A Kernel Test of Goodness of Fit
A Kernel Test of Goodness of Fit
Kacper Chwialkowski, Heiko Strathmann, Arthur Gretton June 21, 2016 Gatsby Unit and CS Department, UCL
1
Motivating example: testing output of approximate MCMC Approximate MCMC: tradeoff between bias and computation (e.g. Austerity in MCMC Land [2]) 4 3 2
θ1 ∼ N (0, 10); θ2 ∼ N (0, 1) Xi ∼ 21 N (θ1 , 4) + 1 2 N (θ1 + θ2 , 4).
1 0 1 2 3 1.5
1.0
0.5
0.0
0.5
1.0
1.5
2.0
How to check if MCMC samples match target distribution?
2
Maximum mean discrepancy: metric between p and q MMD(p, q, F ) = supkf kF
Kacper Chwialkowski, Heiko Strathmann, Arthur Gretton June 21, 2016 Gatsby Unit and CS Department, UCL
1
Motivating example: testing output of approximate MCMC Approximate MCMC: tradeoff between bias and computation (e.g. Austerity in MCMC Land [2]) 4 3 2
θ1 ∼ N (0, 10); θ2 ∼ N (0, 1) Xi ∼ 21 N (θ1 , 4) + 1 2 N (θ1 + θ2 , 4).
1 0 1 2 3 1.5
1.0
0.5
0.0
0.5
1.0
1.5
2.0
How to check if MCMC samples match target distribution?
2
Maximum mean discrepancy: metric between p and q MMD(p, q, F ) = supkf kF
