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![import pymc3 as pm
with pm.Model() as lin_model:
α = pm.Normal("α", 0, 100)
β = pm.Normal("β", 0, 100)
σ = pm.Exponential("σ", 1/100)
μ = α + β*d["area"]
y = pm.Normal("y", μ, σ,
observed=d["price"])
Getting this into Python: PyMC3](https://image.slidesharecdn.com/bayesianworkflowwithpymc3andarviz-191011122556/75/Bayesian-workflow-with-PyMC3-and-ArviZ-17-2048.jpg)
![import pymc3 as pm
with pm.Model() as lin_model:
α = pm.Normal("α", 0, 100)
β = pm.Normal("β", 0, 100)
σ = pm.Exponential("σ", 1/100)
μ = α + β*d["area"]
y = pm.Normal("y", μ, σ,
observed=d["price"])
Getting this into Python: PyMC3](https://image.slidesharecdn.com/bayesianworkflowwithpymc3andarviz-191011122556/75/Bayesian-workflow-with-PyMC3-and-ArviZ-18-2048.jpg)
![import pymc3 as pm
with pm.Model() as lin_model:
α = pm.Normal("α", 0, 100)
β = pm.Normal("β", 0, 100)
σ = pm.Exponential("σ", 1/100)
μ = α + β*d["area"]
y = pm.Normal("y", μ, σ,
observed=d["price"])
Getting this into Python: PyMC3](https://image.slidesharecdn.com/bayesianworkflowwithpymc3andarviz-191011122556/75/Bayesian-workflow-with-PyMC3-and-ArviZ-19-2048.jpg)
![Getting this into Python: PyMC3
import pymc3 as pm
with pm.Model() as lin_model:
α = pm.Normal("α", 0, 100)
β = pm.Normal("β", 0, 100)
σ = pm.Exponential("σ", 1/100)
μ = α + β*d["area"]
y = pm.Normal("y", μ, σ,
observed=d["price"])](https://image.slidesharecdn.com/bayesianworkflowwithpymc3andarviz-191011122556/75/Bayesian-workflow-with-PyMC3-and-ArviZ-20-2048.jpg)
![with pm.Model() as hier_model:
μ_α = pm.Normal("μ_α", 0, 100)
μ_β = ...
σ = pm.Exponential("σ", 1/100)
σ_α = σ_β = ...
α = pm.Normal("α", μ_α, σ_α,
shape=num_zip)
β = pm.Normal("β", μ_β, σ_β,
shape=num_zip)
μ = α[d["zip"]] + β[d["zip"]]*d["area"]
y = pm.Normal("y", μ, σ,
observed=d["price"])
Getting this into Python: PyMC3](https://image.slidesharecdn.com/bayesianworkflowwithpymc3andarviz-191011122556/75/Bayesian-workflow-with-PyMC3-and-ArviZ-21-2048.jpg)
![with pm.Model() as hier_model:
μ_α = pm.Normal("μ_α", 0, 100)
μ_β = ...
σ = pm.Exponential("σ", 1/100)
σ_α = σ_β = ...
α = pm.Normal("α", μ_α, σ_α,
shape=num_zip)
β = pm.Normal("β", μ_β, σ_β,
shape=num_zip)
μ = α[d["zip"]] + β[d["zip"]]*d["area"]
y = pm.Normal("y", μ, σ,
observed=d["price"])
Getting this into Python: PyMC3](https://image.slidesharecdn.com/bayesianworkflowwithpymc3andarviz-191011122556/75/Bayesian-workflow-with-PyMC3-and-ArviZ-22-2048.jpg)
![with pm.Model() as hier_model:
μ_α = pm.Normal("μ_α", 0, 100)
μ_β = ...
σ = pm.Exponential("σ", 1/100)
σ_α = σ_β = ...
α = pm.Normal("α", μ_α, σ_α,
shape=num_zip)
β = pm.Normal("β", μ_β, σ_β,
shape=num_zip)
μ = α[d["zip"]] + β[d["zip"]]*d["area"]
y = pm.Normal("y", μ, σ,
observed=d["price"])
Getting this into Python: PyMC3](https://image.slidesharecdn.com/bayesianworkflowwithpymc3andarviz-191011122556/75/Bayesian-workflow-with-PyMC3-and-ArviZ-23-2048.jpg)
![with pm.Model() as hier_model:
μ_α = pm.Normal("μ_α", 0, 100)
μ_β = ...
σ = pm.Exponential("σ", 1/100)
σ_α = σ_β = ...
α = pm.Normal("α", μ_α, σ_α,
shape=num_zip)
β = pm.Normal("β", μ_β, σ_β,
shape=num_zip)
μ = α[d["zip"]] + β[d["zip"]]*d["area"]
y = pm.Normal("y", μ, σ,
observed=d["price"])
Getting this into Python: PyMC3](https://image.slidesharecdn.com/bayesianworkflowwithpymc3andarviz-191011122556/75/Bayesian-workflow-with-PyMC3-and-ArviZ-24-2048.jpg)
![with pm.Model() as hier_model:
μ_α = pm.Normal("μ_α", 0, 20)
μ_β = pm.Normal("μ_β", 0, 5)
σ = pm.Exponential("σ", 1/5)
σ_α = σ_β = ...
α = pm.Normal("α", μ_α, σ_α,
shape=num_zip)
β = pm.Normal("β", μ_β, σ_β,
shape=num_zip)
μ = α[d["zip"]] + β[d["zip"]]*d["area"]
y = pm.Normal("y", μ, σ,
observed=d["price"])
trace = pm.sample()
What about the priors?](https://image.slidesharecdn.com/bayesianworkflowwithpymc3andarviz-191011122556/75/Bayesian-workflow-with-PyMC3-and-ArviZ-36-2048.jpg)
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Similar to Bayesian workflow with PyMC3 and ArviZ
Bayesian workflow with PyMC3 and ArviZ
- 1. Bayesian Workflow with PyMCand ArviZ Corrie Bartelheimer Data Scientist at Europace AG @corrieaar
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- 16. Getting this intoPython
- 17. import pymc3 aspm with pm.Model() as lin_model: α = pm.Normal("α", 0, 100) β = pm.Normal("β", 0, 100) σ = pm.Exponential("σ", 1/100) μ = α + β*d["area"] y = pm.Normal("y", μ, σ, observed=d["price"]) Getting this into Python: PyMC3
- 18. import pymc3 aspm with pm.Model() as lin_model: α = pm.Normal("α", 0, 100) β = pm.Normal("β", 0, 100) σ = pm.Exponential("σ", 1/100) μ = α + β*d["area"] y = pm.Normal("y", μ, σ, observed=d["price"]) Getting this into Python: PyMC3
- 19. import pymc3 aspm with pm.Model() as lin_model: α = pm.Normal("α", 0, 100) β = pm.Normal("β", 0, 100) σ = pm.Exponential("σ", 1/100) μ = α + β*d["area"] y = pm.Normal("y", μ, σ, observed=d["price"]) Getting this into Python: PyMC3
- 20. Getting this intoPython: PyMC3 import pymc3 as pm with pm.Model() as lin_model: α = pm.Normal("α", 0, 100) β = pm.Normal("β", 0, 100) σ = pm.Exponential("σ", 1/100) μ = α + β*d["area"] y = pm.Normal("y", μ, σ, observed=d["price"])
- 21. with pm.Model() ashier_model: μ_α = pm.Normal("μ_α", 0, 100) μ_β = ... σ = pm.Exponential("σ", 1/100) σ_α = σ_β = ... α = pm.Normal("α", μ_α, σ_α, shape=num_zip) β = pm.Normal("β", μ_β, σ_β, shape=num_zip) μ = α[d["zip"]] + β[d["zip"]]*d["area"] y = pm.Normal("y", μ, σ, observed=d["price"]) Getting this into Python: PyMC3
- 22. with pm.Model() ashier_model: μ_α = pm.Normal("μ_α", 0, 100) μ_β = ... σ = pm.Exponential("σ", 1/100) σ_α = σ_β = ... α = pm.Normal("α", μ_α, σ_α, shape=num_zip) β = pm.Normal("β", μ_β, σ_β, shape=num_zip) μ = α[d["zip"]] + β[d["zip"]]*d["area"] y = pm.Normal("y", μ, σ, observed=d["price"]) Getting this into Python: PyMC3
- 23. with pm.Model() ashier_model: μ_α = pm.Normal("μ_α", 0, 100) μ_β = ... σ = pm.Exponential("σ", 1/100) σ_α = σ_β = ... α = pm.Normal("α", μ_α, σ_α, shape=num_zip) β = pm.Normal("β", μ_β, σ_β, shape=num_zip) μ = α[d["zip"]] + β[d["zip"]]*d["area"] y = pm.Normal("y", μ, σ, observed=d["price"]) Getting this into Python: PyMC3
- 24. with pm.Model() ashier_model: μ_α = pm.Normal("μ_α", 0, 100) μ_β = ... σ = pm.Exponential("σ", 1/100) σ_α = σ_β = ... α = pm.Normal("α", μ_α, σ_α, shape=num_zip) β = pm.Normal("β", μ_β, σ_β, shape=num_zip) μ = α[d["zip"]] + β[d["zip"]]*d["area"] y = pm.Normal("y", μ, σ, observed=d["price"]) Getting this into Python: PyMC3
- 25. What about thepriors?
- 26. What about thepriors?
- 27. What about thepriors? with model: prior = pm.sample_prior_predictive()
- 28. with model: prior =pm.sample_prior_predictive() What about the priors?
- 29. with model: prior =pm.sample_prior_predictive() What about the priors?
- 30. with model: prior =pm.sample_prior_predictive() What about the priors?
- 31. What about thepriors?
- 32. What about thepriors?
- 33. What about thepriors?
- 34. What about thepriors?
- 35. What about thepriors?
- 36. with pm.Model() ashier_model: μ_α = pm.Normal("μ_α", 0, 20) μ_β = pm.Normal("μ_β", 0, 5) σ = pm.Exponential("σ", 1/5) σ_α = σ_β = ... α = pm.Normal("α", μ_α, σ_α, shape=num_zip) β = pm.Normal("β", μ_β, σ_β, shape=num_zip) μ = α[d["zip"]] + β[d["zip"]]*d["area"] y = pm.Normal("y", μ, σ, observed=d["price"]) trace = pm.sample() What about the priors?
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- 38. Did it converge? importarviz as az az.plot_trace(trace)
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- 40. Did it converge? SomeBad Examples
- 41. Did it converge? SomeBad Examples
- 42. Did it converge? SomeBad Examples
- 43. Did it converge? SomeBad Examples
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- 48. Did it converge? Rhatstatistic smaller 1.05? Effective sample size / iterations greater 10%? Monte Carlo se / posterior sd smaller 10%?
- 49. How good doesmy model fit the data?
- 50. How good doesmy model fit the data? with hier_model: posterior_predictive = pm.sample_posterior_predictive(trace)
- 51. How good doesmy model fit the data?
- 52. How good doesmy model fit the data?
- 53. How good doesmy model fit the data?
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- 60. What’s next? ● Iterate! ●More predictors! ○ Year of construction ○ House type ○ ... ● More hierarchies! ● Add group predictors! ○ Percentage of green areas ○ Economical indices ● Try different likelihoods ● Probably save more money...
- 61. Further resources RichardMcElreath: Statistical Rethinking - Port to PyMC3 Prior Recommendation by Stan Team Michael Betancourts Case Studies BerlinBayesians Icons by icons8
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