are we there yet? testing the effectiveness of graphics as mcmc … · experimental method bad...
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Are we there yet? Testing the effectiveness of
graphics as MCMC diagnostics
Nicholas Tierney, Monash University, Australianj_tierney
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Johns Hopkins University
Wednesday 9th January, 2019
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Why care about convergence?
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Converged?
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Converged?
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We know when it looks converged.
Right?
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Yes, and no.
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Research Question
Can visualisations be used to detect convergence?
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Research Question
Can visualisations be used to detect convergence?
Are some visualisations better than others for detecting convergence?
Is confidence related to detecting convergence?
Is experience with Bayesian statistics related to detecting convergence?
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Experimental Method
Bad Specification
60,000 Burn in
10,000 Samples
Good Specification
60,000 Burn in
10,000 Samples
Model
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Experimental Method
Slice 10,000 samples into 10 sets
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Experimental Method
Select nine bad and one good
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Experimental Method
Generate graphics
Select the one that is most converged 12
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Statistical inference for
exploratory data analysis and
model diagnostic
Buja, A.et al (2009).
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Experimental Method
Generate graphics
Select the one that is most converged 14
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Demo
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model{ for( i in 1 : N ) { y[i] ~ dnorm(mu[i], tau) mu[i] <- lambda[T[i]] T[i] ~ dcat(P[]) } P[1:maxT] ~ ddirch(alpha[]) lambda[1] ~ dnorm(0.0, 1.0E-6) for (j in 2:maxT){ lambda[j] <- lambda[j-1] + theta[j-1] theta[j-1] ~ dnorm(0.0, 1.0E-6)I(0.0, ) } tau ~ dgamma(0.001, 0.001) sigma <- 1 / sqrt(tau)}
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Bad Model
22 Mixtures
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Good Model
2 Mixtures
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The Data: “eyes”Size Group
529 NA
530 NA
532 NA
533 NA
534 NA
534 NA
534 NA
535 NA
535 NA
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Results Descriptive statistics
N = 16Expertise N
Some Experience 3
Moderate Experience 6
Very Experienced 4
Expert 1
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Results Descriptive statistics
N = 16Expertise N
0 - 1 years 2
1 - 2 years 1
2 - 3 years 2
3 - 4 years 3
5 plus years 8
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Results Can visualisations be used to detect convergence?
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Results Are some visualisations better than others?
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Results Is confidence related to detecting convergence?
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Results Is confidence related to detecting convergence?
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Results How Is Experience Related?
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Expertise N
Some Experience 3
Moderate Experience 6
Very Experienced 4
Expert 1
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Results How Is Experience Related?
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Expertise N
0 - 1 years 2
1 - 2 years 1
2 - 3 years 2
3 - 4 years 3
5 plus years 8
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Results How Is Experience Related?
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Expertise N
Some Experience 3
Moderate 6
Very Experienced 4
Expert 1
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Results How Is Experience Related?
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Expertise N
0 - 1 years 2
1 - 2 years 1
2 - 3 years 2
3 - 4 years 3
5 plus years 8
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Summary
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Can visualisations be used to detect convergence?
Are some visualisations better than others for detecting convergence?
Is confidence related to detecting convergence?
Is experience with Bayesian statistics related to detecting convergence?
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Summary
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Can visualisations be used to detect convergence?
Are some visualisations better than others for detecting convergence?
Is confidence related to detecting convergence?
Is experience with Bayesian statistics related to detecting convergence?
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Summary
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Can visualisations be used to detect convergence?
Are some visualisations better than others for detecting convergence?
Is confidence related to detecting convergence?
Is experience with Bayesian statistics related to detecting convergence?
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Summary
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Can visualisations be used to detect convergence?
Are some visualisations better than others for detecting convergence?
Is confidence related to detecting convergence?
Is experience with Bayesian statistics related to detecting convergence?
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Summary
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Can visualisations be used to detect convergence?
Are some visualisations better than others for detecting convergence?
Is confidence related to detecting convergence?
Is experience with Bayesian statistics related to detecting convergence?
Are they effective?
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Summary
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Can visualisations be used to detect convergence?
Are some visualisations better than others for detecting convergence?
Is confidence related to detecting convergence?
Is experience with Bayesian statistics related to detecting convergence?
Are they effective?Are we there yet?
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Summary
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Can visualisations be used to detect convergence?
Are some visualisations better than others for detecting convergence?
Is confidence related to detecting convergence?
Is experience with Bayesian statistics related to detecting convergence?
Are they effective?Are we there yet?
Yeah, Nah
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10 things I hate
about
you
MCMC
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10 things I hate
learned about
you
MCMC
…Experiments?47
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#1: Shiny is not optimised for experiments
Sending/storing responses to a cloud is not trivial
Efficiently presenting many experiments and tracking responses is challenging
Do we track the time taken? Is that interesting? Is that difficult?
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#2: Creating good and bad convergence?
I have definitely created bad samples accidentally
I found it hard to create bad samples AND understand the implication
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#3: More Chains
Looking at only one chain requires you to know more about the distribution
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#4: Design and simulate the data first
We only had one observation per person per plot
Designing the model and simulating collected data would have helped
It also helps you understand what you are most interested in
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#5: No context diagnostics are weird
But explaining and comprehending an entire Bayesian model takes time
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#6: Are these diagnostics real?
If a diagnostic fails and no one sees it, did it even diagnose anything?
Can we design better, more obvious / usable diagnostics?
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#7: Are we measuring the right thing?
Should people be picking the good out of the bad, or the bad out of the good?
We are actually asking people to pick the mis-specified model, is that useful?
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#8: We should do some training/testing
Explaining what convergence is
So that users can understand what is good and bad
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#9: Comparing diagnostics?
0.99, 0.98 0.97, 0.96, 1.00, 0.95, 0.93, 0.92, 0.89, 0.88
Can we compare a single number diagnostic to vis?
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#10: Your turn
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Acknowledgements
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Dr. David Frazier for his helpful suggestions on the methodology
Dr. Sam Clifford for discussions on the model implementation, and writing the JAGS code to create the “Good” and “Bad” models.
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Colophon
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Colours generated from the ochRe package
github.com/ropenscilabs/ochRe
Fonts used: Helvetica, impact.
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ReferencesBuja, A., Cook, D., Hofmann, H., Lawrence, M., Lee, E. K., Swayne, D. F., & Wickham, H. (2009). Statistical inference for exploratory data analysis and model diagnostics. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 367(1906), 4361-4383.x
Gelman, A., & Shirley, K. (2011). Inference from simulations and monitoring convergence. Handbook of Markov Chain Monte Carlo.
Loy, A., Hofmann, H., & Cook, D. (2017). Model Choice and Diagnostics for Linear Mixed-Effects Models Using Statistics on Street Corners. Journal of Computational and Graphical Statistics
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