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
MODELLING
SIMULATION
Dynamics
Equations
Computer
FORMAL
Language
ANALYSIS
Special
DYNAMO
CSMP
CSSL
General
BASIC
DYNAMIC MODEL (2)
DIAGRAMS
SYMBOLS
RELATIONAL
LEVELS
AUXILIARY
VARIABLES
RATE
EQUATIONS
PARAMETER
SINK
MATERIAL
FLOW
INFORMATION
FLOW
DYNAMIC MODEL: (3)
ORIGINS
Abstraction
Computers
Equations
Steps
Hypothesis
Discriminant
Function
Simulation
Other
functions
Exponentials
Logistic
Undestanding
MATRIX MODEL
MATHEMATICS
Operations
Additions
Substraction
Multiplication
Inversion
Matrices
Eigen value
Elements
Dominant
Types
Eigen vector
Square
Rectangular
Diagonal
Identity
Vectors
Row
Column
Scalars
MATRIX MODEL (2)
DEVELOPMENT
Interactions
Groups
Materials
cycles
Size
Development
stages
Stochastic
Markov
Models
STOCHASTIC MODEL
STOCHASTIC
Probabilities
History
Statistical
method
Other Models
Dynamics
Stability
STOCHASTIC MODEL (2)
Spatial patern
Distribution
Pisson
Example
Poisson
Negative
Binomial
Binomial
Negative
Binomial
Others
Test
Fitting
STOCHASTIC MODEL (3)
ADDITIVE MODELS
Example
Basic Model
Error
Estimates
Analysis
Parameter
Variance
Orthogonal
Block
Effects
Experimental
Treatments
Significance
STOCHASTIC MODEL (4)
REGRESSION
Model
Example
Error
Linear/ Nonlinear functions
Decomposition
Equation
Theoritical
base
Oxygen uptake
Reactions
Experimental
Assumptions
Empirical base
STOCHASTIC MODEL (5)
MARKOV
Analysis
Example
Assumptions
Analysis
Transition
probabilities
Raised mire
Disadvantage
Advantages
MULTIVARIATE MODELS(1)
METHODS
VARIATE
Variable
Classification
Dependent
Independent
Descriptive
Principal
Component
Analysis
Predictive
Discriminant
Analysis
Cluster
Analysis
Reciprocal
averaging
Canonical
Analysis
MULTIVARIATE MODEL (2)
PRINCIPLE COMPONENT ANALYSIS
Requirement
Example
Environment
Organism
Regions
Correlation
Eigenvalues
Objectives
Eigenvectors
MULTIVARIATE MODEL (3)
CLUSTER ANALYSIS
Example
Spanning tree
Multivariate
space
Demography
Rainfall
regimes
Minimum
Similarity
Single linkage
Distance
Settlement
patern
MULTIVARIATE MODEL (4)
CANONICAL CORRELATION
Example
Correlation
Partitioned
Watershed
Urban area
Eigenvalues
Irrigation
regions
Eigenvectors
MULTIVARIATE MODEL (5)
Discriminant Function
Example
Discriminant
Calculation
Villages
Vehicles
Test
Structures
OPTIMIZATION MODEL
OPTIMIZATION
Dynamic
Meanings
Indirect
Simulation
Minimization
Experimentation
NonLinear
Linear
Objective function
Constraints
Solution
Examples
Maximization
Optimum Transportation Routes
Optimum irrigation scheme
Optimum Regional Spacing