Learning Outcomes • Mahasiswa dapat memahami pemodelan kuantitaif yang ada di bidang Matematika danStatistika..
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Learning Outcomes• Mahasiswa dapat memahami pemodelan
kuantitaif yang ada di bidang Matematika danStatistika..
Outline Materi:
• Pengertian Model Matematika & Statistika• Sistem Modelling• Dynamic model• Matrix model• Stochastic model• Multivariate model• Optimization model
PEMODELAN KUANTITATIF : MATEMATIKA DAN STATISTIKA
MODEL STATISTIKA:FENOMENA STOKASTIK
MODEL MATEMATIKA:FENOMENA DETERMINISTIK
DYNAMIC MODEL DYNAMIC MODEL
MODELLINGMODELLING
DynamicsDynamics SIMULATIONSIMULATION
LanguageLanguage
EquationsEquations
Computer Computer
GeneralGeneralSpecialSpecial
DYNAMOCSMPCSSL
DYNAMOCSMPCSSL
BASICBASIC
FORMALFORMAL
ANALYSISANALYSIS
DYNAMIC MODEL (2) DYNAMIC MODEL (2)
DIAGRAMSDIAGRAMS
RELATIONALRELATIONAL SYMBOLSSYMBOLS
RATE EQUATIONS
RATE EQUATIONS
LEVELS LEVELS
PARAMETERPARAMETER
INFORMATION FLOW
INFORMATION FLOWSINKSINK
AUXILIARY VARIABLES
AUXILIARY VARIABLES
MATERIAL FLOW
MATERIAL FLOW
DYNAMIC MODEL: (3) DYNAMIC MODEL: (3)
ORIGINSORIGINS
ComputersComputers EquationsEquations
Other functions
Other functions
StepsSteps
Discriminant Function
Discriminant Function
UndestandingUndestanding
SimulationSimulation
AbstractionAbstraction
HypothesisHypothesis
LogisticLogisticExponentialsExponentials
MATRIX MODEL MATRIX MODEL
MATHEMATICSMATHEMATICS
OperationsOperations MatricesMatrices
TypesTypes
Eigen valueEigen value
Elements Elements
SquareSquareRectangularRectangular
Diagonal Identity
Diagonal Identity VectorsVectors
DominantDominant
Eigen vectorEigen vector
ScalarsScalars
RowColumn
RowColumn
AdditionsSubstraction
MultiplicationInversion
AdditionsSubstraction
MultiplicationInversion
MATRIX MODEL (2)MATRIX MODEL (2)
DEVELOPMENTDEVELOPMENT
InteractionsInteractions GroupsGroups
Development stages
Development stages
StochasticStochastic
Size Size Materials
cycles
Materials cycles Markov
Models
Markov Models
STOCHASTIC MODEL STOCHASTIC MODEL
STOCHASTICSTOCHASTIC
ProbabilitiesProbabilities HistoryHistory
StabilityStability
Other ModelsOther Models
Statistical method
Statistical method
DynamicsDynamics
STOCHASTIC MODEL (2) STOCHASTIC MODEL (2)
Spatial paternSpatial patern
DistributionDistribution ExampleExample
BinomialBinomial
PissonPisson Poisson Poisson
Negative Binomial
Negative Binomial
OthersOthers
Negative Binomial
Negative Binomial
Fitting Fitting Test Test
STOCHASTIC MODEL (3) STOCHASTIC MODEL (3)
ADDITIVE MODELSADDITIVE MODELS
Basic ModelBasic Model ExampleExample
ParameterParameter
ErrorError Estimates Estimates
BlockBlock
TreatmentsTreatments
AnalysisAnalysis
Effects Effects
Orthogonal Orthogonal
ExperimentalExperimentalSignificance Significance
Variance Variance
STOCHASTIC MODEL (4) STOCHASTIC MODEL (4)
REGRESSIONREGRESSION
ModelModel ExampleExample
Linear/ Non-linear functions
Linear/ Non-linear functions
ErrorError Decomposition Decomposition
AssumptionsAssumptions
EquationEquation
Reactions Reactions
Oxygen uptake Oxygen uptake
ExperimentalExperimentalEmpirical base
Empirical base
Theoritical base
Theoritical base
STOCHASTIC MODEL (5) STOCHASTIC MODEL (5)
MARKOVMARKOV
ExampleExample AssumptionsAssumptions
Transition probabilities
Transition probabilities
AnalysisAnalysis Disadvantage Disadvantage
Raised mireRaised mire
AdvantagesAdvantages
Analysis Analysis
MULTIVARIATE MODELS(1) MULTIVARIATE MODELS(1)
METHODSMETHODS
VariableVariable ClassificationClassification
IndependentIndependent
DependentDependent Descriptive Descriptive PredictivePredictive
VARIATE VARIATE
Principal Component
Analysis
Principal Component
Analysis
Cluster Analysis
Cluster Analysis
Reciprocal averaging
Reciprocal averaging
Canonical Analysis
Canonical Analysis
Discriminant Analysis
Discriminant Analysis
MULTIVARIATE MODEL (2) MULTIVARIATE MODEL (2)
PRINCIPLE COMPONENT ANALYSISPRINCIPLE COMPONENT ANALYSIS
ExampleExample CorrelationCorrelation
OrganismOrganism
EnvironmentEnvironment Eigenvalues Eigenvalues
RegionsRegions
ObjectivesObjectives
Requirement Requirement
Eigenvectors Eigenvectors
MULTIVARIATE MODEL (3)
CLUSTER ANALYSISCLUSTER ANALYSIS
ExampleExample Spanning treeSpanning tree
Rainfall regimes
Rainfall regimes
DemographyDemography
Minimum Minimum
Settlement patern
Settlement patern
Multivariate space
Multivariate space
Similarity Similarity
Distance Distance
Single linkage Single linkage
MULTIVARIATE MODEL (4) MULTIVARIATE MODEL (4)
CANONICAL CORRELATIONCANONICAL CORRELATION
ExampleExample Correlation Correlation
Urban areaUrban area
WatershedWatershedPartitioned Partitioned
Irrigation regions
Irrigation regions
Eigenvalues Eigenvalues Eigenvectors Eigenvectors
MULTIVARIATE MODEL (5) MULTIVARIATE MODEL (5)
Discriminant FunctionDiscriminant Function
ExampleExample Discriminant Discriminant
VehiclesVehicles
VillagesVillagesCalculation Calculation
StructuresStructures
Test Test
OPTIMIZATION MODEL OPTIMIZATION MODEL
OPTIMIZATIONOPTIMIZATION
MeaningsMeanings Indirect Indirect
MinimizationMinimization
SimulationSimulationObjective function Objective function
MaximizationMaximization
Linear Linear
ExperimentationExperimentation
ConstraintsConstraints
SolutionSolution
ExamplesExamples
Non-Linear
Non-Linear
Dynamic Dynamic
Optimum Transportation RoutesOptimum irrigation schemeOptimum Regional Spacing
Optimum Transportation RoutesOptimum irrigation schemeOptimum Regional Spacing
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