Reliable ABC model choice via random forests

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Reliable ABC model choice via random forests
Pierre Pudlo y, Jean-Michel Marin y , Arnaud Estoup z, Jean-Marie Cornuet ...

ts the data
with random forests and computing an associated posterior error
rate. Compared with past implementations of ...

fty), and (iv) it includes an embedded and cost-free error evalua-
tion conditional on the actual analyzed dataset. Rando...

cation and regression tree; SNP, single nucleotide polymorphism
Since its introduction (1, 2, 3), the approximate Bayesia...

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cally, the major feature in
this calibration process involves selecting a vector of summary
statistics that quanti

es the dierence between the observed
data and the simulated data. The construction of this vec-
tor is therefore paramou...

c choices
of those statistics. In particular, in the setting of ABC model
choice, the summaries play a crucial role in p...

cation of the way ABC
model selection is conducted: we propose to both step away
from a mere mimicking of exact Bayesian...

er. The
statistical technique of random forests (RF) (13) represents
a trustworthy machine learning tool well adapted to...

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cation methods
in signi

cantly reducing both the classi

cation error and the
computational expense.
Model choice
Bayesian model choice (14, 15) compares the

t of M mod-
els to an observed dataset x0. It relies on a hierarchical
modelling, setting

rst prior probabilities on model indices
m 2 f1; : : : ;Mg and then prior distributions (jm) on the
parameter of each m...

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ned by the
distance between s0 and the simulated S(x)'s.
Selecting a model means choosing the model with the high-
est ...

tute the so-called reference table. In fact, this interpretation
provides a useful path to convergence properties of ABC ...

elds (18).
Algorithm 1 General ABC algorithm
(A) Generate Nref simulations (m; ; S(x)) from the joint
(m)(jm)f(xjm; ). ...

c goal
of model selection, the ABC approximation to the posterior
probabilities will eventually produce a right ordering...

t
of competing models to the observed data and thus will select
the right model for a speci

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c class of statistics when the in-
formation carried by the data becomes important (12). The
state-of-the-art evaluation...

cation method sec-
tion). Given the fundamental diculty in producing reliable
tools for model choice based on summary st...

ers.
ABC model choice via random forests. SI provides a review
of classi

cation methods. The so-called Bayesian classi

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