writing bayesian hierarchical models
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Writing Bayesian Hierarchical Models
Models for Socio-Environmental Data
Chris Che-Castaldo, Mary B. Collins, N. Thompson Hobbs
December 18, 2020
Che-Castaldo, Collins, Hobbs DBI-1052875, DBI-1639145, DEB 1145200 1 / 4
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Examples of
I Multi-level models (aka random e↵ects)
I Sampling error in x’s and y’s
I Calibration error in y’s
All of these will appear in the exercises.
Che-Castaldo, Collins, Hobbs DBI-1052875, DBI-1639145, DEB 1145200 2 / 4
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Things to watch for today
Partitioning uncertainty
I Process variance
I Sampling variance
I Calibration variance (aka observation variance)
I Group level variance
Che-Castaldo, Collins, Hobbs DBI-1052875, DBI-1639145, DEB 1145200 3 / 4
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Steps in writing Bayesian models
1. Write your deterministic model. Be careful about support.
2. Draw Bayesian network (DAG) describing relationships
between observed and unobserved quantities.
3. Use the Bayesian network to write proportionality between
posterior and joint distributions using bracket notation [ | ].3.1 Posterior distribution: [unobserved quantities |data]3.2 Joint distribution
3.2.1 All nodes in Bayesian network at the heads of arrows (children)must be on the left hand side of a conditioning symbol.
3.2.2 All nodes in Bayesian network at the tails of arrows (parents)must be on the right hand side of a conditioning symbol |.
3.2.3 All nodes at the end of an arrow with no arrow coming intothem must be expressed unconditionally, i.e., they must havenumeric arguments.
4. Assign specific PDF or PMF to each of the brackets.
5. Choose numeric values for parameters of prior distributions.
Do this sensibly! Do not default to vague priors. (Do as I say,
not as I do.)
Che-Castaldo, Collins, Hobbs DBI-1052875, DBI-1639145, DEB 1145200 4 / 4
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Be careful with choice of likelihood andmoment match
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If you want to use the lognormcl :
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