posterior_variance

Computes posterior variance from normal-normal conjugate model.

Computes posterior variance from normal-normal conjugate model.

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Signature

{{ posterior_variance(n_col, observation_variance_expr, prior_variance_expr) }}

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Arguments

Argument	Description
n_col	column name or expression for sample size (e.g., ‘panel_observations_n’)
observation_variance_expr	expression for observation variance σ² (e.g., ‘0.0001’ for small noise)
prior_variance_expr	expression for prior variance σ₀² (e.g., a column or constant)

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Returns

scalar expression composable in SELECT lists (posterior variance, ≥0).

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Notes

observation variance: σ² (e.g., from a fitted model’s residual variance) prior variance: σ₀² sample size: n The posterior variance (precision-weighted average) is: posterior_var = 1 / (n / σ² + 1 / σ₀²) This is the inverse of the sum of precisions. Returns NULL if either variance is NULL or ≤0.

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Usage

SELECT
      driver_id,
      shrunken_estimate,
      SQRT({{ posterior_variance('sample_count', '0.0001', 'prior_var') }}) as posterior_se
    FROM panel_data