diff --git a/cxx/distributions/BUILD b/cxx/distributions/BUILD
index cb5f564..b5852ac 100644
--- a/cxx/distributions/BUILD
+++ b/cxx/distributions/BUILD
@@ -117,6 +117,7 @@ cc_library(
     deps = [
         ":base",
         ":dirichlet_categorical",
+        "//emissions:string_alignment",
     ],
 )
 
@@ -232,6 +233,15 @@ cc_test(
     ],
 )
 
+cc_test(
+    name = "string_nat_test",
+    srcs = ["string_nat_test.cc"],
+    deps = [
+        ":string_nat",
+        "@boost//:test",
+    ],
+)
+
 cc_test(
     name = "zero_mean_normal_test",
     srcs = ["zero_mean_normal_test.cc"],
diff --git a/cxx/distributions/adapter.hh b/cxx/distributions/adapter.hh
index b50bc7f..cb9594f 100644
--- a/cxx/distributions/adapter.hh
+++ b/cxx/distributions/adapter.hh
@@ -57,5 +57,8 @@ class DistributionAdapter : public Distribution<std::string> {
   void init_theta(std::mt19937* prng) { d->init_theta(prng); }
   void transition_theta(std::mt19937* prng) { d->transition_theta(prng); }
 
+  // TODO(thomaswc): Define nearest methods for the DistributionAdapter
+  // instantiations we use.
+
   ~DistributionAdapter() { delete d; }
 };
diff --git a/cxx/distributions/base.hh b/cxx/distributions/base.hh
index ffd19ab..32cff7c 100644
--- a/cxx/distributions/base.hh
+++ b/cxx/distributions/base.hh
@@ -48,5 +48,11 @@ class Distribution {
   // NonconjugateDistribution need define this.
   virtual void transition_theta(std::mt19937* prng) {};
 
+  // Return the value nearest to x that is given non-zero probability by
+  // this distribution.
+  virtual T nearest(const T& x) const {
+    return x;
+  }
+
   virtual ~Distribution() = default;
 };
diff --git a/cxx/distributions/dirichlet_categorical.cc b/cxx/distributions/dirichlet_categorical.cc
index 1eb5f2f..7cb683b 100644
--- a/cxx/distributions/dirichlet_categorical.cc
+++ b/cxx/distributions/dirichlet_categorical.cc
@@ -59,3 +59,14 @@ void DirichletCategorical::transition_hyperparameters(std::mt19937* prng) {
     alpha = alphas[i];
   }
 }
+
+int DirichletCategorical::nearest(const int& x) const {
+  if (x < 0) {
+    return 0;
+  }
+  // x can't be negative here, so safe to cast to size_t.
+  if (size_t(x) >= counts.size()) {
+    return counts.size() - 1;
+  }
+  return x;
+}
diff --git a/cxx/distributions/dirichlet_categorical.hh b/cxx/distributions/dirichlet_categorical.hh
index cea7bca..6595913 100644
--- a/cxx/distributions/dirichlet_categorical.hh
+++ b/cxx/distributions/dirichlet_categorical.hh
@@ -27,4 +27,6 @@ class DirichletCategorical : public Distribution<int> {
   int sample(std::mt19937* prng);
 
   void transition_hyperparameters(std::mt19937* prng);
+
+  int nearest(const int& x) const;
 };
diff --git a/cxx/distributions/dirichlet_categorical_test.cc b/cxx/distributions/dirichlet_categorical_test.cc
index f78e96a..2ca12bb 100644
--- a/cxx/distributions/dirichlet_categorical_test.cc
+++ b/cxx/distributions/dirichlet_categorical_test.cc
@@ -162,3 +162,11 @@ BOOST_AUTO_TEST_CASE(test_sample_and_log_prob) {
     BOOST_TEST(abs(probs[i] - approx_p) <= 3 * stddev);
   }
 }
+
+BOOST_AUTO_TEST_CASE(test_nearest) {
+  DirichletCategorical dc(12);
+
+  BOOST_TEST(dc.nearest(-5) == 0);
+  BOOST_TEST(dc.nearest(99) == 11);
+  BOOST_TEST(dc.nearest(7) == 7);
+}
diff --git a/cxx/distributions/string_nat.hh b/cxx/distributions/string_nat.hh
index 79f5349..5acd2d9 100644
--- a/cxx/distributions/string_nat.hh
+++ b/cxx/distributions/string_nat.hh
@@ -3,6 +3,8 @@
 
 #pragma once
 
+#include <cctype>
+
 #include "distributions/bigram.hh"
 
 // A distribution over natural numbers represented as strings of digits.
@@ -12,4 +14,14 @@
 class StringNat : public Bigram {
  public:
   StringNat(size_t _max_length = 20): Bigram(_max_length, '0', '9') {}
+
+  std::string nearest(const std::string& x) const {
+    std::string s;
+    for (const char& c : x) {
+      if (std::isdigit(c)) {
+        s += c;
+      }
+    }
+    return s;
+  }
 };
diff --git a/cxx/distributions/string_nat_test.cc b/cxx/distributions/string_nat_test.cc
new file mode 100644
index 0000000..1e8284c
--- /dev/null
+++ b/cxx/distributions/string_nat_test.cc
@@ -0,0 +1,24 @@
+// Apache License, Version 2.0, refer to LICENSE.txt
+
+#define BOOST_TEST_MODULE test StringNat
+
+#include "distributions/string_nat.hh"
+
+#include <boost/test/included/unit_test.hpp>
+
+BOOST_AUTO_TEST_CASE(test_simple) {
+  StringNat sn;
+
+  sn.incorporate("42");
+  sn.incorporate("0");
+  BOOST_TEST(sn.N == 2);
+  sn.unincorporate("0");
+  BOOST_TEST(sn.N == 1);
+}
+
+BOOST_AUTO_TEST_CASE(test_nearest) {
+  StringNat sn;
+
+  BOOST_TEST(sn.nearest("1234") == "1234");
+  BOOST_TEST(sn.nearest("a77z99") == "7799");
+}
diff --git a/cxx/distributions/stringcat.cc b/cxx/distributions/stringcat.cc
index 1e199ed..38200d9 100644
--- a/cxx/distributions/stringcat.cc
+++ b/cxx/distributions/stringcat.cc
@@ -3,7 +3,9 @@
 
 #include <algorithm>
 #include <cassert>
+#include <limits>
 #include "distributions/stringcat.hh"
+#include "emissions/string_alignment.hh"
 
 int StringCat::string_to_index(const std::string& s) const {
   auto it = std::find(strings.begin(), strings.end(), s);
@@ -33,3 +35,23 @@ std::string StringCat::sample(std::mt19937* prng) {
 void StringCat::transition_hyperparameters(std::mt19937* prng) {
   dc.transition_hyperparameters(prng);
 }
+
+std::string StringCat::nearest(const std::string& x) const {
+  if (std::find(strings.begin(), strings.end(), x) != strings.end()) {
+    return x;
+  }
+
+  const std::string *nearest = &(strings[0]);
+  double lowest_distance = std::numeric_limits<double>::max();
+  for (const std::string& s : strings) {
+    std::vector<StrAlignment> alignments;
+    topk_alignments(1, s, x, edit_distance, &alignments);
+    double d = alignments[0].cost;
+    if (d < lowest_distance) {
+      lowest_distance = d;
+      nearest = &s;
+    }
+  }
+
+  return *nearest;
+}
diff --git a/cxx/distributions/stringcat.hh b/cxx/distributions/stringcat.hh
index 8fdec44..9aa2ced 100644
--- a/cxx/distributions/stringcat.hh
+++ b/cxx/distributions/stringcat.hh
@@ -31,4 +31,6 @@ class StringCat : public Distribution<std::string> {
   void set_alpha(double alphat);
 
   void transition_hyperparameters(std::mt19937* prng);
+
+  std::string nearest(const std::string& x) const;
 };
diff --git a/cxx/distributions/stringcat_test.cc b/cxx/distributions/stringcat_test.cc
index c23f71c..9e56b90 100644
--- a/cxx/distributions/stringcat_test.cc
+++ b/cxx/distributions/stringcat_test.cc
@@ -30,4 +30,7 @@ BOOST_AUTO_TEST_CASE(test_simple) {
   auto it = std::find(strings.begin(), strings.end(), samp);
   bool found = (it != strings.end());
   BOOST_TEST(found);
+
+  BOOST_TEST(sc.nearest("test") == "test");
+  BOOST_TEST(sc.nearest("otter") == "other");
 }