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# Bayesian Models with SQL | ||
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Because `conjugate-models` works with [general numerical inputs](../generalized-inputs), we can use Bayesian models in SQL | ||
with the SQL builder, `PyPika`. | ||
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For the example, we will estimate use normal model to estimate the | ||
total sales amount by group. | ||
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The example table is called `events` and we will assume a normal model for the | ||
column `sales` for each value of the column `group`. | ||
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We can create the sufficient statistics needed for `normal_normal_inverse_gamma` | ||
directly with the SQL builder. | ||
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```python | ||
from pypika import Query, Table, functions as fn | ||
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event_table = Table("events") | ||
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sales = event_table.sales | ||
sales_squared = sales**2 | ||
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# Sufficient statistics | ||
x_total = fn.Sum(sales) | ||
x2_total = fn.Sum(sales_squared) | ||
n = fn.Count("*") | ||
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# Start a query for a groupby | ||
query = ( | ||
Query.from_(event_table) | ||
.groupby(event_table.group) | ||
.select( | ||
event_table.group, | ||
) | ||
) | ||
``` | ||
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Perform the Bayesian inference as usual, but using the variables reflecting | ||
the columns. | ||
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```python | ||
from conjugate.distributions import NormalInverseGamma | ||
from conjugate.models import ( | ||
normal_normal_inverse_gamma, | ||
normal_normal_inverse_gamma_posterior_predictive, | ||
) | ||
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# Bayesian Inference | ||
prior = NormalInverseGamma(mu=0, nu=1 / 10, alpha=1 / 10, beta=1) | ||
posterior = normal_normal_inverse_gamma( | ||
x_total=x_total, | ||
x2_total=x2_total, | ||
n=n, | ||
normal_inverse_gamma_prior=prior, | ||
) | ||
posterior_predictive = normal_normal_inverse_gamma_posterior_predictive(posterior) | ||
``` | ||
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Then add the columns we want from the inference | ||
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``` | ||
# Add the posterior predictive estimate | ||
query = query.select( | ||
posterior_predictive.mu.as_("mu"), | ||
posterior_predictive.sigma.as_("sigma"), | ||
posterior_predictive.nu.as_("nu"), | ||
) | ||
``` | ||
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Which results in this query: | ||
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```sql | ||
SELECT "group", | ||
(0.0+COUNT(*)*SUM("sales")/COUNT(*))/(0.1+COUNT(*)) "mu", | ||
POW((1+0.5*(0.0+SUM(POW("sales", 2))-POW((0.0+COUNT(*)*SUM("sales")/COUNT(*))/(0.1+COUNT(*)), 2)*(0.1+COUNT(*))))*(0.1+COUNT(*)+1)/((0.1+COUNT(*))*(0.1+COUNT(*)/2)), 0.5) "sigma", | ||
2*(0.1+COUNT(*)/2) "nu" | ||
FROM "events" | ||
GROUP BY "group" | ||
``` | ||
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