IAIN MURRAY ([email protected]) MATTHEW M. GRAHAM (m.m...
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Pseudo-Marginal Slice Sampling IAIN MURRAY ([email protected]) MATTHEW M. GRAHAM ([email protected]) 0 1 2 0 0.2 0.4 step size − accept rate 0 1 2 0 0.005 0.01 − − effective sample rate 0 1 2 0 0.5 1 step size − accept rate 0 1 2 0 0.01 0.02 − − effective sample rate PROBLEM This work was supported in part by grants EP/F500385/1 and BB/F529254/1 for the University of Edinburgh School of Informatics Doctoral Training Centre in Neuroinformatics and Computational Neuroscience (www.anc.ac.uk/dtc) from the UK Engineering and Physical Sciences Research Council (EPSRC), UK Biotechnology and Biological Sciences Research Council (BBSRC), and the UK Medical Research Council (MRC). SPECIAL CASES EXPERIMENTS CONCLUSION STANDARD APPROACH REFERENCES OUR APPROACH SLICE SAMPLING DOUBLY-INTRACTABLE DISTRIBUTIONS LATENT VARIABLE MODELS initial state on-slice proposal off-slice proposal random direction true slice initial bracket Reflective slice sampling Elliptical slice sampling Slice sampling initial state on-slice proposal off-slice proposal random height true slice initial bracket initial state on-slice proposal off-slice proposal random ellipse true slice initial bracket Standard PM MH APM MI+MH ×10 4 1 2 3 4 -0.1 0 0.1 0.2 ×10 4 1 2 3 4 -0.1 0 0.1 0.2 Trace plot for standard PM MH Update number Trace plot for APM SS+SS Update number 0 10 20 30 40 50 -0.1 0 0.1 0.2 0.3 0.4 0.5 PM MH APM MI+MH APM SS+MH 0 10 20 30 40 50 -0.2 0 0.2 0.4 0.6 PM MH APM MI+MH APM SS+MH Length-scale autocorrelation, Pima Length-scale autocorrelation, Breast Lag Lag
Transcript of IAIN MURRAY ([email protected]) MATTHEW M. GRAHAM (m.m...
Pseudo-Marginal Slice SamplingIAIN MURRAY ([email protected]) MATTHEW M. GRAHAM ([email protected])
0 1 20
0.2
0.4
step size
− a
ccep
t ra
te
0 1 20
0.005
0.01
− −
effec
tive
sam
ple
rate
0 1 20
0.5
1
step size
− a
ccep
t ra
te
0 1 20
0.01
0.02
− −
effec
tive
sam
ple
rate
PROB
LEM
This work was supported in part by grants EP/F500385/1 and BB/F529254/1 for the University of Edinburgh School of Informatics Doctoral Training Centre in Neuroinformatics and Computational Neuroscience (www.anc.ac.uk/dtc) from the UK Engineering and Physical Sciences Research Council (EPSRC), UK Biotechnology and Biological Sciences Research Council (BBSRC), and the UK Medical Research Council (MRC).
SPECIAL CASESEX
PERIM
ENTS
CONC
LUSIO
NST
ANDA
RD AP
PROA
CHREFERENCES
OUR APPROACHSL
ICE SA
MPLIN
G
DOUB
LY-IN
TRAC
TABL
EDIS
TRIBU
TIONS
LATE
NT VA
RIABL
EMO
DELS
initial state
on-slice proposal
off-slice proposal
random direction
true slice
initial bracket
Reflective
slice sampling
Elliptical
slice sampling
Slice sampling
initial state
on-slice proposal
off-slice proposal
random height
true slice
initial bracket
initial state
on-slice proposal
off-slice proposal
random ellipse
true slice
initial bracket
Standard PM MH APM MI+MH
×10 41 2 3 4
-0.1
0
0.1
0.2
×10 41 2 3 4
-0.1
0
0.1
0.2Trace plot for standard PM MH
Update number
Trace plot for APM SS+SS
Update number0 10 20 30 40 50
-0.1
0
0.1
0.2
0.3
0.4
0.5PM MH
APM MI+MH
APM SS+MH
0 10 20 30 40 50-0.2
0
0.2
0.4
0.6PM MH
APM MI+MH
APM SS+MH
Length-scale autocorrelation, Pima Length-scale autocorrelation, Breast
Lag Lag
