monte Carlo technique. As a test case, we apply this model to the Type IIP SN sample from the Pan-STARRS1 Medium Deep Survey, consisting of 18,837 photometric observations of 76 SNe, corresponding to a joint posterior distribution with 9176 parameters under our model. Our hierarchical model fits provide improved constraints on light curve parameters relevant to the physical properties of their progenitor stars relative to modeling individual light curves alone. Moreover, we directly evaluate the probability for occurrence rates of unseen light curve characteristics from the model hyperparameters, addressing observational biases in survey methodology. We view this modeling framework as an unsupervised machine learning technique with the ability to maximize scientific returns from data to be collected by future wide field transient searches like LSST.},

doi = {10.1088/0004-637X/800/1/36},

journal = {Astrophysical Journal},

number = 1,

volume = 800,

place = {United States},

year = {Tue Feb 10 00:00:00 EST 2015},

month = {Tue Feb 10 00:00:00 EST 2015}

}