• We reproduced a same state-of-the-art result (Green et al. 2008.03312) for GW150914 and applied the formulism to the other GW events. Normalized flow model and how we pre-processing the data will be explained by pedagogy. (may be omitted) Some on-going works are also mentioned.
  • I have to explain this in Chinese for clarity...๐Ÿ™

Statistical inference with normalized flow for BBHs in O1/O2

He Wang

First demonstration of early warning gravitational wave alerts. (2102.04555)

Motivation

  • Higher, faster, stronger \(\Rightarrow\)ย  More, Better, Faster

Motivation

Parameter Estimation Bias From Overlapping Binary Black Hole Events In Second Generation Interferometers. (2103.16225)

  • Can we find overlapping GW events at the same time?

"If the signals are greater than ~0.1 seconds apart they can be distinguished separately.

Less than this and the second signal will cause significant bias."

\begin{aligned} 10 \mathrm{M}_{\odot} \leq & m_{i} \leq 80 \mathrm{M}_{\odot} \\ 100 \mathrm{Mpc} \leq & d_{L} \leq 1000 \mathrm{Mpc} \end{aligned}

GW150914

Green et al. [2002.07656, 2008.03312] (MAF, CVAE+, Flow-based)

  • optimal results for now

Results

  • We can reproduce the complete parameter inference result for GW150914.
\begin{aligned} 10 \mathrm{M}_{\odot} \leq & m_{i} \leq 80 \mathrm{M}_{\odot} \\ 100 \mathrm{Mpc} \leq & d_{L} \leq 1000 \mathrm{Mpc} \end{aligned}

Results

GW150914

  • But not perfect....

GW151012

GW151226

\begin{aligned} 3 \mathrm{M}_{\odot} \leq & m_{i} \leq 80 \mathrm{M}_{\odot} \\ 100 \mathrm{Mpc} \leq & d_{L} \leq 1000 \mathrm{Mpc} \end{aligned}
\begin{aligned} 5 \mathrm{M}_{\odot} \leq & m_{i} \leq 80 \mathrm{M}_{\odot} \\ 100 \mathrm{Mpc} \leq & d_{L} \leq 2000 \mathrm{Mpc} \end{aligned}

Results

  • Even worse on other events in O1

GW170104

Results

GW170823

  • Even worse on other events in O1 and O2

Results

  • Even worse on other events in O1 and O2
  • We need more understanding and exploration on the model.
    • Objective 1: A Model trained on a event can estimate the event well. (current)
    • Objective 2: A Model trained can estimate all the events well.

Trained from GW151226, testing on GW150914

\text{PSD}_{det}

1024 sec

8 sec

ref_time

GPS time

6 sec

\text{PSD}_{det}

1024 sec

8 sec

ref_time

GPS time

6 sec

\text{PSD}_{det}

1024 sec

8 sec

ref_time

GPS time

6 sec

Training

\text{PSD}_{det}

1024 sec

8 sec

ref_time

GPS time

6 sec

Training

\text{PSD}_{det}

1024 sec

8 sec

ref_time

GPS time

6 sec

Testing

On-going works (1/2)

GW150914, SNR = 36.30
  • It the outputs from the model sharing the same behavior like MCMC?

On-going works (1/2)

GW150914, SNR = 36.30
  • It the outputs from the model sharing the same behavior like MCMC?
    • YES!

On-going works (2/2)

  • It the outputs from the model sharing the same behavior like MCMC?
    • YES!
  • How much lowerย achievableย SNR for the model?
    • Comparing with MCMC...

Expected

(The Final Slice)