Bayesian Calculator

// maXbox5 / maXbox6 Script: Bayesian Precision Conversion Calculator
// Demonstrates how Bayes' Theorem calculates Precision from Recall, FPR, and Prevalence Tutor: 3

program Bayes_Precision_Conversion;

var
  TP, FN, FP, TN, Total: Double;
  Recall, FPR, Prevalence, OneMinusPrev: Double;
  BayesNum, BayesDenom, BayesPrecision: Double;
  EmpiricalPrecision: Double;

procedure CalculateBayesPrecision;
begin
  // Given Confusion Matrix Counts: TP = 6, FN = 4, FP = 8, TN = 3
  TP:= 6.0;
  FN:= 4.0;
  FP:= 8.0;
  TN:= 3.0;

  Total:= TP + FN + FP + TN; // 21

  // 1. Derived Bayesian Parameters
  Recall:= TP / (TP + FN);                    // 6 / 10 = 0.6000 (60.00%)
  FPR:= FP / (FP + TN);                       // 8 / 11 = 0.7273 (72.73%)
  Prevalence:= (TP + FN) / Total;             // 10 / 21 = 0.4762 (47.62%)
  OneMinusPrev:= 1.0 - Prevalence;            // 11 / 21 = 0.5238 (52.38%)

  // 2. Bayesian Precision Formula:
  // Precision = (Recall * Prevalence) / [ (Recall * Prevalence) + (FPR * (1 - Prevalence)) ]
  BayesNum:= Recall * Prevalence;             // (6/10) * (10/21) = 6/21 = 0.2857
  BayesDenom:= BayesNum + (FPR * OneMinusPrev); // (6/21) + (8/21) = 14/21 = 0.6667
  BayesPrecision:= (BayesNum / BayesDenom) * 100.0; // (6/14) * 100 = 42.86%

  // 3. Empirical Precision Verification: TP / (TP + FP)
  EmpiricalPrecision:= (TP / (TP + FP)) * 100.0; // 6 / 14 = 42.86%

  // 4. Output Results to Console
  Writeln('================================================================');
  Writeln('       BAYESIAN PRECISION CONVERSION CALCULATOR (maXbox)');
  Writeln('================================================================');
  Writeln('1. CONFUSION MATRIX INPUTS:');
  Writeln('   True Positives  (TP) : ' + FloatToStr(TP));
  Writeln('   False Negatives (FN) : ' + FloatToStr(FN));
  Writeln('   False Positives (FP) : ' + FloatToStr(FP));
  Writeln('   True Negatives  (TN) : ' + FloatToStr(TN));
  Writeln('   Total Population     : ' + FloatToStr(Total));
  Writeln('');
  Writeln('2. DERIVED BAYESIAN PARAMETERS:');
  Writeln('   Recall (TPR)         : ' + FormatFloat('0.00%', Recall * 100.0) + '  [6/10]');
  Writeln('   False Positive Rate  : ' + FormatFloat('0.00%', FPR * 100.0) + '  [8/11]');
  Writeln('   Class Prevalence     : ' + FormatFloat('0.00%', Prevalence * 100.0) + '  [10/21]');
  Writeln('   1 - Prevalence       : ' + FormatFloat('0.00%', OneMinusPrev * 100.0) + '  [11/21]');
  Writeln('');
  Writeln('3. BAYESIAN FORMULA STEP-BY-STEP:');
  Writeln('   Numerator (Rec * Prev) : ' + FormatFloat('0.0000', BayesNum) + '  [6/21]');
  Writeln('   Denominator            : ' + FormatFloat('0.0000', BayesDenom) + '  [14/21]');
  Writeln('');
  Writeln('4. PRECISION RESULT COMPARISON:');
  Writeln('   Bayesian Precision     : '+ FormatFloat('0.00%', BayesPrecision) +'  [3/7 = 42.86%]');
  Writeln('   Empirical Precision    : '+ FormatFloat('0.00%', EmpiricalPrecision)+'  [6/14 = 42.86%]');
  Writeln('================================================================');
end;

begin //@main
setDebugOff;
  maxform1.setconsole; //setConsole
  memo2.font.name:= 'Courier';
  memo2.font.size:= 10;
  CalculateBayesPrecision;
end.