[6.4][ML] Correct the multimodal prior confidence interval calculation (#178)

Backport of #176.

Author: tveasey

docs/CHANGELOG.asciidoc

@@ -50,6 +50,9 @@ Fix corner case failing to calculate lgamma values and the correspoinding log er
 Influence count per bucket for metric population analyses was wrong and lead to wrong influencer scoring ({pull}#150[#150])
 Fix a possible SIGSEGV for jobs with multivariate by fields enabled which would lead to the job failing ({pull}#170[#170])
 
+Correct the model bounds and typical value calculation for time series models which use a multimodal distribution.
+This issue could cause "Unable to bracket left percentile =..." errors to appear in the logs. ({pull}#176[#176])
+
 === Regressions
 
 === Known Issues

include/maths/CMultimodalPriorUtils.h

@@ -206,8 +206,8 @@ class MATHS_EXPORT CMultimodalPriorUtils : private core::CNonInstantiatable {
             return support;
         }
 
-        double p1 = std::log((1.0 - percentage) / 2.0);
-        double p2 = std::log((1.0 + percentage) / 2.0);
+        double p1 = maths_t::count(weights) * std::log((1.0 - percentage) / 2.0);
+        double p2 = maths_t::count(weights) * std::log((1.0 + percentage) / 2.0);
 
         CLogCdf<PRIOR> fl(CLogCdf<PRIOR>::E_Lower, prior, weights);
         CLogCdf<PRIOR> fu(CLogCdf<PRIOR>::E_Upper, prior, weights);

lib/maths/unittest/CMultimodalPriorTest.cc

@@ -941,10 +941,10 @@ void CMultimodalPriorTest::testMarginalLikelihoodConfidenceInterval() {
 
     using TMeanAccumulator = maths::CBasicStatistics::SSampleMean<double>::TAccumulator;
 
+    test::CRandomNumbers rng;
+
     LOG_DEBUG(<< "Synthetic");
     {
-        test::CRandomNumbers rng;
-
         double w1 = 0.2;
         double location1 = 0.1;
         double squareScale1 = 0.2;
@@ -1047,6 +1047,33 @@ void CMultimodalPriorTest::testMarginalLikelihoodConfidenceInterval() {
         CPPUNIT_ASSERT_DOUBLES_EQUAL(-111.0, i90.first, 0.5);
         CPPUNIT_ASSERT_DOUBLES_EQUAL(158952.0, i90.second, 0.5);
     }
+
+    LOG_DEBUG(<< "Non-unit count weight");
+    {
+        // The confidence interval should be independent of the sample
+        // count weight.
+
+        TDoubleVec modes[2];
+        rng.generateNormalSamples(10.0, 2.0, 50, modes[0]);
+        rng.generateNormalSamples(20.0, 2.0, 50, modes[1]);
+        TDoubleVec samples(modes[0].begin(), modes[0].end());
+        samples.insert(samples.end(), modes[1].begin(), modes[1].end());
+
+        CMultimodalPrior filter(makePrior());
+        filter.addSamples(samples);
+
+        CPPUNIT_ASSERT_EQUAL(std::size_t(2), filter.numberModes());
+
+        TDoubleDoublePr interval{filter.marginalLikelihoodConfidenceInterval(
+            90.0, maths_t::countWeight(1.0))};
+        TDoubleDoublePr weightedInterval{filter.marginalLikelihoodConfidenceInterval(
+            90.0, maths_t::countWeight(0.3))};
+        LOG_DEBUG(<< "interval = " << core::CContainerPrinter::print(interval));
+        LOG_DEBUG(<< "weightedInterval = "
+                  << core::CContainerPrinter::print(weightedInterval));
+        CPPUNIT_ASSERT_EQUAL(core::CContainerPrinter::print(interval),
+                             core::CContainerPrinter::print(weightedInterval));
+    }
 }
 
 void CMultimodalPriorTest::testSampleMarginalLikelihood() {