calibrax.metrics.functional.statistical

Statistical correlation and agreement functions. Includes Pearson and Spearman correlation, Kendall's tau, Lin's concordance correlation coefficient, and adjusted R-squared.

Statistical correlation and agreement metrics.

Pure functions for measuring statistical relationships between variables. Covers linear correlation, rank correlation, and agreement measures.

Includes 5 functions: pearson_correlation, spearman_rank_correlation, kendall_tau, concordance_correlation, r_squared_adjusted.

pearson_correlation(a: Any, b: Any) -> Any

Pearson correlation coefficient.

Linear correlation: cov(a,b) / (std(a) * std(b)).

Note

Direction: HIGHER (1.0 = perfect positive correlation). Range: [-1, 1]. Measures linear association only.

Parameters:

Name	Type	Description	Default
a	Any	First variable.	required
b	Any	Second variable.	required

Returns:

Type	Description
Any	Pearson r as a scalar value.

Examples:

>>> import jax.numpy as jnp
>>> pearson_correlation(jnp.array([1.0, 2.0, 3.0]),
...                     jnp.array([1.0, 2.0, 3.0]))
1.0

spearman_rank_correlation(a: Any, b: Any) -> Any

Spearman's rank correlation coefficient.

Pearson correlation computed on ranks. Measures monotonic association.

Note

Direction: HIGHER (1.0 = perfect monotonic relationship). Range: [-1, 1].

Parameters:

Name	Type	Description	Default
a	Any	First variable.	required
b	Any	Second variable.	required

Returns:

Type	Description
Any	Spearman rho as a scalar value.

Examples:

>>> import jax.numpy as jnp
>>> spearman_rank_correlation(jnp.array([1.0, 2.0, 3.0]),
...                          jnp.array([1.0, 2.0, 3.0]))
1.0

kendall_tau(a: Any, b: Any) -> Any

Kendall rank correlation coefficient (tau-b).

(concordant - discordant) / (n*(n-1)/2).

Note

Direction: HIGHER (1.0 = perfect agreement). Range: [-1, 1].

Parameters:

Name	Type	Description	Default
a	Any	First variable.	required
b	Any	Second variable.	required

Returns:

Type	Description
Any	Kendall tau as a scalar value.

Examples:

>>> import jax.numpy as jnp
>>> kendall_tau(jnp.array([1.0, 2.0, 3.0]),
...             jnp.array([1.0, 2.0, 3.0]))
1.0

concordance_correlation(a: Any, b: Any) -> Any

Lin's concordance correlation coefficient.

Measures agreement (not just correlation). Penalizes deviations from the identity line, unlike Pearson which only measures linear association.

Note

Direction: HIGHER (1.0 = perfect agreement). Range: [-1, 1]. CCC <= |Pearson r|. Equal only when means and variances match.

Parameters:

Name	Type	Description	Default
a	Any	First variable.	required
b	Any	Second variable.	required

Returns:

Type	Description
Any	Concordance correlation as a scalar value.

Examples:

>>> import jax.numpy as jnp
>>> concordance_correlation(jnp.array([1.0, 2.0, 3.0]),
...                         jnp.array([1.0, 2.0, 3.0]))
1.0

r_squared_adjusted(predictions: Any, targets: Any, *, num_predictors: int) -> Any

Adjusted R-squared.

1 - (1-R^2)(n-1)/(n-p-1) where p is number of predictors. Penalizes adding predictors that don't improve fit.

Note

Direction: HIGHER (1.0 = perfect fit). Range: (-inf, 1].

Parameters:

Name	Type	Description	Default
predictions	Any	Predicted values.	required
targets	Any	Ground truth values.	required
num_predictors	int	Number of predictors in the model.	required

Returns:

Type	Description
Any	Adjusted R-squared as a scalar value.