minor correction in sampling.py and starting.py

pymc3/sampling.py

@@ -22,7 +22,7 @@
 import warnings
 
 from collections import defaultdict
-from copy import copy
+from copy import copy, deepcopy
 from typing import Any, Dict, Iterable, List, Optional, Set, Union, cast
 
 import arviz
@@ -423,6 +423,7 @@ def sample(
         p  0.609  0.047   0.528    0.699
     """
     model = modelcontext(model)
+    start = deepcopy(start)
     if start is None:
         check_start_vals(model.test_point, model)
     else:

pymc3/tests/test_sampling.py

@@ -285,6 +285,27 @@ def callback(trace, draw):
             assert len(trace) == trace_cancel_length
 
 
+def test_sample_find_MAP_does_not_modify_start():
+    # see https://github.com/pymc-devs/pymc3/pull/4458
+    with pm.Model():
+        pm.Lognormal("untransformed")
+
+        # make sure find_Map does not modify the start dict
+        start = {"untransformed": 2}
+        pm.find_MAP(start=start)
+        assert start == {"untransformed": 2}
+
+        # make sure sample does not modify the start dict
+        start = {"untransformed": 0.2}
+        pm.sample(draws=10, step=pm.Metropolis(), tune=5, start=start, chains=3)
+        assert start == {"untransformed": 0.2}
+
+        # make sure sample does not modify the start when passes as list of dict
+        start = [{"untransformed": 2}, {"untransformed": 0.2}]
+        pm.sample(draws=10, step=pm.Metropolis(), tune=5, start=start, chains=2)
+        assert start == [{"untransformed": 2}, {"untransformed": 0.2}]
+
+
 def test_empty_model():
     with pm.Model():
         pm.Normal("a", observed=1)

pymc3/tuning/starting.py

@@ -17,6 +17,8 @@
 
 @author: johnsalvatier
 """
+import copy
+
 import numpy as np
 import theano.gradient as tg
 
@@ -96,7 +98,7 @@ def find_MAP(
     vars = inputvars(vars)
     disc_vars = list(typefilter(vars, discrete_types))
     allinmodel(vars, model)
-
+    start = copy.deepcopy(start)
     if start is None:
         start = model.test_point
     else: