YOU DON’T NEED TO DETREND YOUR...
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100 1000 ms s COMPUTATION TIME NUMBER OF DATAPOINTS YOU DON’T NEED TO DETREND YOUR DATA Dan Foreman-Mackey Center for Cosmology & Particle Physics, NYU dfm.io — github.com/dfm — @exoplaneteer p(data | model) = N [f ; μ(✓ ), ⌃(↵)] likelihood function Gaussian process model includes: physics (Kepler’s equation, N-body, etc.) geometry (limb darkening, etc.) covariance includes: observational uncertainties systematics (trends, discontinuities, etc.) observations includes: “raw” photometry auxiliary measurements (optional) a generalization of standard χ² likelihood Δt ⌃ explicit sparsity 3-parameter kernel function SuiteSparse 1 state-of-the art sparse linear algebra O (N ⇠2 ) O (N 3 ) SEARCH CHARACTERIZATION -3 -2 -1 0 1 2 3 time since transit [days] -3 -2 -1 0 1 2 3 time since transit [days] 1 cise.ufl.edu/research/sparse/SuiteSparse 2 github.com/dfm/george George 2 an open source implementation C (+Python bindings) computationally tractable log(period) phase Δ log(likelihood) search is the process of mining light curves for new candidates. Writing this question as a hypothesis test lets us incorporate a better likelihood function and search without median filtering the data. We find: Kepler is sensitive to Earth-analog transits! anywhere that one might use a χ² likelihood function, this Gaussian process is a drop-in replacement. For characterizing planet candidates, all we need to do is trivially update the computation of the probability function in the MCMC loop. It’s even easy to marginalize the kernel parameters! check out code.dfm.io for open source code and demos
Transcript of YOU DON’T NEED TO DETREND YOUR...
100 1000
ms
s
COM
PUTATION TIM
E
NUMBER OF DATAPOINTS
YOU DON’T NEED TO DETREND YOUR DATADan Foreman-Mackey
Center for Cosmology & Particle Physics, NYU dfm.io — github.com/dfm — @exoplaneteer
p(data |model) = N [f ; µ(✓), ⌃(↵)]
likelihood functionGaussian process
model includes: physics (Kepler’s equation, N-body, etc.) geometry (limb darkening, etc.)
covariance includes: observational uncertainties systematics (trends, discontinuities, etc.)
observations includes: “raw” photometry auxiliary measurements (optional)
a generalization of standard χ² likelihood
�t
⌃
explicit sparsity
3-parameter kernel
function
SuiteSparse1 state-of-the art sparse linear
algebra
O(N⇠2)
O(N3)
SEARCH CHARACTERIZATION
�3 �2 �1 0 1 2 3time since transit [days]
�3 �2 �1 0 1 2 3time since transit [days]
1 cise.ufl.edu/research/sparse/SuiteSparse 2 github.com/dfm/george
George2 an open source implementation
C (+Python bindings)
computationally tractable
log(period)
phas
e
Δ log(likelihood) search is the process of mining light curves for new candidates. Writing this question as a hypothesis test lets us incorporate a better likelihood function and search without median filtering the data. We find: Kepler is sensitive to Earth-analog transits!
anywhere that one might use a χ² likelihood function, this Gaussian process is a drop-in replacement. For characterizing planet candidates, all we need to do is trivially update the computation of the probability function in the MCMC loop. It’s even easy to marginalize the kernel parameters!
check out code.dfm.io for open source code and demos
