diff --git a/gtsam/discrete/DiscreteConditional.cpp b/gtsam/discrete/DiscreteConditional.cpp
index 9cf19638c7..3f0c9f5118 100644
--- a/gtsam/discrete/DiscreteConditional.cpp
+++ b/gtsam/discrete/DiscreteConditional.cpp
@@ -465,6 +465,12 @@ string DiscreteConditional::html(const KeyFormatter& keyFormatter,
 double DiscreteConditional::evaluate(const HybridValues& x) const {
   return this->evaluate(x.discrete());
 }
+
+/* ************************************************************************* */
+double DiscreteConditional::negLogConstant() const {
+  return 0.0;
+}
+
 /* ************************************************************************* */
 
 }  // namespace gtsam
diff --git a/gtsam/discrete/DiscreteConditional.h b/gtsam/discrete/DiscreteConditional.h
index 4c7af14896..e16100d0aa 100644
--- a/gtsam/discrete/DiscreteConditional.h
+++ b/gtsam/discrete/DiscreteConditional.h
@@ -264,11 +264,12 @@ class GTSAM_EXPORT DiscreteConditional
   }
 
   /**
-   * logNormalizationConstant K is just zero, such that
-   * logProbability(x) = log(evaluate(x)) = - error(x)
-   * and hence error(x) = - log(evaluate(x)) > 0 for all x.
+   * negLogConstant is just zero, such that
+   * -logProbability(x) = -log(evaluate(x)) = error(x)
+   * and hence error(x) > 0 for all x.
+   * Thus -log(K) for the normalization constant k is 0.
    */
-  double logNormalizationConstant() const override { return 0.0; }
+  double negLogConstant() const override;
 
   /// @}
 
diff --git a/gtsam/discrete/discrete.i b/gtsam/discrete/discrete.i
index 0bdebd0e17..55c8f9e227 100644
--- a/gtsam/discrete/discrete.i
+++ b/gtsam/discrete/discrete.i
@@ -112,7 +112,7 @@ virtual class DiscreteConditional : gtsam::DecisionTreeFactor {
                       const std::vector<double>& table);
 
   // Standard interface
-  double logNormalizationConstant() const;
+  double negLogConstant() const;
   double logProbability(const gtsam::DiscreteValues& values) const;
   double evaluate(const gtsam::DiscreteValues& values) const;
   double error(const gtsam::DiscreteValues& values) const;
diff --git a/gtsam/hybrid/HybridConditional.cpp b/gtsam/hybrid/HybridConditional.cpp
index 3cb3bba65d..cac2adcf87 100644
--- a/gtsam/hybrid/HybridConditional.cpp
+++ b/gtsam/hybrid/HybridConditional.cpp
@@ -161,18 +161,18 @@ double HybridConditional::logProbability(const HybridValues &values) const {
 }
 
 /* ************************************************************************ */
-double HybridConditional::logNormalizationConstant() const {
+double HybridConditional::negLogConstant() const {
   if (auto gc = asGaussian()) {
-    return gc->logNormalizationConstant();
+    return gc->negLogConstant();
   }
   if (auto gm = asHybrid()) {
-    return gm->logNormalizationConstant();  // 0.0!
+    return gm->negLogConstant();  // 0.0!
   }
   if (auto dc = asDiscrete()) {
-    return dc->logNormalizationConstant();  // 0.0!
+    return dc->negLogConstant();  // 0.0!
   }
   throw std::runtime_error(
-      "HybridConditional::logProbability: conditional type not handled");
+      "HybridConditional::negLogConstant: conditional type not handled");
 }
 
 /* ************************************************************************ */
diff --git a/gtsam/hybrid/HybridConditional.h b/gtsam/hybrid/HybridConditional.h
index 51eeeb5bb6..588c44e0bc 100644
--- a/gtsam/hybrid/HybridConditional.h
+++ b/gtsam/hybrid/HybridConditional.h
@@ -193,11 +193,12 @@ class GTSAM_EXPORT HybridConditional
   double logProbability(const HybridValues& values) const override;
 
   /**
-   * Return the log normalization constant.
+   * Return the negative log of the normalization constant.
+   * This shows up in the error as -(error(x) + negLogConstant)
    * Note this is 0.0 for discrete and hybrid conditionals, but depends
    * on the continuous parameters for Gaussian conditionals.
    */
-  double logNormalizationConstant() const override;
+  double negLogConstant() const override;
 
   /// Return the probability (or density) of the underlying conditional.
   double evaluate(const HybridValues& values) const override;
diff --git a/gtsam/hybrid/HybridGaussianConditional.cpp b/gtsam/hybrid/HybridGaussianConditional.cpp
index fb943366cb..ef38237f2b 100644
--- a/gtsam/hybrid/HybridGaussianConditional.cpp
+++ b/gtsam/hybrid/HybridGaussianConditional.cpp
@@ -36,7 +36,7 @@ HybridGaussianFactor::FactorValuePairs GetFactorValuePairs(
     // Check if conditional is pruned
     if (conditional) {
       // Assign log(\sqrt(|2πΣ|)) = -log(1 / sqrt(|2πΣ|))
-      value = -conditional->logNormalizationConstant();
+      value = conditional->negLogConstant();
     }
     return {std::dynamic_pointer_cast<GaussianFactor>(conditional), value};
   };
@@ -51,14 +51,14 @@ HybridGaussianConditional::HybridGaussianConditional(
                  discreteParents, GetFactorValuePairs(conditionals)),
       BaseConditional(continuousFrontals.size()),
       conditionals_(conditionals) {
-  // Calculate logConstant_ as the minimum of the log normalizers of the
-  // conditionals, by visiting the decision tree:
-  logConstant_ = std::numeric_limits<double>::infinity();
+  // Calculate negLogConstant_ as the minimum of the negative-log normalizers of
+  // the conditionals, by visiting the decision tree:
+  negLogConstant_ = std::numeric_limits<double>::infinity();
   conditionals_.visit(
       [this](const GaussianConditional::shared_ptr &conditional) {
         if (conditional) {
-          this->logConstant_ = std::min(
-              this->logConstant_, -conditional->logNormalizationConstant());
+          this->negLogConstant_ =
+              std::min(this->negLogConstant_, conditional->negLogConstant());
         }
       });
 }
@@ -84,8 +84,7 @@ GaussianFactorGraphTree HybridGaussianConditional::asGaussianFactorGraphTree()
   auto wrap = [this](const GaussianConditional::shared_ptr &gc) {
     // First check if conditional has not been pruned
     if (gc) {
-      const double Cgm_Kgcm =
-          -this->logConstant_ - gc->logNormalizationConstant();
+      const double Cgm_Kgcm = gc->negLogConstant() - this->negLogConstant_;
       // If there is a difference in the covariances, we need to account for
       // that since the error is dependent on the mode.
       if (Cgm_Kgcm > 0.0) {
@@ -156,8 +155,7 @@ void HybridGaussianConditional::print(const std::string &s,
     std::cout << "(" << formatter(dk.first) << ", " << dk.second << "), ";
   }
   std::cout << std::endl
-            << " logNormalizationConstant: " << logNormalizationConstant()
-            << std::endl
+            << " logNormalizationConstant: " << -negLogConstant() << std::endl
             << std::endl;
   conditionals_.print(
       "", [&](Key k) { return formatter(k); },
@@ -215,8 +213,7 @@ std::shared_ptr<HybridGaussianFactor> HybridGaussianConditional::likelihood(
       [&](const GaussianConditional::shared_ptr &conditional)
           -> GaussianFactorValuePair {
         const auto likelihood_m = conditional->likelihood(given);
-        const double Cgm_Kgcm =
-            -logConstant_ - conditional->logNormalizationConstant();
+        const double Cgm_Kgcm = conditional->negLogConstant() - negLogConstant_;
         if (Cgm_Kgcm == 0.0) {
           return {likelihood_m, 0.0};
         } else {
diff --git a/gtsam/hybrid/HybridGaussianConditional.h b/gtsam/hybrid/HybridGaussianConditional.h
index 4a5fdcc89e..9c70cf6cb9 100644
--- a/gtsam/hybrid/HybridGaussianConditional.h
+++ b/gtsam/hybrid/HybridGaussianConditional.h
@@ -66,7 +66,7 @@ class GTSAM_EXPORT HybridGaussianConditional
   Conditionals conditionals_;  ///< a decision tree of Gaussian conditionals.
   ///< Negative-log of the normalization constant (log(\sqrt(|2πΣ|))).
   ///< Take advantage of the neg-log space so everything is a minimization
-  double logConstant_;
+  double negLogConstant_;
 
   /**
    * @brief Convert a HybridGaussianConditional of conditionals into
@@ -150,9 +150,15 @@ class GTSAM_EXPORT HybridGaussianConditional
   /// Returns the continuous keys among the parents.
   KeyVector continuousParents() const;
 
-  /// The log normalization constant is max of the the individual
-  /// log-normalization constants.
-  double logNormalizationConstant() const override { return -logConstant_; }
+  /**
+   * @brief Return log normalization constant in negative log space.
+   *
+   * The log normalization constant is the min of the individual
+   * log-normalization constants.
+   *
+   * @return double
+   */
+  inline double negLogConstant() const override { return negLogConstant_; }
 
   /**
    * Create a likelihood factor for a hybrid Gaussian conditional,
diff --git a/gtsam/hybrid/HybridGaussianFactorGraph.cpp b/gtsam/hybrid/HybridGaussianFactorGraph.cpp
index a6fe955eb3..82828bb41e 100644
--- a/gtsam/hybrid/HybridGaussianFactorGraph.cpp
+++ b/gtsam/hybrid/HybridGaussianFactorGraph.cpp
@@ -233,18 +233,18 @@ continuousElimination(const HybridGaussianFactorGraph &factors,
 
 /* ************************************************************************ */
 /**
- * @brief Exponentiate log-values, not necessarily normalized, normalize, and
- * return as AlgebraicDecisionTree<Key>.
+ * @brief Exponentiate (not necessarily normalized) negative log-values,
+ * normalize, and then return as AlgebraicDecisionTree<Key>.
  *
  * @param logValues DecisionTree of (unnormalized) log values.
  * @return AlgebraicDecisionTree<Key>
  */
-static AlgebraicDecisionTree<Key> probabilitiesFromLogValues(
+static AlgebraicDecisionTree<Key> probabilitiesFromNegativeLogValues(
     const AlgebraicDecisionTree<Key> &logValues) {
   // Perform normalization
-  double max_log = logValues.max();
+  double min_log = logValues.min();
   AlgebraicDecisionTree<Key> probabilities = DecisionTree<Key, double>(
-      logValues, [&max_log](const double x) { return exp(x - max_log); });
+      logValues, [&min_log](const double x) { return exp(-(x - min_log)); });
   probabilities = probabilities.normalize(probabilities.sum());
 
   return probabilities;
@@ -265,13 +265,13 @@ discreteElimination(const HybridGaussianFactorGraph &factors,
       auto logProbability =
           [&](const GaussianFactor::shared_ptr &factor) -> double {
         if (!factor) return 0.0;
-        return -factor->error(VectorValues());
+        return factor->error(VectorValues());
       };
       AlgebraicDecisionTree<Key> logProbabilities =
           DecisionTree<Key, double>(gmf->factors(), logProbability);
 
       AlgebraicDecisionTree<Key> probabilities =
-          probabilitiesFromLogValues(logProbabilities);
+          probabilitiesFromNegativeLogValues(logProbabilities);
       dfg.emplace_shared<DecisionTreeFactor>(gmf->discreteKeys(),
                                              probabilities);
 
@@ -321,23 +321,23 @@ using Result = std::pair<std::shared_ptr<GaussianConditional>,
 static std::shared_ptr<Factor> createDiscreteFactor(
     const DecisionTree<Key, Result> &eliminationResults,
     const DiscreteKeys &discreteSeparator) {
-  auto logProbability = [&](const Result &pair) -> double {
+  auto negLogProbability = [&](const Result &pair) -> double {
     const auto &[conditional, factor] = pair;
     static const VectorValues kEmpty;
     // If the factor is not null, it has no keys, just contains the residual.
     if (!factor) return 1.0;  // TODO(dellaert): not loving this.
 
-    // Logspace version of:
+    // Negative logspace version of:
     // exp(-factor->error(kEmpty)) / conditional->normalizationConstant();
-    // We take negative of the logNormalizationConstant `log(k)`
-    // to get `log(1/k) = log(\sqrt{|2πΣ|})`.
-    return -factor->error(kEmpty) - conditional->logNormalizationConstant();
+    // negLogConstant gives `-log(k)`
+    // which is `-log(k) = log(1/k) = log(\sqrt{|2πΣ|})`.
+    return factor->error(kEmpty) - conditional->negLogConstant();
   };
 
-  AlgebraicDecisionTree<Key> logProbabilities(
-      DecisionTree<Key, double>(eliminationResults, logProbability));
+  AlgebraicDecisionTree<Key> negLogProbabilities(
+      DecisionTree<Key, double>(eliminationResults, negLogProbability));
   AlgebraicDecisionTree<Key> probabilities =
-      probabilitiesFromLogValues(logProbabilities);
+      probabilitiesFromNegativeLogValues(negLogProbabilities);
 
   return std::make_shared<DecisionTreeFactor>(discreteSeparator, probabilities);
 }
@@ -355,8 +355,9 @@ static std::shared_ptr<Factor> createHybridGaussianFactor(
       auto hf = std::dynamic_pointer_cast<HessianFactor>(factor);
       if (!hf) throw std::runtime_error("Expected HessianFactor!");
       // Add 2.0 term since the constant term will be premultiplied by 0.5
-      // as per the Hessian definition
-      hf->constantTerm() += 2.0 * conditional->logNormalizationConstant();
+      // as per the Hessian definition,
+      // and negative since we want log(k)
+      hf->constantTerm() += -2.0 * conditional->negLogConstant();
     }
     return {factor, 0.0};
   };
diff --git a/gtsam/hybrid/hybrid.i b/gtsam/hybrid/hybrid.i
index ef179eb9d8..82881ac478 100644
--- a/gtsam/hybrid/hybrid.i
+++ b/gtsam/hybrid/hybrid.i
@@ -61,7 +61,7 @@ virtual class HybridConditional {
   size_t nrParents() const;
 
   // Standard interface:
-  double logNormalizationConstant() const;
+  double negLogConstant() const;
   double logProbability(const gtsam::HybridValues& values) const;
   double evaluate(const gtsam::HybridValues& values) const;
   double operator()(const gtsam::HybridValues& values) const;
diff --git a/gtsam/hybrid/tests/testHybridGaussianConditional.cpp b/gtsam/hybrid/tests/testHybridGaussianConditional.cpp
index dde493685b..adcf6c70fd 100644
--- a/gtsam/hybrid/tests/testHybridGaussianConditional.cpp
+++ b/gtsam/hybrid/tests/testHybridGaussianConditional.cpp
@@ -61,11 +61,11 @@ const HybridGaussianConditional hybrid_conditional({Z(0)}, {X(0)}, mode,
 TEST(HybridGaussianConditional, Invariants) {
   using namespace equal_constants;
 
-  // Check that the conditional normalization constant is the max of all
-  // constants which are all equal, in this case, hence:
-  const double K = hybrid_conditional.logNormalizationConstant();
-  EXPECT_DOUBLES_EQUAL(K, conditionals[0]->logNormalizationConstant(), 1e-8);
-  EXPECT_DOUBLES_EQUAL(K, conditionals[1]->logNormalizationConstant(), 1e-8);
+  // Check that the conditional (negative log) normalization constant is the min
+  // of all constants which are all equal, in this case, hence:
+  const double K = hybrid_conditional.negLogConstant();
+  EXPECT_DOUBLES_EQUAL(K, conditionals[0]->negLogConstant(), 1e-8);
+  EXPECT_DOUBLES_EQUAL(K, conditionals[1]->negLogConstant(), 1e-8);
 
   EXPECT(HybridGaussianConditional::CheckInvariants(hybrid_conditional, hv0));
   EXPECT(HybridGaussianConditional::CheckInvariants(hybrid_conditional, hv1));
@@ -180,15 +180,16 @@ TEST(HybridGaussianConditional, Error2) {
 
   // Check result.
   DiscreteKeys discrete_keys{mode};
-  double logNormalizer0 = -conditionals[0]->logNormalizationConstant();
-  double logNormalizer1 = -conditionals[1]->logNormalizationConstant();
-  double minLogNormalizer = std::min(logNormalizer0, logNormalizer1);
+  double negLogConstant0 = conditionals[0]->negLogConstant();
+  double negLogConstant1 = conditionals[1]->negLogConstant();
+  double minErrorConstant = std::min(negLogConstant0, negLogConstant1);
 
-  // Expected error is e(X) + log(|2πΣ|).
-  // We normalize log(|2πΣ|) with min(logNormalizers) so it is non-negative.
+  // Expected error is e(X) + log(sqrt(|2πΣ|)).
+  // We normalize log(sqrt(|2πΣ|)) with min(negLogConstant)
+  // so it is non-negative.
   std::vector<double> leaves = {
-      conditionals[0]->error(vv) + logNormalizer0 - minLogNormalizer,
-      conditionals[1]->error(vv) + logNormalizer1 - minLogNormalizer};
+      conditionals[0]->error(vv) + negLogConstant0 - minErrorConstant,
+      conditionals[1]->error(vv) + negLogConstant1 - minErrorConstant};
   AlgebraicDecisionTree<Key> expected(discrete_keys, leaves);
 
   EXPECT(assert_equal(expected, actual, 1e-6));
@@ -196,9 +197,9 @@ TEST(HybridGaussianConditional, Error2) {
   // Check for non-tree version.
   for (size_t mode : {0, 1}) {
     const HybridValues hv{vv, {{M(0), mode}}};
-    EXPECT_DOUBLES_EQUAL(conditionals[mode]->error(vv) -
-                             conditionals[mode]->logNormalizationConstant() -
-                             minLogNormalizer,
+    EXPECT_DOUBLES_EQUAL(conditionals[mode]->error(vv) +
+                             conditionals[mode]->negLogConstant() -
+                             minErrorConstant,
                          hybrid_conditional.error(hv), 1e-8);
   }
 }
@@ -230,8 +231,8 @@ TEST(HybridGaussianConditional, Likelihood2) {
     CHECK(jf1->rows() == 2);
 
     // Check that the constant C1 is properly encoded in the JacobianFactor.
-    const double C1 = hybrid_conditional.logNormalizationConstant() -
-                      conditionals[1]->logNormalizationConstant();
+    const double C1 =
+        conditionals[1]->negLogConstant() - hybrid_conditional.negLogConstant();
     const double c1 = std::sqrt(2.0 * C1);
     Vector expected_unwhitened(2);
     expected_unwhitened << 4.9 - 5.0, -c1;
diff --git a/gtsam/hybrid/tests/testHybridGaussianFactor.cpp b/gtsam/hybrid/tests/testHybridGaussianFactor.cpp
index cd12d4f109..4b664b8b4a 100644
--- a/gtsam/hybrid/tests/testHybridGaussianFactor.cpp
+++ b/gtsam/hybrid/tests/testHybridGaussianFactor.cpp
@@ -780,9 +780,8 @@ static HybridGaussianFactorGraph CreateFactorGraph(
   // Create HybridGaussianFactor
   // We take negative since we want
   // the underlying scalar to be log(\sqrt(|2πΣ|))
-  std::vector<GaussianFactorValuePair> factors{
-      {f0, -model0->logNormalizationConstant()},
-      {f1, -model1->logNormalizationConstant()}};
+  std::vector<GaussianFactorValuePair> factors{{f0, model0->negLogConstant()},
+                                               {f1, model1->negLogConstant()}};
   HybridGaussianFactor motionFactor({X(0), X(1)}, m1, factors);
 
   HybridGaussianFactorGraph hfg;
diff --git a/gtsam/hybrid/tests/testHybridNonlinearFactorGraph.cpp b/gtsam/hybrid/tests/testHybridNonlinearFactorGraph.cpp
index 347cc5f1fe..495444c79d 100644
--- a/gtsam/hybrid/tests/testHybridNonlinearFactorGraph.cpp
+++ b/gtsam/hybrid/tests/testHybridNonlinearFactorGraph.cpp
@@ -902,9 +902,8 @@ static HybridNonlinearFactorGraph CreateFactorGraph(
   // Create HybridNonlinearFactor
   // We take negative since we want
   // the underlying scalar to be log(\sqrt(|2πΣ|))
-  std::vector<NonlinearFactorValuePair> factors{
-      {f0, -model0->logNormalizationConstant()},
-      {f1, -model1->logNormalizationConstant()}};
+  std::vector<NonlinearFactorValuePair> factors{{f0, model0->negLogConstant()},
+                                                {f1, model1->negLogConstant()}};
 
   HybridNonlinearFactor mixtureFactor({X(0), X(1)}, m1, factors);
 
diff --git a/gtsam/inference/Conditional-inst.h b/gtsam/inference/Conditional-inst.h
index 9377e8cc49..c21a75d265 100644
--- a/gtsam/inference/Conditional-inst.h
+++ b/gtsam/inference/Conditional-inst.h
@@ -59,16 +59,8 @@ double Conditional<FACTOR, DERIVEDCONDITIONAL>::evaluate(
 
 /* ************************************************************************* */
 template <class FACTOR, class DERIVEDCONDITIONAL>
-double Conditional<FACTOR, DERIVEDCONDITIONAL>::logNormalizationConstant()
-    const {
-  throw std::runtime_error(
-      "Conditional::logNormalizationConstant is not implemented");
-}
-
-/* ************************************************************************* */
-template <class FACTOR, class DERIVEDCONDITIONAL>
-double Conditional<FACTOR, DERIVEDCONDITIONAL>::normalizationConstant() const {
-  return std::exp(logNormalizationConstant());
+double Conditional<FACTOR, DERIVEDCONDITIONAL>::negLogConstant() const {
+  throw std::runtime_error("Conditional::negLogConstant is not implemented");
 }
 
 /* ************************************************************************* */
@@ -83,13 +75,9 @@ bool Conditional<FACTOR, DERIVEDCONDITIONAL>::CheckInvariants(
   const double logProb = conditional.logProbability(values);
   if (std::abs(prob_or_density - std::exp(logProb)) > 1e-9)
     return false;  // logProb is not consistent with prob_or_density
-  if (std::abs(conditional.logNormalizationConstant() -
-               std::log(conditional.normalizationConstant())) > 1e-9)
-    return false;  // log normalization constant is not consistent with
-                   // normalization constant
   const double error = conditional.error(values);
   if (error < 0.0) return false;  // prob_or_density is negative.
-  const double expected = conditional.logNormalizationConstant() - error;
+  const double expected = -(conditional.negLogConstant() + error);
   if (std::abs(logProb - expected) > 1e-9)
     return false;  // logProb is not consistent with error
   return true;
diff --git a/gtsam/inference/Conditional.h b/gtsam/inference/Conditional.h
index c76c05ab15..f9da36b7bc 100644
--- a/gtsam/inference/Conditional.h
+++ b/gtsam/inference/Conditional.h
@@ -34,11 +34,13 @@ namespace gtsam {
    * `logProbability` is the main methods that need to be implemented in derived
    * classes. These two methods relate to the `error` method in the factor by:
    *   probability(x) = k exp(-error(x))
-   * where k is a normalization constant making \int probability(x) == 1.0, and
-   *   logProbability(x) = K - error(x)
-   * i.e., K = log(K). The normalization constant K is assumed to *not* depend
+   * where k is a normalization constant making
+   * \int probability(x) = \int k exp(-error(x)) == 1.0, and
+   * logProbability(x) = -(K + error(x))
+   * i.e., K = -log(k). The normalization constant k is assumed to *not* depend
    * on any argument, only (possibly) on the conditional parameters.
-   * This class provides a default logNormalizationConstant() == 0.0.
+   * This class provides a default negative log normalization constant
+   * negLogConstant() == 0.0.
    * 
    * There are four broad classes of conditionals that derive from Conditional:
    *
@@ -163,13 +165,12 @@ namespace gtsam {
     }
 
     /**
-     * All conditional types need to implement a log normalization constant to
-     * make it such that error>=0.
+     * @brief All conditional types need to implement this as the negative log
+     * of the normalization constant to make it such that error>=0.
+     *
+     * @return double
      */
-    virtual double logNormalizationConstant() const;
-
-    /** Non-virtual, exponentiate logNormalizationConstant. */
-    double normalizationConstant() const;
+    virtual double negLogConstant() const;
 
     /// @}
     /// @name Advanced Interface
@@ -208,9 +209,9 @@ namespace gtsam {
      *  - evaluate >= 0.0
      *  - evaluate(x) == conditional(x)
      *  - exp(logProbability(x)) == evaluate(x)
-     *  - logNormalizationConstant() = log(normalizationConstant())
+     *  - negLogConstant() = -log(normalizationConstant())
      *  - error >= 0.0
-     *  - logProbability(x) == logNormalizationConstant() - error(x)
+     *  - logProbability(x) == -(negLogConstant() + error(x))
      *
      * @param conditional The conditional to test, as a reference to the derived type.
      * @tparam VALUES HybridValues, or a more narrow type like DiscreteValues.
diff --git a/gtsam/linear/GaussianBayesNet.cpp b/gtsam/linear/GaussianBayesNet.cpp
index 861e19cc9e..f8c4ddc4c2 100644
--- a/gtsam/linear/GaussianBayesNet.cpp
+++ b/gtsam/linear/GaussianBayesNet.cpp
@@ -243,23 +243,24 @@ namespace gtsam {
   }
 
   /* ************************************************************************* */
-  double GaussianBayesNet::logNormalizationConstant() const {
+  double GaussianBayesNet::negLogConstant() const {
     /*
     normalization constant = 1.0 / sqrt((2*pi)^n*det(Sigma))
-    logConstant = -0.5 * n*log(2*pi) - 0.5 * log det(Sigma)
-    
-    log det(Sigma)) = -2.0 * logDeterminant()
-    thus, logConstant = -0.5*n*log(2*pi) + logDeterminant()
-
-    BayesNet logConstant = sum(-0.5*n_i*log(2*pi) + logDeterminant_i())
-    = sum(-0.5*n_i*log(2*pi)) + sum(logDeterminant_i())
-    = sum(-0.5*n_i*log(2*pi)) + bn->logDeterminant()
+    negLogConstant = -log(normalizationConstant)
+      = 0.5 * n*log(2*pi) + 0.5 * log(det(Sigma))
+
+    log(det(Sigma)) = -2.0 * logDeterminant()
+    thus, negLogConstant = 0.5*n*log(2*pi) - logDeterminant()
+
+    BayesNet negLogConstant = sum(0.5*n_i*log(2*pi) - logDeterminant_i())
+    = sum(0.5*n_i*log(2*pi)) + sum(logDeterminant_i())
+    = sum(0.5*n_i*log(2*pi)) + bn->logDeterminant()
     */
-    double logNormConst = 0.0;
+    double negLogNormConst = 0.0;
     for (const sharedConditional& cg : *this) {
-      logNormConst += cg->logNormalizationConstant();
+      negLogNormConst += cg->negLogConstant();
     }
-    return logNormConst;
+    return negLogNormConst;
   }
 
   /* ************************************************************************* */
diff --git a/gtsam/linear/GaussianBayesNet.h b/gtsam/linear/GaussianBayesNet.h
index ea1cb8603c..e858bbe43d 100644
--- a/gtsam/linear/GaussianBayesNet.h
+++ b/gtsam/linear/GaussianBayesNet.h
@@ -235,12 +235,12 @@ namespace gtsam {
     double logDeterminant() const;
 
     /**
-     * @brief Get the log of the normalization constant corresponding to the
-     * joint Gaussian density represented by this Bayes net.
+     * @brief Get the negative log of the normalization constant corresponding
+     * to the joint Gaussian density represented by this Bayes net.
      *
      * @return double
      */
-    double logNormalizationConstant() const;
+    double negLogConstant() const;
 
     /**
      * Backsubstitute with a different RHS vector than the one stored in this BayesNet.
diff --git a/gtsam/linear/GaussianConditional.cpp b/gtsam/linear/GaussianConditional.cpp
index 585bbdb331..7735e5129b 100644
--- a/gtsam/linear/GaussianConditional.cpp
+++ b/gtsam/linear/GaussianConditional.cpp
@@ -121,7 +121,7 @@ namespace gtsam {
       const auto mean = solve({});  // solve for mean.
       mean.print("  mean", formatter);
     }
-    cout << "  logNormalizationConstant: " << logNormalizationConstant() << endl;
+    cout << "  logNormalizationConstant: " << -negLogConstant() << endl;
     if (model_)
       model_->print("  Noise model: ");
     else
@@ -181,24 +181,24 @@ namespace gtsam {
 
   /* ************************************************************************* */
   //  normalization constant = 1.0 / sqrt((2*pi)^n*det(Sigma))
-  //  log = - 0.5 * n*log(2*pi) - 0.5 * log det(Sigma)
-  double GaussianConditional::logNormalizationConstant() const {
+  //  neg-log = 0.5 * n*log(2*pi) + 0.5 * log det(Sigma)
+  double GaussianConditional::negLogConstant() const {
     constexpr double log2pi = 1.8378770664093454835606594728112;
     size_t n = d().size();
     // Sigma = (R'R)^{-1}, det(Sigma) = det((R'R)^{-1}) = det(R'R)^{-1}
     // log det(Sigma) = -log(det(R'R)) = -2*log(det(R))
     // Hence, log det(Sigma)) = -2.0 * logDeterminant()
-    // which gives log = -0.5*n*log(2*pi) - 0.5*(-2.0 * logDeterminant())
-    //     = -0.5*n*log(2*pi) + (0.5*2.0 * logDeterminant())
-    //     = -0.5*n*log(2*pi) + logDeterminant()
-    return -0.5 * n * log2pi + logDeterminant();
+    // which gives neg-log = 0.5*n*log(2*pi) + 0.5*(-2.0 * logDeterminant())
+    //     = 0.5*n*log(2*pi) - (0.5*2.0 * logDeterminant())
+    //     = 0.5*n*log(2*pi) - logDeterminant()
+    return 0.5 * n * log2pi - logDeterminant();
   }
 
   /* ************************************************************************* */
   //  density = k exp(-error(x))
   //  log = log(k) - error(x)
   double GaussianConditional::logProbability(const VectorValues& x) const {
-    return logNormalizationConstant() - error(x);
+    return -(negLogConstant() + error(x));
   }
 
   double GaussianConditional::logProbability(const HybridValues& x) const {
diff --git a/gtsam/linear/GaussianConditional.h b/gtsam/linear/GaussianConditional.h
index 420efabca9..27270fece1 100644
--- a/gtsam/linear/GaussianConditional.h
+++ b/gtsam/linear/GaussianConditional.h
@@ -133,10 +133,14 @@ namespace gtsam {
     /// @{
 
     /**
-     * normalization constant = 1.0 / sqrt((2*pi)^n*det(Sigma))
-     * log = - 0.5 * n*log(2*pi) - 0.5 * log det(Sigma)
+     * @brief Return the negative log of the normalization constant.
+     *
+     * normalization constant k = 1.0 / sqrt((2*pi)^n*det(Sigma))
+     * -log(k) = 0.5 * n*log(2*pi) + 0.5 * log det(Sigma)
+     *
+     * @return double 
      */
-    double logNormalizationConstant() const override;
+    double negLogConstant() const override;
 
     /**
      * Calculate log-probability log(evaluate(x)) for given values `x`:
diff --git a/gtsam/linear/NoiseModel.cpp b/gtsam/linear/NoiseModel.cpp
index de69fdce97..1236f1b946 100644
--- a/gtsam/linear/NoiseModel.cpp
+++ b/gtsam/linear/NoiseModel.cpp
@@ -255,18 +255,17 @@ double Gaussian::logDeterminant() const {
 }
 
 /* *******************************************************************************/
-double Gaussian::logNormalizationConstant() const {
+double Gaussian::negLogConstant() const {
   // log(det(Sigma)) = -2.0 * logDetR
-  // which gives log = -0.5*n*log(2*pi) - 0.5*(-2.0 * logDetR())
-  //     = -0.5*n*log(2*pi) + (0.5*2.0 * logDetR())
-  //     = -0.5*n*log(2*pi) + logDetR()
+  // which gives neg-log = 0.5*n*log(2*pi) + 0.5*(-2.0 * logDetR())
+  //     = 0.5*n*log(2*pi) - (0.5*2.0 * logDetR())
+  //     = 0.5*n*log(2*pi) - logDetR()
   size_t n = dim();
   constexpr double log2pi = 1.8378770664093454835606594728112;
-  // Get 1/log(\sqrt(|2pi Sigma|)) = -0.5*log(|2pi Sigma|)
-  return -0.5 * n * log2pi + logDetR();
+  // Get -log(1/\sqrt(|2pi Sigma|)) = 0.5*log(|2pi Sigma|)
+  return 0.5 * n * log2pi - logDetR();
 }
 
-
 /* ************************************************************************* */
 // Diagonal
 /* ************************************************************************* */
diff --git a/gtsam/linear/NoiseModel.h b/gtsam/linear/NoiseModel.h
index 91c11d4101..34fa63e4cc 100644
--- a/gtsam/linear/NoiseModel.h
+++ b/gtsam/linear/NoiseModel.h
@@ -272,14 +272,12 @@ namespace gtsam {
       double logDeterminant() const;
 
       /**
-       * @brief Method to compute the normalization constant
-       * for a Gaussian noise model k = \sqrt(1/|2πΣ|).
-       * We compute this in the log-space for numerical accuracy,
-       * thus returning log(k).
-       *
-       * @return double
-       */
-      double logNormalizationConstant() const;
+       * @brief Compute the negative log of the normalization constant
+       * for a Gaussian noise model k = 1/\sqrt(|2πΣ|).
+       * 
+       * @return double 
+       */
+      double negLogConstant() const;
 
      private:
 #ifdef GTSAM_ENABLE_BOOST_SERIALIZATION
diff --git a/gtsam/linear/linear.i b/gtsam/linear/linear.i
index 9c448de50b..af6c2ee225 100644
--- a/gtsam/linear/linear.i
+++ b/gtsam/linear/linear.i
@@ -548,7 +548,7 @@ virtual class GaussianConditional : gtsam::JacobianFactor {
   bool equals(const gtsam::GaussianConditional& cg, double tol) const;
   
   // Standard Interface
-  double logNormalizationConstant() const;
+  double negLogConstant() const;
   double logProbability(const gtsam::VectorValues& x) const;
   double evaluate(const gtsam::VectorValues& x) const;
   double error(const gtsam::VectorValues& x) const;
diff --git a/gtsam/linear/tests/testGaussianBayesNet.cpp b/gtsam/linear/tests/testGaussianBayesNet.cpp
index 99453ee4ef..b1cfbe12ca 100644
--- a/gtsam/linear/tests/testGaussianBayesNet.cpp
+++ b/gtsam/linear/tests/testGaussianBayesNet.cpp
@@ -76,12 +76,11 @@ TEST(GaussianBayesNet, Evaluate1) {
   // the normalization constant 1.0/sqrt((2*pi*Sigma).det()).
   // The covariance matrix inv(Sigma) = R'*R, so the determinant is
   const double constant = sqrt((invSigma / (2 * M_PI)).determinant());
-  EXPECT_DOUBLES_EQUAL(log(constant),
-                       smallBayesNet.at(0)->logNormalizationConstant() +
-                           smallBayesNet.at(1)->logNormalizationConstant(),
-                       1e-9);
-  EXPECT_DOUBLES_EQUAL(log(constant), smallBayesNet.logNormalizationConstant(),
+  EXPECT_DOUBLES_EQUAL(-log(constant),
+                       smallBayesNet.at(0)->negLogConstant() +
+                           smallBayesNet.at(1)->negLogConstant(),
                        1e-9);
+  EXPECT_DOUBLES_EQUAL(-log(constant), smallBayesNet.negLogConstant(), 1e-9);
   const double actual = smallBayesNet.evaluate(mean);
   EXPECT_DOUBLES_EQUAL(constant, actual, 1e-9);
 }
diff --git a/gtsam/linear/tests/testGaussianConditional.cpp b/gtsam/linear/tests/testGaussianConditional.cpp
index dcd8218894..68894c3142 100644
--- a/gtsam/linear/tests/testGaussianConditional.cpp
+++ b/gtsam/linear/tests/testGaussianConditional.cpp
@@ -486,16 +486,17 @@ TEST(GaussianConditional, Error) {
 
 /* ************************************************************************* */
 // Similar test for multivariate gaussian but with sigma 2.0
-TEST(GaussianConditional, LogNormalizationConstant) {
+TEST(GaussianConditional, NegLogConstant) {
   double sigma = 2.0;
   auto conditional = GaussianConditional::FromMeanAndStddev(X(0), Vector3::Zero(), sigma);
   VectorValues x;
   x.insert(X(0), Vector3::Zero());
   Matrix3 Sigma = I_3x3 * sigma * sigma;
-  double expectedLogNormalizingConstant = log(1 / sqrt((2 * M_PI * Sigma).determinant()));
+  double expectedNegLogConstant =
+      -log(1 / sqrt((2 * M_PI * Sigma).determinant()));
 
-  EXPECT_DOUBLES_EQUAL(expectedLogNormalizingConstant,
-                       conditional.logNormalizationConstant(), 1e-9);
+  EXPECT_DOUBLES_EQUAL(expectedNegLogConstant, conditional.negLogConstant(),
+                       1e-9);
 }
 
 /* ************************************************************************* */
diff --git a/gtsam/linear/tests/testGaussianDensity.cpp b/gtsam/linear/tests/testGaussianDensity.cpp
index 97eb0de704..b2861e833e 100644
--- a/gtsam/linear/tests/testGaussianDensity.cpp
+++ b/gtsam/linear/tests/testGaussianDensity.cpp
@@ -55,7 +55,7 @@ TEST(GaussianDensity, FromMeanAndStddev) {
   double expected1 = 0.5 * e.dot(e);
   EXPECT_DOUBLES_EQUAL(expected1, density.error(values), 1e-9);
 
-  double expected2 = density.logNormalizationConstant()- 0.5 * e.dot(e);
+  double expected2 = -(density.negLogConstant() + 0.5 * e.dot(e));
   EXPECT_DOUBLES_EQUAL(expected2, density.logProbability(values), 1e-9);
 }
 
diff --git a/gtsam/linear/tests/testNoiseModel.cpp b/gtsam/linear/tests/testNoiseModel.cpp
index 6aea154ee4..2518e4c497 100644
--- a/gtsam/linear/tests/testNoiseModel.cpp
+++ b/gtsam/linear/tests/testNoiseModel.cpp
@@ -807,50 +807,50 @@ TEST(NoiseModel, NonDiagonalGaussian)
   }
 }
 
-TEST(NoiseModel, LogNormalizationConstant1D) {
+TEST(NoiseModel, NegLogNormalizationConstant1D) {
   // Very simple 1D noise model, which we can compute by hand.
   double sigma = 0.1;
-  // For expected values, we compute 1/log(sqrt(|2πΣ|)) by hand.
-  // = -0.5*(log(2π) + log(Σ)) (since it is 1D)
-  double expected_value = -0.5 * log(2 * M_PI * sigma * sigma);
+  // For expected values, we compute -log(1/sqrt(|2πΣ|)) by hand.
+  // = 0.5*(log(2π) - log(Σ)) (since it is 1D)
+  double expected_value = 0.5 * log(2 * M_PI * sigma * sigma);
 
   // Gaussian
   {
     Matrix11 R;
     R << 1 / sigma;
     auto noise_model = Gaussian::SqrtInformation(R);
-    double actual_value = noise_model->logNormalizationConstant();
+    double actual_value = noise_model->negLogConstant();
     EXPECT_DOUBLES_EQUAL(expected_value, actual_value, 1e-9);
   }
   // Diagonal
   {
     auto noise_model = Diagonal::Sigmas(Vector1(sigma));
-    double actual_value = noise_model->logNormalizationConstant();
+    double actual_value = noise_model->negLogConstant();
     EXPECT_DOUBLES_EQUAL(expected_value, actual_value, 1e-9);
   }
   // Isotropic
   {
     auto noise_model = Isotropic::Sigma(1, sigma);
-    double actual_value = noise_model->logNormalizationConstant();
+    double actual_value = noise_model->negLogConstant();
     EXPECT_DOUBLES_EQUAL(expected_value, actual_value, 1e-9);
   }
   // Unit
   {
     auto noise_model = Unit::Create(1);
-    double actual_value = noise_model->logNormalizationConstant();
+    double actual_value = noise_model->negLogConstant();
     double sigma = 1.0;
-    expected_value = -0.5 * log(2 * M_PI * sigma * sigma);
+    expected_value = 0.5 * log(2 * M_PI * sigma * sigma);
     EXPECT_DOUBLES_EQUAL(expected_value, actual_value, 1e-9);
   }
 }
 
-TEST(NoiseModel, LogNormalizationConstant3D) {
+TEST(NoiseModel, NegLogNormalizationConstant3D) {
   // Simple 3D noise model, which we can compute by hand.
   double sigma = 0.1;
   size_t n = 3;
-  // We compute the expected values just like in the LogNormalizationConstant1D
+  // We compute the expected values just like in the NegLogNormalizationConstant1D
   // test, but we multiply by 3 due to the determinant.
-  double expected_value = -0.5 * n * log(2 * M_PI * sigma * sigma);
+  double expected_value = 0.5 * n * log(2 * M_PI * sigma * sigma);
 
   // Gaussian
   {
@@ -859,27 +859,27 @@ TEST(NoiseModel, LogNormalizationConstant3D) {
         0, 1 / sigma, 4,   //
         0, 0, 1 / sigma;
     auto noise_model = Gaussian::SqrtInformation(R);
-    double actual_value = noise_model->logNormalizationConstant();
+    double actual_value = noise_model->negLogConstant();
     EXPECT_DOUBLES_EQUAL(expected_value, actual_value, 1e-9);
   }
   // Diagonal
   {
     auto noise_model = Diagonal::Sigmas(Vector3(sigma, sigma, sigma));
-    double actual_value = noise_model->logNormalizationConstant();
+    double actual_value = noise_model->negLogConstant();
     EXPECT_DOUBLES_EQUAL(expected_value, actual_value, 1e-9);
   }
   // Isotropic
   {
     auto noise_model = Isotropic::Sigma(n, sigma);
-    double actual_value = noise_model->logNormalizationConstant();
+    double actual_value = noise_model->negLogConstant();
     EXPECT_DOUBLES_EQUAL(expected_value, actual_value, 1e-9);
   }
   // Unit
   {
     auto noise_model = Unit::Create(3);
-    double actual_value = noise_model->logNormalizationConstant();
+    double actual_value = noise_model->negLogConstant();
     double sigma = 1.0;
-    expected_value = -0.5 * n * log(2 * M_PI * sigma * sigma);
+    expected_value = 0.5 * n * log(2 * M_PI * sigma * sigma);
     EXPECT_DOUBLES_EQUAL(expected_value, actual_value, 1e-9);
   }
 }
diff --git a/python/gtsam/tests/test_HybridBayesNet.py b/python/gtsam/tests/test_HybridBayesNet.py
index 2f7dd4a987..bf2b6a0330 100644
--- a/python/gtsam/tests/test_HybridBayesNet.py
+++ b/python/gtsam/tests/test_HybridBayesNet.py
@@ -90,8 +90,7 @@ def check_invariance(self, conditional, values):
         self.assertTrue(probability >= 0.0)
         logProb = conditional.logProbability(values)
         self.assertAlmostEqual(probability, np.exp(logProb))
-        expected = conditional.logNormalizationConstant() - \
-            conditional.error(values)
+        expected = -(conditional.negLogConstant() + conditional.error(values))
         self.assertAlmostEqual(logProb, expected)
 
 
diff --git a/python/gtsam/tests/test_NonlinearOptimizer.py b/python/gtsam/tests/test_NonlinearOptimizer.py
index a47c5ad620..1b4209509e 100644
--- a/python/gtsam/tests/test_NonlinearOptimizer.py
+++ b/python/gtsam/tests/test_NonlinearOptimizer.py
@@ -14,15 +14,16 @@
 
 import unittest
 
-import gtsam
-from gtsam import (
-    DoglegOptimizer, DoglegParams, DummyPreconditionerParameters, GaussNewtonOptimizer,
-    GaussNewtonParams, GncLMParams, GncLossType, GncLMOptimizer, LevenbergMarquardtOptimizer,
-    LevenbergMarquardtParams, NonlinearFactorGraph, Ordering, PCGSolverParameters, Point2,
-    PriorFactorPoint2, Values
-)
 from gtsam.utils.test_case import GtsamTestCase
 
+import gtsam
+from gtsam import (DoglegOptimizer, DoglegParams,
+                   DummyPreconditionerParameters, GaussNewtonOptimizer,
+                   GaussNewtonParams, GncLMOptimizer, GncLMParams, GncLossType,
+                   LevenbergMarquardtOptimizer, LevenbergMarquardtParams,
+                   NonlinearFactorGraph, Ordering, PCGSolverParameters, Point2,
+                   PriorFactorPoint2, Values)
+
 KEY1 = 1
 KEY2 = 2
 
@@ -136,7 +137,7 @@ def test_gnc_params(self):
         # Test optimizer params
         optimizer = GncLMOptimizer(self.fg, self.initial_values, params)
         for ict_factor in (0.9, 1.1):
-            new_ict = ict_factor * optimizer.getInlierCostThresholds()
+            new_ict = ict_factor * optimizer.getInlierCostThresholds().item()
             optimizer.setInlierCostThresholds(new_ict)
             self.assertAlmostEqual(optimizer.getInlierCostThresholds(), new_ict)
         for w_factor in (0.8, 0.9):