public void LogLikelihoodDerivative_MultipleResponses_MatchesFiniteDifferenceDerivative()
{
double alpha1 = .3;
double delta1 = .1;
double chi1 = .2;
ThreeParamModelParameters modelParameters1 = new ThreeParamModelParameters(alpha1, delta1, chi1);
double alpha2 = .5;
double delta2 = .6;
double chi2 = .7;
ThreeParamModelParameters modelParameters2 = new ThreeParamModelParameters(alpha2, delta2, chi2);
double alpha3 = .1;
double delta3 = .2;
double chi3 = .4;
ThreeParamModelParameters modelParameters3 = new ThreeParamModelParameters(alpha2, delta2, chi2);
List<IModelParameters> modelParameterList = new List<IModelParameters>();
modelParameterList.Add(modelParameters1);
modelParameterList.Add(modelParameters2);
modelParameterList.Add(modelParameters3);
LogLikelihoodFunction logLikelihoodFunction = new LogLikelihoodFunction(modelParameterList);
double theta = .4;
List<int> responseVector = new List<int>() { 1, 0, 1 };
OneDimensionalFunction function = x => logLikelihoodFunction.LogLikelihood(responseVector, x);
FiniteDifferencer finiteDifferencer = new FiniteDifferencer(function);
double logLikelihoodDerivative = logLikelihoodFunction.LogLikelihoodFirstDerivative(responseVector, theta);
double finiteDifferenceDerivative = finiteDifferencer.ApproximateDerivative(theta);
Assert.AreEqual(finiteDifferenceDerivative, logLikelihoodDerivative, Tolerance);
}
public void ApproximateDerivative_SimpleQuadraticAtZeroDerivative_ReturnsApproxDerivativeWithinTolerance()
{
OneDimensionalFunction f = x => x*x;
FiniteDifferencer finiteDifferencer = new FiniteDifferencer(f);
var approxDerivative = finiteDifferencer.ApproximateDerivative(0);
double expectedDerivative = 0;
CheckWithinTolerance(expectedDerivative, approxDerivative);
}
public void ApproximateDerivative_CosAtNonZeroDerivative_ReturnsApproxDerivativeWithinTolerance()
{
OneDimensionalFunction f = Math.Cos;
FiniteDifferencer finiteDifferencer = new FiniteDifferencer(f);
double x = 1;
var approxDerivative = finiteDifferencer.ApproximateDerivative(x);
double expectedDerivative = -Math.Sin(x);
CheckWithinTolerance(expectedDerivative, approxDerivative);
}
public void SecondThetaDerivative_NonTrivialInput_CloseToFiniteDifferenceValue()
{
double alpha = .2;
double delta = .3;
TwoParamModelParameters parameters = new TwoParamModelParameters(alpha, delta);
TwoParamProbabilityFunction probabilityFunction = new TwoParamProbabilityFunction(parameters);
FiniteDifferencer finiteDifferencer = new FiniteDifferencer(x => probabilityFunction.FirstThetaDerivative(x));
double theta = .1;
double secondDerivative = probabilityFunction.SecondThetaDerivative(theta);
double approxSecondDerivative = finiteDifferencer.ApproximateDerivative(theta);
Assert.IsTrue(Math.Abs(secondDerivative - approxSecondDerivative) < Tolerance);
}
public void FirstThetaDerivative_NonTrivialInput_CloseToFiniteDifferenceValue()
{
double alpha = .2;
double delta = .3;
double chi = .4;
ThreeParamModelParameters parameters = new ThreeParamModelParameters(alpha, delta, chi);
ThreeParamProbabilityFunction probabilityFunction = new ThreeParamProbabilityFunction(parameters);
FiniteDifferencer finiteDifferencer = new FiniteDifferencer(x => probabilityFunction.ProbabilityOfCorrectResponse(x));
double theta = .1;
double derivative = probabilityFunction.FirstThetaDerivative(theta);
double approxDerivative = finiteDifferencer.ApproximateDerivative(theta);
Assert.IsTrue(Math.Abs(derivative - approxDerivative) < Tolerance);
}
