diff --git a/nnpdf_data/nnpdf_data/commondata/ATLAS_WJ_8TEV/filter.py b/nnpdf_data/nnpdf_data/commondata/ATLAS_WJ_8TEV/filter.py
index 198746a573..b9f3de63ea 100644
--- a/nnpdf_data/nnpdf_data/commondata/ATLAS_WJ_8TEV/filter.py
+++ b/nnpdf_data/nnpdf_data/commondata/ATLAS_WJ_8TEV/filter.py
@@ -1,3 +1,23 @@
+'''
+Filter script for ATLAS_WJ_8TEV
+
+Log:
+- Central data and kinematics implemented from hepdata
+- Central data and kinematics checked with legacy: passed
+- The bin values in `uncertainties_legacy_WX-PT.yaml` and `uncertainties_legacy_WX-PT_sys_ATLAS.yaml`
+  are exactly the same (checked with notebook). The difference between
+  these two variants is in the definition of the uncertainties. See notebook for
+  differences.
+- For the treatment of systematic uncertainties, refer to https://arxiv.org/pdf/2112.11266.
+  There are 50 sources of CORRELATED systematic uncertainty.
+
+29 / 11 / 2024
+- Implemented uncertaintiy definitions
+- Construction of the uncertainty file is still missing. Remember that
+  for the symmetrised case you account for the shifts.
+- Xq2 is missing (?)
+'''
+
 import logging
 
 from filter_utils import Extractor
diff --git a/nnpdf_data/nnpdf_data/commondata/ATLAS_WJ_8TEV/filter_utils.py b/nnpdf_data/nnpdf_data/commondata/ATLAS_WJ_8TEV/filter_utils.py
index b3fe3459e4..27b9069fcb 100644
--- a/nnpdf_data/nnpdf_data/commondata/ATLAS_WJ_8TEV/filter_utils.py
+++ b/nnpdf_data/nnpdf_data/commondata/ATLAS_WJ_8TEV/filter_utils.py
@@ -5,12 +5,16 @@
 import pandas as pd
 import yaml
 
-from nnpdf_data.filter_utils.utils import prettify_float
+from nnpdf_data.filter_utils.utils import matlist_to_matrix, prettify_float, symmetrize_errors
 
 yaml.add_representer(float, prettify_float)
 
 SQRTS = 8000
 
+# List of systematic uncertainties that shuold
+# be considered uncorrelated
+UNCORR_SYS_UNC = ['BkgMCstat', 'UnfoldMCstat', 'QCDfitUncert']
+
 
 class Extractor:
     """
@@ -54,6 +58,11 @@ def __init__(self, metadata_file, observable, mult_factor=1):
         else:
             raise Exception(f'{self.observable} is an unknown observable.')
 
+        # Collect diagonal absoulute uncertainties
+        self.diag_unc = self.__collect_diag_unc()
+        self.unc_labels = list(self.diag_unc[0].keys())
+        self.unc_labels.pop(0)
+
     def __extract_kinematics(self, table: dict, tab_number: int):
         """
         Extracts the kinematic variables of the single differential
@@ -116,7 +125,10 @@ def __retrieve_table(self, table_id):
                 table = tab_dict
         return table
 
-    def generate_kinematics(self):
+    def get_table(self, table_id):
+        return self.__retrieve_table(table_id)
+
+    def generate_kinematics(self, save_to_yaml=True):
         """
         Function that generates the kinematics by looping over all the
         tables specified in the metadata file. The resulting kinematics
@@ -129,11 +141,12 @@ def generate_kinematics(self):
         # Initialise kinematics list
         kinematics = []
         ndata = 0
-        for table in self.metadata["tables"]:
-            tab_dict = self.__retrieve_table(table)
-            kin = self.__extract_kinematics(tab_dict, table)
-            kinematics = np.concatenate([kinematics, kin])
-            ndata += len(kin)
+        table = self.metadata["tables"][0]
+        tab_dict = self.__retrieve_table(table)
+        kin = self.__extract_kinematics(tab_dict, table)
+        kinematics = np.concatenate([kinematics, kin])
+        ndata += len(kin)
+        self.kinematics = kinematics.tolist()
         kinematics_yaml = {'bins': kinematics.tolist()}
 
         # Check number of data agrees with metadata
@@ -146,45 +159,217 @@ def generate_kinematics(self):
                 f" The correct number is {ndata}. Please, update the metafile."
             )
 
-        # Dump into file
-        logging.info("Dumping kinematics to file...")
-        with open(self.metadata['kinematics']['file'], 'w') as kin_out_file:
-            yaml.dump(kinematics_yaml, kin_out_file, sort_keys=False)
-        logging.info("Done!")
+        if save_to_yaml:
+            # Dump into file
+            logging.info("Dumping kinematics to file...")
+            with open(self.metadata['kinematics']['file'], 'w') as kin_out_file:
+                yaml.dump(kinematics_yaml, kin_out_file, sort_keys=False)
+            logging.info("Done!")
+        else:
+            return 1
 
-    def generate_data_central(self):
+    def generate_data_central(self, save_to_yaml=True):
         """
         Same as `generate_kinematics`, but for central data points.
         """
         logging.info(f"Generating central data for ATLAS_{self.observable}...")
         dat_central = []
-        for table in self.metadata['tables']:
-            tab_dict = self.__retrieve_table(table)
+        table = self.metadata['tables'][0]
+        tab_dict = self.__retrieve_table(table)
 
-            # Select the chosen combination
-            values = next(
-                (
-                    head['values']
-                    for head in tab_dict["dependent_variables"]
-                    if self.observable_latex in head['header']['name']
-                ),
-                1,
-            )
-            if values == 1:
-                logging.error(
-                    f"{self.observable} not found in table {table} under the LaTeX name {self.observable_latex}. The available options are:"
-                )
-                for head in tab_dict["dependent_variables"]:
-                    print(f"     - {head['header']['name']}")
-                exit(-1)
+        # Select the chosen combination
+        values = self.__select_bins_by_observable(tab_dict)
 
-            data = [dat['value'] * self.mult_factor for dat in values]
-            dat_central = np.concatenate([dat_central, data])
+        data = [dat['value'] * self.mult_factor for dat in values]
+        dat_central = np.concatenate([dat_central, data])
+        self.dat_central = dat_central
 
         dat_central_yaml = {'data_central': dat_central.tolist()}
 
-        # Dump into file
-        logging.info("Dumping kinematics to file...")
-        with open(self.metadata['data_central'], 'w') as dat_out_file:
-            yaml.dump(dat_central_yaml, dat_out_file, sort_keys=False)
-        logging.info("Done!")
+        if save_to_yaml:
+            # Dump into file
+            logging.info("Dumping kinematics to file...")
+            with open(self.metadata['data_central'], 'w') as dat_out_file:
+                yaml.dump(dat_central_yaml, dat_out_file, sort_keys=False)
+            logging.info("Done!")
+        else:
+            return 1
+
+    def __build_abs_stat_covmat(self):
+        """Builds the statistical covmat given the diagonal statistical uncertainties."""
+        ndata = self.metadata['ndata']
+        table_id = self.metadata['tables'][1]
+        with open(f'./rawdata/data{table_id}.yaml', 'r') as tab:
+            stat = yaml.load(tab, yaml.Loader)
+        matlist = [val['value'] for val in stat['dependent_variables'][0]['values']]
+        statmat_rel = matlist_to_matrix(ndata, ndata, matlist)
+
+        # Retrieve statistical diagonal entries
+        abs_stat_diag = [float(d['Stat']['error']) for d in self.diag_unc]
+        statmat_abs = np.zeros_like(statmat_rel)
+        for i in range(statmat_rel.shape[0]):
+            for j in range(statmat_rel.shape[1]):
+                statmat_abs[i, j] = statmat_rel[i, j] * abs_stat_diag[i] * abs_stat_diag[j]
+
+        return statmat_abs
+
+    def __collect_diag_unc(self):
+        """Collect the absolute values of the diagonal uncertainties"""
+        table_idx = self.metadata['tables'][0]
+        tab_dict = self.__retrieve_table(table_idx)
+
+        # Select the chosen combination
+        bins = self.__select_bins_by_observable(tab_dict)
+
+        abs_unc_by_bin = []
+        for bin in bins:
+            bin_err = bin['errors']
+            unc_dict = {
+                unc['label']: {'type': list(unc.keys())[1], 'error': list(unc.values())[1]}
+                for unc in bin_err
+            }
+            abs_unc_by_bin.append(unc_dict)
+        return abs_unc_by_bin
+
+    # TODO and TOCHECK
+    # Some plus uncertainties are actually lower than minus uncertainties
+    # Also, some symmetric uncertainties are negative.
+    def symmetrized_sys_unc(self):
+        symmetrized_uncs = []
+        for bin in self.diag_unc:
+            unc_dict = {}
+            for source in self.unc_labels:
+                if bin[source]['type'] == 'asymerror':
+                    error = bin[source]['error']
+                    plus = error['plus']
+                    minus = error['minus']
+                    if plus < minus:
+                        aux = minus
+                        minus = plus
+                        plus = aux
+                    data_delta, sym_error = symmetrize_errors(error['plus'], error['minus'])
+                    unc_dict[source] = {'shift': data_delta, 'sym_error': sym_error}
+                elif bin[source]['type'] == 'symerror':
+                    # TODO
+                    # I'm not sure I need the abs value here
+                    unc_dict[source] = {'shift': 0, 'sym_error': abs(bin[source]['error'])}
+            symmetrized_uncs.append(unc_dict)
+        return symmetrized_uncs
+
+    # def __cms_treatment_sys_unc(self):
+    # """In the legacy implementation, all systematic uncertainties (even for symmetric uncertanties),
+    #   are treated using the prescription outlined in eq. (6) of https://arxiv.org/pdf/1703.01630.
+    #   Specifically, positive and negative bounds are treated as follows
+    #
+    #   C_{ij}^{sys} = \frac{1}{2} \sum_{k'}( C_{jk'}^{+} C_{ik'}^{+} + C_{jk'}^{-} C_{ik'}^{-})
+    #
+    #   With this prescription, asymmetric uncertainties are not symmetrized.
+    # """
+
+    def get_diag_unc(self):
+        if hasattr(self, 'diag_unc'):
+            return self.diag_unc
+        else:
+            self.diag_unc = self.__collect_diag_unc()
+            return self.diag_unc
+
+    def get_abs_stat_covmat(self):
+        if hasattr(self, 'abs_stat_covmat'):
+            return self.abs_stat_covmat
+        else:
+            self.abs_stat_covmat = self.__build_abs_stat_covmat()
+            return self.abs_stat_covmat
+
+    def __select_bins_by_observable(self, tab_dict):
+        """This dataset colelcts differential xsecs for either W+ and W- in the
+        same yaml file. This function returns the part of this yaml file relevant
+        for the selected boson sign."""
+        values = next(
+            (
+                head['values']
+                for head in tab_dict["dependent_variables"]
+                if self.observable_latex in head['header']['name']
+            ),
+            1,
+        )
+        if values == 1:
+            logging.error(
+                f"{self.observable} not found in table under the LaTeX name {self.observable_latex}. The available options are:"
+            )
+            for head in tab_dict["dependent_variables"]:
+                print(f"     - {head['header']['name']}")
+            exit(-1)
+        else:
+            return values
+
+    def build_definitions(self, variant='default'):
+        unc_definitions = {}
+
+        # Statistical uncertainties are always the same
+        for idx in range(self.dat_central.size):
+            unc_definitions[f'art_stat_corr_{idx + 1}'] = {
+                'description': f'Artificial statistical uncertainty {idx + 1}',
+                'treatment': 'ADD',
+                'type': 'CORR',
+            }
+
+        if variant == 'default':
+            i = 1
+            for label in self.unc_labels:
+                if label == 'LumiUncert':
+                    unc_type = 'ATLASLUMI12'
+                elif label in UNCORR_SYS_UNC:
+                    unc_type = 'UNCORR'
+                else:
+                    unc_type = f'SYSATLASW{i}'
+                    i += 1
+
+                unc_definitions[f'{label}'] = {
+                    'description': f'Systematic: {label}',
+                    'treatment': 'MULT',
+                    'type': unc_type,
+                }
+
+        elif variant == 'cms':
+            i = 1
+            for label in self.unc_labels:
+                if label == 'LumiUncert':
+                    unc_definitions[f'{label}'] = {
+                        'description': f'Systematic: {label}',
+                        'treatment': 'MULT',
+                        'type': 'ATLASLUMI12',
+                    }
+                else:
+                    if label in UNCORR_SYS_UNC:
+                        unc_definitions[f'{label}'] = {
+                            'description': f'Systematic: {label}',
+                            'treatment': 'MULT',
+                            'type': 'UNCORR',
+                        }
+                    else:
+                        unc_definitions[f'{label}_plus'] = {
+                            'description': f'Systematic upper unc.: {label}',
+                            'treatment': 'MULT',
+                            'type': f'SYSATLASW{i}',
+                        }
+                        unc_definitions[f'{label}_minus'] = {
+                            'description': f'Systematic lower unc.: {label}',
+                            'treatment': 'MULT',
+                            'type': f'SYSATLASW{i+1}',
+                        }
+                        i += 2
+
+        elif variant == 'inter_sys':
+            raise ValueError(f'Not yet implemented')
+        else:
+            raise ValueError(f'The variant {variant} is not yet implemented or wrong.')
+
+        return unc_definitions
+
+    @classmethod
+    def generate_artifical_unc(matrix):
+        eigvals, eigvecs = np.linalg.eig(matrix)
+        artificial_unc = np.zeros_like(eigvecs)
+        for i in range(artificial_unc.shape[0]):
+            for j in range(artificial_unc.shape[1]):
+                artificial_unc[i, j] = np.sqrt(eigvals[j]) * eigvecs[i, j]
diff --git a/nnpdf_data/nnpdf_data/commondata/ATLAS_WJ_8TEV/metadata.yaml b/nnpdf_data/nnpdf_data/commondata/ATLAS_WJ_8TEV/metadata.yaml
index 0d8ab29503..5becd8b240 100644
--- a/nnpdf_data/nnpdf_data/commondata/ATLAS_WJ_8TEV/metadata.yaml
+++ b/nnpdf_data/nnpdf_data/commondata/ATLAS_WJ_8TEV/metadata.yaml
@@ -23,7 +23,7 @@ implemented_observables:
     label: ATLAS $W^-$+jet 8 TeV
     units: '[fb]'
   process_type: DY_CC_PT
-  tables: [13]
+  tables: [13, 14]
   ndata: 16
   plotting:
     kinematics_override: identity
@@ -68,7 +68,7 @@ implemented_observables:
     label: ATLAS $W^+$+jet 8 TeV
     units: '[fb]'
   process_type: DY_CC_PT
-  tables: [13]
+  tables: [13, 15]
   ndata: 16
   plotting:
     kinematics_override: identity
diff --git a/nnpdf_data/nnpdf_data/commondata/ATLAS_WJ_8TEV/rawdata/data14.yaml b/nnpdf_data/nnpdf_data/commondata/ATLAS_WJ_8TEV/rawdata/data14.yaml
new file mode 100644
index 0000000000..aa8fe7c263
--- /dev/null
+++ b/nnpdf_data/nnpdf_data/commondata/ATLAS_WJ_8TEV/rawdata/data14.yaml
@@ -0,0 +1,784 @@
+dependent_variables:
+- header: {name: '$\rho^{W^+}(p_\text{T}^\text{W})$'}
+  qualifiers:
+  - {name: 'Correlation for cross section', value: 'W+ (electron channel)'}
+  - {name: 'ABS(ETARAP(ELECTRON))', value: '< 2.5'}
+  - {name: 'ABS(YRAP(JET))', value: '< 4.4'}
+  - {name: 'PT(JET)', units: 'GEV', value: '> 30'}
+  - {name: 'PT(LEPTON)', units: 'GEV', value: '> 25'}
+  - {name: 'RE', value: 'P P --> W JET(S) X'}
+  - {name: 'SQRT(S)', units: 'GEV', value: '8000.0'}
+  values:
+  - {value: +1.000000}
+  - {value: +0.442678}
+  - {value: -0.026622}
+  - {value: -0.062553}
+  - {value: -0.016604}
+  - {value: -0.001635}
+  - {value: +0.000300}
+  - {value: +0.000199}
+  - {value: +0.000040}
+  - {value: +0.000002}
+  - {value: -0.000007}
+  - {value: -0.000010}
+  - {value: -0.000010}
+  - {value: -0.000004}
+  - {value: -0.000007}
+  - {value: -0.000017}
+  - {value: +0.442678}
+  - {value: +1.000000}
+  - {value: +0.409170}
+  - {value: -0.048645}
+  - {value: -0.061283}
+  - {value: -0.014545}
+  - {value: -0.001104}
+  - {value: +0.000400}
+  - {value: +0.000148}
+  - {value: +0.000018}
+  - {value: -0.000006}
+  - {value: -0.000022}
+  - {value: +0.000018}
+  - {value: -0.000007}
+  - {value: -0.000021}
+  - {value: -0.000028}
+  - {value: -0.026622}
+  - {value: +0.409170}
+  - {value: +1.000000}
+  - {value: +0.409340}
+  - {value: -0.045459}
+  - {value: -0.064544}
+  - {value: -0.016317}
+  - {value: -0.001577}
+  - {value: +0.000387}
+  - {value: +0.000099}
+  - {value: -0.000033}
+  - {value: +0.000028}
+  - {value: -0.000024}
+  - {value: -0.000022}
+  - {value: +0.000020}
+  - {value: -0.000041}
+  - {value: -0.062553}
+  - {value: -0.048645}
+  - {value: +0.409340}
+  - {value: +1.000000}
+  - {value: +0.427921}
+  - {value: -0.045540}
+  - {value: -0.072139}
+  - {value: -0.021082}
+  - {value: -0.001160}
+  - {value: +0.000350}
+  - {value: +0.000131}
+  - {value: -0.000015}
+  - {value: -0.000020}
+  - {value: -0.000003}
+  - {value: -0.000025}
+  - {value: -0.000051}
+  - {value: -0.016604}
+  - {value: -0.061283}
+  - {value: -0.045459}
+  - {value: +0.427921}
+  - {value: +1.000000}
+  - {value: +0.449054}
+  - {value: -0.041381}
+  - {value: -0.081285}
+  - {value: -0.017331}
+  - {value: +0.000129}
+  - {value: +0.000265}
+  - {value: +0.000021}
+  - {value: +0.000003}
+  - {value: -0.000000}
+  - {value: -0.000004}
+  - {value: -0.000018}
+  - {value: -0.001635}
+  - {value: -0.014545}
+  - {value: -0.064544}
+  - {value: -0.045540}
+  - {value: +0.449054}
+  - {value: +1.000000}
+  - {value: +0.469414}
+  - {value: -0.026294}
+  - {value: -0.072196}
+  - {value: -0.007730}
+  - {value: +0.000710}
+  - {value: +0.000179}
+  - {value: +0.000022}
+  - {value: +0.000001}
+  - {value: -0.000010}
+  - {value: -0.000009}
+  - {value: +0.000300}
+  - {value: -0.001104}
+  - {value: -0.016317}
+  - {value: -0.072139}
+  - {value: -0.041381}
+  - {value: +0.469414}
+  - {value: +1.000000}
+  - {value: +0.522590}
+  - {value: -0.069841}
+  - {value: -0.045502}
+  - {value: -0.002703}
+  - {value: +0.000666}
+  - {value: +0.000067}
+  - {value: -0.000006}
+  - {value: -0.000024}
+  - {value: -0.000021}
+  - {value: +0.000199}
+  - {value: +0.000400}
+  - {value: -0.001577}
+  - {value: -0.021082}
+  - {value: -0.081285}
+  - {value: -0.026294}
+  - {value: +0.522590}
+  - {value: +1.000000}
+  - {value: +0.333983}
+  - {value: -0.094374}
+  - {value: -0.027180}
+  - {value: +0.000252}
+  - {value: +0.000593}
+  - {value: +0.000059}
+  - {value: -0.000122}
+  - {value: -0.000064}
+  - {value: +0.000040}
+  - {value: +0.000148}
+  - {value: +0.000387}
+  - {value: -0.001160}
+  - {value: -0.017331}
+  - {value: -0.072196}
+  - {value: -0.069841}
+  - {value: +0.333983}
+  - {value: +1.000000}
+  - {value: +0.148737}
+  - {value: -0.076883}
+  - {value: -0.019191}
+  - {value: -0.000140}
+  - {value: +0.000362}
+  - {value: +0.000087}
+  - {value: -0.000132}
+  - {value: +0.000002}
+  - {value: +0.000018}
+  - {value: +0.000099}
+  - {value: +0.000350}
+  - {value: +0.000129}
+  - {value: -0.007730}
+  - {value: -0.045502}
+  - {value: -0.094374}
+  - {value: +0.148737}
+  - {value: +1.000000}
+  - {value: +0.177779}
+  - {value: -0.082374}
+  - {value: -0.024344}
+  - {value: -0.000477}
+  - {value: +0.000269}
+  - {value: +0.000034}
+  - {value: -0.000007}
+  - {value: -0.000006}
+  - {value: -0.000033}
+  - {value: +0.000131}
+  - {value: +0.000265}
+  - {value: +0.000710}
+  - {value: -0.002703}
+  - {value: -0.027180}
+  - {value: -0.076883}
+  - {value: +0.177779}
+  - {value: +1.000000}
+  - {value: +0.202385}
+  - {value: -0.088239}
+  - {value: -0.029429}
+  - {value: -0.001028}
+  - {value: +0.000115}
+  - {value: -0.000010}
+  - {value: -0.000022}
+  - {value: +0.000028}
+  - {value: -0.000015}
+  - {value: +0.000021}
+  - {value: +0.000179}
+  - {value: +0.000666}
+  - {value: +0.000252}
+  - {value: -0.019191}
+  - {value: -0.082374}
+  - {value: +0.202385}
+  - {value: +1.000000}
+  - {value: +0.245531}
+  - {value: -0.094095}
+  - {value: -0.024182}
+  - {value: +0.000293}
+  - {value: -0.000010}
+  - {value: +0.000018}
+  - {value: -0.000024}
+  - {value: -0.000020}
+  - {value: +0.000003}
+  - {value: +0.000022}
+  - {value: +0.000067}
+  - {value: +0.000593}
+  - {value: -0.000140}
+  - {value: -0.024344}
+  - {value: -0.088239}
+  - {value: +0.245531}
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+  - {low: 125.0, high: 150.0}
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+  - {low: 200.0, high: 250.0}
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diff --git a/nnpdf_data/nnpdf_data/commondata/ATLAS_WJ_8TEV/rawdata/data15.yaml b/nnpdf_data/nnpdf_data/commondata/ATLAS_WJ_8TEV/rawdata/data15.yaml
new file mode 100644
index 0000000000..a8b141d9c1
--- /dev/null
+++ b/nnpdf_data/nnpdf_data/commondata/ATLAS_WJ_8TEV/rawdata/data15.yaml
@@ -0,0 +1,784 @@
+dependent_variables:
+- header: {name: '$\rho^{W^-}(p_\text{T}^\text{W})$'}
+  qualifiers:
+  - {name: 'Correlation for cross section', value: 'W- (electron channel)'}
+  - {name: 'ABS(ETARAP(ELECTRON))', value: '< 2.5'}
+  - {name: 'ABS(YRAP(JET))', value: '< 4.4'}
+  - {name: 'PT(JET)', units: 'GEV', value: '> 30'}
+  - {name: 'PT(LEPTON)', units: 'GEV', value: '> 25'}
+  - {name: 'RE', value: 'P P --> W JET(S) X'}
+  - {name: 'SQRT(S)', units: 'GEV', value: '8000.0'}
+  values:
+  - {value: +1.000000}
+  - {value: +0.443117}
+  - {value: -0.027961}
+  - {value: -0.062189}
+  - {value: -0.016126}
+  - {value: -0.001595}
+  - {value: +0.000267}
+  - {value: +0.000165}
+  - {value: +0.000042}
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+  - {value: +0.000010}
+  - {value: -0.000012}
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+  - {value: -0.000003}
+  - {value: +0.443117}
+  - {value: +1.000000}
+  - {value: +0.402593}
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+  - {value: -0.060171}
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+  - {value: +0.402593}
+  - {value: +1.000000}
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+  - {value: +1.000000}
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+  - {value: -0.016987}
+  - {value: +1.000000}
+independent_variables:
+- header: {name: '$p_\text{T}^\text{W}\text{ [GeV]}$'}
+  values:
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