DOCSUP-2407: Documented the bayesAB function (#15599)

* Docs for the bayesAB function, english.

* Note edited.
Co-authored-by: NOlga Revyakina <revolg@yandex-team.ru>

docs/en/sql-reference/functions/machine-learning-functions.md

@@ -16,3 +16,82 @@ The [stochasticLinearRegression](../../sql-reference/aggregate-functions/referen
 ## stochasticLogisticRegression {#stochastic-logistic-regression}
 
 The [stochasticLogisticRegression](../../sql-reference/aggregate-functions/reference/stochasticlogisticregression.md#agg_functions-stochasticlogisticregression) aggregate function implements stochastic gradient descent method for binary classification problem. Uses `evalMLMethod` to predict on new data.
+
+## bayesAB {#bayesab}
+
+Compares test groups (variants) and calculates for each group the probability to be the best one. The first group is used as a control group.
+
+**Syntax** 
+
+``` sql
+bayesAB(distribution_name, higher_is_better, variant_names, x, y)
+```
+
+**Parameters** 
+
+-   `distribution_name` — Name of the probability distribution. [String](../../sql-reference/data-types/string.md). Possible values:
+
+    -   `beta` for [Beta distribution](https://en.wikipedia.org/wiki/Beta_distribution)
+    -   `gamma` for [Gamma distribution](https://en.wikipedia.org/wiki/Gamma_distribution)
+
+-   `higher_is_better` — Boolean flag. [Boolean](../../sql-reference/data-types/boolean.md). Possible values:
+
+    -    `0` - lower values are considered to be better than higher
+    -    `1` - higher values are considered to be better than lower
+
+-   `variant_names` - Variant names. [Array](../../sql-reference/data-types/array.md)([String](../../sql-reference/data-types/string.md)).
+
+-   `x` - Numbers of tests for the corresponding variants. [Array](../../sql-reference/data-types/array.md)([Float64](../../sql-reference/data-types/float.md)).
+
+-   `y` - Numbers of successful tests for the corresponding variants. [Array](../../sql-reference/data-types/array.md)([Float64](../../sql-reference/data-types/float.md)).
+
+!!! note "Note"
+    All three arrays must have the same size. All `x` and `y` values must be non-negative constant numbers. `y` cannot be larger than `x`.
+
+**Returned values**
+
+For each variant the function calculates:
+-   `beats_control` - long-term probability to out-perform the first (control) variant
+-   `to_be_best` - long-term probability to out-perform all other variants
+
+Type: JSON.
+
+**Example**
+
+Query:
+
+``` sql
+SELECT bayesAB('beta', 1, ['Control', 'A', 'B'], [3000., 3000., 3000.], [100., 90., 110.]) FORMAT PrettySpace;
+```
+
+Result:
+
+``` text
+{
+   "data":[
+      {
+         "variant_name":"Control",
+         "x":3000,
+         "y":100,
+         "beats_control":0,
+         "to_be_best":0.22619
+      },
+      {
+         "variant_name":"A",
+         "x":3000,
+         "y":90,
+         "beats_control":0.23469,
+         "to_be_best":0.04671
+      },
+      {
+         "variant_name":"B",
+         "x":3000,
+         "y":110,
+         "beats_control":0.7580899999999999,
+         "to_be_best":0.7271
+      }
+   ]
+}
+```
+
+[Original article](https://clickhouse.tech/docs/en/query_language/functions/machine-learning-functions/) <!--hide-->