Bayesian v. Frequentist
A fundamental difference in philosophy
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Bayesian v. Frequentist
A fundamental difference in philosophy
…that usually get you to similar results*
*for simple problems
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YOU
HOW DO
DEFINE
PROBABILITY?
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Related to our degree of belief / certainty
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Related to our degree of belief / certainty
Related to the frequency of repeated events
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Related to our degree of belief / certainty
↳ Bayesian
↳ Frequentist
Related to the frequency of repeated events
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“There is a 50% chance it will
rain tomorrow”
Bayesian
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“There is a 50% chance it will
rain tomorrow”
“If we observe many tomorrows,
50% of the time it will rain”
Bayesian
Frequentist
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“There is a 50% chance it will
rain tomorrow”
“If we observe many tomorrows,
50% of the time it will rain”
Bayesian
Frequentist
lolwut
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Can be more expensive
(computationally)
Priors (ahhhhhhh)
No way to make decisions
Why to not go Bayesian?
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Prior information
Nuisance parameters
Hierarchical models
Interpretation of uncertainty
Why go Bayesian?
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Prior information
Nuisance parameters
Hierarchical models
Interpretation of uncertainty
Why go Bayesian?
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The controversy
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The controversy
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The controversy
ya, s’ok
Frequentist
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The controversy
ya, s’ok
Frequentist
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The controversy
ya, s’ok
wtf m8?
Frequentist
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The controversy
ya, s’ok
wtf m8?
Frequentist
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The controversy
ya, s’ok
wtf m8?
Frequentist
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Priors
In Bayesian inference, you always need to
specify a prior.
!
Everyone brings prior information into
modeling, you just make it explicit.
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Priors
They mathematically specify your personal
or subjective beliefs.
They tend not to matter with enough data
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Priors
They mathematically specify your personal
or subjective beliefs.
They tend not to matter with enough data
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Priors
They mathematically specify your personal
or subjective beliefs.
They tend not to matter with enough data
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Priors
They mathematically specify your personal
or subjective beliefs.
They tend not to matter with enough data
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Rules of thumb
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Rules of thumb
“Principle of transformation groups”
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Rules of thumb
“Principle of transformation groups”
Priors on location parameters should be
translation independent.
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Rules of thumb
“Principle of transformation groups”
Priors on location parameters should be
translation independent.
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Rules of thumb
“Principle of transformation groups”
Priors on location parameters should be
translation independent.
Priors on scale parameters should be scale
invariant.
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DO NOT look at your data, then assign a prior
based on the data.
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DO NOT look at your data, then assign a prior
based on the data.
DO NOT always use uniform (flat) priors.
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DO NOT look at your data, then assign a prior
based on the data.
DO NOT always use uniform (flat) priors.
DO NOT try to use conjugate priors, unless
you are hardcore…
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Nuisance parameters
We don’t care about it, but we must account
for it to properly model the data
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Nuisance parameters
We don’t care about it, but we must account
for it to properly model the data
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Nuisance parameters
We don’t care about it, but we must account
for it to properly model the data
marginal posterior
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You go to The Telescope™ and
measure the flux from a star with no
variability.
Example: Nuisance parameters
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Example: Nuisance parameters
time, t
flux, f
yer model
f = c
10
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Example: Nuisance parameters
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Example: Nuisance parameters
WE
SUCK
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Example: Nuisance parameters
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Example: Nuisance parameters
but then…
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Example: Nuisance parameters
but then…
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Example: Nuisance parameters
The marginal
posterior
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WE SUCK…
LESS?
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You are at The Telescope™ and you
compute that there is a 40% chance
of rain tonight.
Wat do?
Making decisions