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oleh: [email protected]
“Semua benda hidup dan mati yg terdapat secara alamiah di
bumi,
Bermanfaat bagi manusia,
Dapat dimanfaatkan oleh manusia,
untuk memenuhi kebutuhan hidupnya
Keberadaannya & ketersediaannya:
1. Sebaran geografisnya tdk merata
2. Pemanfaatannya tgt teknologi
3. Kalau diolah menghasilkan produk dan limbah
A Comprehensive Model
Land (Resources) use = is a way of managing a large part of the
human environment in order to obtain benefits for human.
Resources use
development
The complex
problems
Systems theory
is an interdisciplinary theory about the nature of
complex systems in nature, society, and
science, and is a framework by which one can
investigate and/or describe any group of objects
that work together to produce some result.
The Comprehensive Model
FIVE GEOMETRIES IN RESOURCES USE SYSTEM
Natural resources
geometry
Human demand
geometry
NATURAL RESOURCES
USE GEOMETRY
Natural Resources
Geometry
Resources Degradation
Geometry
SISTEM
sbg suatu pendekatan
1. Filosofis
Systems thinking is the process of
predicting, on the basis of anything at all,
how something influences another thing.
2. Prosedural
It has been defined as an approach to
problem solving, by viewing "problems" as
3. Alat bantu
parts of an overall system, rather than
analisis
reacting to present outcomes or events and
potentially contributing to further
development of the undesired issue or
problem.
FILOSOFI
“Sistem”:
Gugusan elemen-elemen yg
saling
berinteraksi
dan
terorganisir peri-lakunya ke
arah tujuan tertentu
Science systems thinkers consider that:
A system is a dynamic and complex whole, interacting as a structured functional unit;
Energy, material and information flow among the different elements that compose the
system;
A system is a community situated within an environment;
energy, material and information flow from and to the surrounding environment via
semi-permeable membranes or boundaries;
Systems are often composed of entities seeking equilibrium but can exhibit
oscillating, chaotic, or exponential behavior.
“Tiga prasyarat aplikasinya”:
1. Tujuan dirumuskan dengan jelas
2. Proses pengambilan keputusan sentralisasi logis
3. Sekala waktu -------- jangka panjang
PROSEDUR
A conceptual framework is used in research
to outline possible courses of action or to
present a preferred approach to a system
analysis project.
The framework is built from a set of
concepts linked to a planned or existing
system of methods, behaviors, functions,
relationships, and objects. A conceptual
framework might, in computing terms, be
thought of as a relational model.
For example a conceptual framework of
accounting "seeks to identify the nature,
subject, purpose and broad content of
general-purpose financial reporting and the
qualitative characteristics that financial
information should possess".
“Tahapan Pokok”:
1. Analisis Kelayakan
2. Pemodelan Abstrak
3. Disain Sistem
4. Implementasi Sistem
5. Operasi Sistem
Need Assesment
Tahapan Pokok:
Evaluasi
Outcomes
“Model Abstrak”:
Perilaku esensialnya sama
dengan dunia nyata
ALAT BANTU
“digunakan dalam”:
1. Perancangan / Disain Sistem
2. Menganalisis SISTEM ……………strukturnya
INPUT …...…….. beragam
STRUKTUR …….. fixed
OUTPUT ……….. Diamati perilakunya
3. Simulasi SISTEM
untuk sistem yang kompleks
SIMULASI
SISTEM:
“Penggunaan Komputer ”:
OPERASINYA
A model is a simplified abstract view of the
complex reality.
A scientific model represents empirical objects,
phenomena, and physical processes in a logical way.
Attempts to formalize the principles of the empirical
sciences, use an interpretation to model reality, in the
same way logicians axiomatize the principles of logic.
The aim of these attempts is to construct a formal
system for which reality is the only interpretation. The
world is an interpretation (or model) of these sciences,
only insofar as these sciences are true.
Simulasi Komputer:
Disain Sistem
Strategi Pengelolaan Sistem
MODEL SISTEM
programming
For the scientist, a model is also a way in which the
human thought processes can be amplified.
Models that are rendered in software allow scientists to
leverage computational power to simulate, visualize,
manipulate and gain intuition about the entity,
phenomenon or process being represented.
PROGRAM
KOMPUTER
“Model dasar”: Model Matematik
SIMULASI
SISTEM:
METODOLOGI
Model lain diformulasikan menjadi
model matematik
“tahapan”:
1. Identifikasi subsistem / komponen sistem
2. Peubah input ( U(t) ) ……….. Stimulus
3. Peubah internal = peubah keadaan = peubah struktural, X(t)
4. Peubah Output, Y(t)
5. Formulasi hubungan teoritik antara U(t), X(t), dan Y(t)
6. Menjelaskan peubah eksogen
7. Interaksi antar komponen ………… DIAGRAM LINGKAR
8. Verifikasi model …….. Uji ……. Revisi
9. Aplikasi Model ……. Problem solving
A simulation is the implementation of a model over time.
A simulation brings a model to life and shows how a particular object or
phenomenon will behave. It is useful for testing, analysis or training where
real-world systems or concepts can be represented by a model
PEMODELAN
SISTEM:
RUANG LINGKUP
“Pemodelan”:
Serangkaian kegiatan pembuatan
model
MODEL: abstraksi dari suatu obyek
atau situasi aktual
MODEL KONSEP
1. Hubungan Langsung
2. Hubungan tidak langsung
3. Keterkaitan Timbal-balik /
Sebab-akibat / Fungsional
MATEMATIKA
4. Peubah - peubah
5. Parameter
Operasi Matematik:
Formula, Tanda, Aksioma
“MODEL SIMBOLIK” :
Simbol-simbol Matematik
JENIS-JENIS
MODEL
Angka
Simbol
Rumus
“Persamaan”
Ketidak-samaan
Fungsi
“MODEL IKONIK” :
“MODEL ANALOG” :
Model Fisik
1. Peta-peta geografis
2. Foto, Gambar, Lukisan
3. Prototipe
Model Diagramatik:
1. Hubungan-hubungan
2. …...
3. …..
A system is a set of interacting or interdependent entities, real or abstract, forming an
integrated whole.
The concept of an 'integrated whole' can also be stated in terms of a system embodying
a set of relationships which are differentiated from relationships of the set to other
12
elements, and from relationships between an element of the set and elements not a part
of the relational regime.
SIFAT
MODEL
PROBABILISTIK / STOKASTIK
Teknik Peluang
Memperhitungkan “uncertainty”
“DETERMINISTIK”:
Tidak memperhitungkan peluang kejadian
Systems Engineering is an interdisciplinary approach and means for enabling the
realization and deployment of successful systems. It can be viewed as the application of
engineering techniques to the engineering of systems, as well as the application of a
systems approach to engineering efforts.
Systems Engineering integrates other disciplines and specialty groups into a team effort,
forming a structured development process that proceeds from concept to production to
operation and disposal.
Systems Engineering considers both the business and the technical needs of all
customers, with the goal of providing a quality product that meets the user needs
MODEL DESKRIPTIF
FUNGSI
MODEL
Deskripsi matematik dari kondisi
dunia nyata
Scientific modelling is the process of generating abstract,
conceptual, graphical and/or mathematical models.
Science offers a growing collection of methods, techniques and
theory about all kinds of specialized scientific modelling.
Also a way to read elements easily which have been broken
down to the simplest form
“MODEL ALOKATIF” :
Komparasi alternatif untuk mendapatkan “optimal solution”
1. Seleksi Konsep
TAHAPAN
PEMODELAN
2. Konstruksi Model:
a. Black Box
b. Structural Approach
3. Implementasi Komputer
4. Validasi (keabsahan representasi)
1. Asumsi Model
2. Konsistensi Internal
3. Data Input ----- hitung parameter
4. Hubungan fungsional antar
peubah-peubah
5. Uji Model vs kondisi aktual
5. Sensitivitas
6. Stabilitas
7. Aplikasi Model
Scientific modelling is the process of generating abstract, conceptual, graphical
and/or mathematical models.
Science offers a growing collection of methods, techniques and theory about all
kinds of specialized scientific modelling.
Also a way to read elements easily which have been broken down to the
simplest form
PHASES OF SYSTEMS ANALYSIS
Recognition….
Definition and bounding of the PROBLEM
Identification of goals and objectives
Generation of solutions
MODELLING
Evaluation of potential courses of action
Implementation of results
Mengapa kita gunakan Analisis Sistem?
1. Kompleksitas obyek / fenomena /substansi penelitian
Multi-atribute
Multi fungsional
Multi dimensional Multi-variabel
2. Interaksi rumit yg melibatkan banyak hal
Korelasional
Pathways
Regresional
Struktural
3. Interaksi dinamik: Time-dependent , and
Constantly changing
4. Feed-back loops
Negative effects vs. Positive effects
Proses Abstraksi & Simplifikasi
PROSES PEMODELAN
INTRODUCTION
DEFINITION
SISTEM - MODEL - PROSES
Bounding - Word Model
Alternatives: Separate - Combination
HYPOTHESES
Relevansi : Indikator - variabel - subsistem
Proses
: Linkages - Impacts
Hubungan : Linear - Non-linear - interaksi
Decision table:
MODELLING
Data
: Plotting - outliers
Analisis : Test - Estimation
Choice :
VALIDATION
INTEGRATION
Verifikasi: Subyektif - reasonable
Uji Kritis: Eksperiment - Analisis/Simulasi
Sensitivity: Uncertainty - Resources - Interaksi
Communication
Conclusions
Proses Pemodelan
SISTEM: Approach
Simulasi Sistem
Analisis Sistem
Model vs. Pemodelan
Mathematical models: An exact science,
Its Practical Application:
1. A high degree of intuition
2. Practical experiences
3. Imagination
4. “Flair”
5. Problem define & bounding
Modelling refers to the process of generating a model as a conceptual representation of
some phenomenon.
Typically a model will refer only to some aspects of the phenomenon in question, and two models of
the same phenomenon may be essentially different, that is in which the difference is more than just a
simple renaming. This may be due to differing requirements of the model's end users or to conceptual
or aesthetic differences by the modellers and decisions made during the modelling process.
Aesthetic considerations that may influence the structure of a model might be the modeller's
preference for a reduced ontology, preferences regarding probabilistic models vis-a-vis deterministic
ones, discrete vs continuous time etc. For this reason users of a model need to understand the19
model's original purpose and the assumptions of its validity
DEFINITION & BOUNDING
IDENTIFIKASI dan PEMBATASAN Masalah penelitian
1. Alokasi sumberdaya penelitian
2. Aktivitas penelitian yang relevan
3. Kelancaran pencapaian tujuan
Proses pembatasan masalah:
1. Bersifat iteratif, tidak mungkin “sekali jadi”
2. Make a start in the right direction
3. Sustain initiative and momentum
System bounding: SPACE - TIME - SUB-SYSTEMS
Sample vs. Population
THE WHOLE SYSTEMS vs. SETS OF SUB-SYSTEMS
COMPLEXITY AND MODELS
The real system
sangat kompleks
The hypotheses
to be tested
MODEL
Sub-systems
Trade-off:
complexity vs. simplicity
Proses Pengujian Model Hipotetik
WORD MODEL
Masalah penelitian dideskripsikan secara verbal, dengan menggunakan kata (istilah) yang relevan dan simple
Simbolisasi kata-kata atau istilah
Setiap simbol (simbol matematik) harus dapat diberi deskripsi penjelasan
maknanya secara jelas
A conceptual schema or conceptual data model is a map of concepts and their
relationships.
This describes the semantics of an organization and represents a series of assertions
about its nature.
Specifically, it describes the things of significance to an organization (entity classes),
about which it is inclined to collect information, and characteristics of (attributes) and
associations between pairs of those things of significance (relationships).
Pengembangan Model simbolik
Hubungan-hubungan verbal dipresentasikan dengan simbol-simbol yang
relevan
GENERATION OF SOLUTION
Alternatif “solusi” jawaban permasalahan , berapa banyak?
Pada awalnya diidentifikasi sebanyak mungkin alternatif jawaban yang
mungkin
Penggabungan beberapa alternatif jawaban yang mungkin
digabungkan
A conceptual schema or conceptual data model is a map of concepts and their
relationships. This describes the semantics of an organization and represents a series of
assertions about its nature. Specifically, it describes the things of significance to an
organization (entity classes), about which it is inclined to collect information, and
characteristics of (attributes) and associations between pairs of those things of
significance (relationships).
A conceptual schema or conceptual data model is a map of concepts and their
relationships. This describes the semantics of an organization and represents a series of
assertions about its nature. Specifically, it describes the things of significance to an
organization (entity classes), about which it is inclined to collect information, and
characteristics of (attributes) and associations between pairs of those things of
significance (relationships).
HYPOTHESES
Tiga macam hipotesis:
1. Hypotheses of relevance: mengidentifikasi & mendefinisikan faktor, variabel, parameter, atau komponen
sistem yang relevan dg permasalahan
2. Hypotheses of processes: merangkaikan faktor-faktor atau komponen-komponen sistem yg relevan dengan
proses / perilaku sistem dan mengidentifikasi dampaknya thd sistem
3. Hypotheses of relationship: hubungan antar faktor, dan representasi hubungan tersebut dengan formulaformula matematika yg relevan, linear, non linear, interaktif.
A conceptual system is a system that is composed of non-physical objects, i.e. ideas or concepts. In
this context a system is taken to mean "an interrelated, interworking set of objects".
A conceptual system is simply a . There are no limitations on this kind of model whatsoever except
those of human imagination. If there is an experimentally verified correspondence between a
conceptual system and a physical system then that conceptual system models the physical system.
"values, ideas, and beliefs that make up every persons view of the world": that is a model of the
world; a conceptual system that is a model of a physical system (the world). The person who has
that model is a physical system.
Penjelasan / justifikasi Hipotesis
Justifikasi secara teoritis
Justifikasi berdasarkan hasil-hasil penelitian yang telah ada
KONSTRUKSI MODEL
Manipulasi matematis
Data dikumpulkan dan diperiksa dg seksama untuk menguji penyimpangannya terhadap
hipotesis.
Grafik dibuat dan digambarkan untuk menganalisis hubungan yang ada dan bagaimana
sifat / bentuk hubungan itu
Uji statistik dilakukan untuk mengetahui tingkat signifikasinya
Simulation is the imitation of some real thing, state of affairs, or process. The act
of simulating something generally entails representing certain key characteristics
or behaviours of a selected physical or abstract system.
Simulation is used in many contexts, including the modeling of natural systems
or human systems in order to gain insight into their functioning.
Other contexts include simulation of technology for performance optimization,
safety engineering, testing, training and education.
Simulation can be used to show the eventual real effects of alternative conditions
and courses of action.
Proses seleksi / uji alternatif yang ada
VERIFICATION & VALIDATION
VERIFIKASI MODEL
1. Menguji apakah “general behavior of a MODEL” mampu
mencerminkan “the real system”
2. Apakah mekanisme atau proses yang di “model” sesuai
dengan yang terjadi dalam sistem
3. Verifikasi: subjective assessment of the success of the modelling
4. Inkonsistensi antara perilaku model dengan real-system harus
dapat diberikan penjelasannya
VALIDASI MODEL
1. Sampai seberapa jauh output dari model sesuai dengan
perilaku sistem yang sesungguhnya
2. Uji prosedur pemodelan
3. Uji statistik untuk mengetahui “adequacy of the model”
4.
Proses Pemodelan
SENSITIVITY ANALYSIS
Perubahan input variabel dan perubahan parameter menghasilkan variasi kinerja
model (diukur dari solusi model) ……… analisis sensitivitas
Variabel atau parameter yang sensitif bagi hasil model harus dicermati lebih
lanjut untuk menelaah apakah proses-proses yg terjadi dalam sistem telah di
“model” dengan benar
Validasi MODEL
Model validation is possibly the most important step in the model
building sequence. It is also one of the most overlooked.
Often the validation of a model seems to consist of nothing more than
quoting the R2 statistic from the fit (which measures the fraction of the
total variability in the response that is accounted for by the model).
PLANNING & INTEGRATION
PLANNING
Integrasi berbagai macam aktivitas, formulasi masalah, hipotesis, pengumpulan
data, penyusunan alternatif rencana dan implementasi rencana. Kegagalan
integrasi ini berdampak pada hilangnya komunikasi :
1. Antara data eksperimentasi dan model development
2. Antara simulasi model dengan implementasi model
3. Antara hasil prediksi model dengan implementasi model
4. Antara management practices dengan pengembangan
hipotesis yang baru
5. Implementasi hasil uji coba dengan hipotesis yg baru
DEVELOPMENT of MODEL
1. Kualitas data dan pemahaman terhadap fenomena sebabakibat (proses yang di model) umumnya POOR
2. Analisis sistem dan pengumpulan data harus dilengkapi
dengan mekanisme umpan-balik
3. Pelatihan dalam analisis sistem sangat diperlukan
4. Model sistem hanya dapat diperbaiki dengan jalan mengatasi
kelemahannya
5. Tim analisis sistem seyogyanya interdisiplin
PEMODELAN KUANTITATIF :
MATEMATIKA DAN STATISTIKA
MODEL STATISTIKA:
FENOMENA STOKASTIK
MODEL MATEMATIKA:
FENOMENA
DETERMINISTIK
WHAT IS SYSTEM MODELLING ?
Worthwhile
Recognition
Problems
Amenable
Compromise
Complexity
Definitions
Bounding
Identification
Simplification
Objectives
Hierarchy
Goals
Priorities
Generality
Solution
Family
Generation
Modelling
Inter-relationship
Feed-back
Selection
Stopping rules
Evaluation
Sensitivity & Assumptions
Implementation
PHASES OF SYSTEM MODELLING
Recognition
Definition and bounding of the problems
Identification of goals and objectives
Generation of solution
MODELLING
Evaluation of potential courses of action
Implementation of results
Model evaluation
A crucial part of the modelling process is the evaluation of whether or not a given
mathematical model describes a system accurately. This question can be difficult to
answer as it involves several different types of evaluation.
Fit to empirical data
Usually the easiest part of model evaluation is checking whether a model fits experimental
measurements or other empirical data. In models with parameters, a common approach to test this
fit is to split the data into two disjoint subsets: training data and verification data. The training data
are used to estimate the model parameters. An accurate model will closely match the verification
data even though this data was not used to set the model's parameters. This practice is referred to
as cross-validation in statistics.
Defining a metric to measure distances between observed and predicted data is
a useful tool of assessing model fit. In statistics, decision theory, and some
economic models, a loss function plays a similar role.
While it is rather straightforward to test the appropriateness of parameters, it can be more difficult
to test the validity of the general mathematical form of a model.
In general, more mathematical tools have been developed to test the fit of statistical models than
models involving Differential equations.
Tools from nonparametric statistics can sometimes be used to evaluate how well data fits a known
distribution or to come up with a general model that makes only minimal assumptions about the
model's mathematical form.
Scope of the model
Assessing the scope of a model, that is, determining what situations the model
is applicable to, can be less straightforward. If the model was constructed based
on a set of data, one must determine for which systems or situations the known
data is a "typical" set of data.
The question of whether the model describes well the properties of the system
between data points is called interpolation, and the same question for events or
data points outside the observed data is called extrapolation.
As an example of the typical limitations of the scope of a model, in evaluating
Newtonian classical mechanics, we can note that Newton made his
measurements without advanced equipment, so he could not measure
properties of particles travelling at speeds close to the speed of light. Likewise,
he did not measure the movements of molecules and other small particles, but
macro particles only.
It is then not surprising that his model does not extrapolate well into these
domains, even though his model is quite sufficient for ordinary life physics.
Philosophical considerations
Many types of modelling implicitly involve claims about causality. This is usually
(but not always) true of models involving differential equations.
As the purpose of modelling is to increase our understanding of the world, the
validity of a model rests not only on its fit to empirical observations, but also on
its ability to extrapolate to situations or data beyond those originally described
in the model.
One can argue that a model is worthless unless it provides some insight which
goes beyond what is already known from direct investigation of the
phenomenon being studied.
An example of such criticism is the argument that the mathematical models of
Optimal foraging theory do not offer insight that goes beyond the commonsense conclusions of evolution and other basic principles of ecology.
MODEL & MATEMATIK: Term
Variabel
Tipe
Konstante
Parameter
Likelihood
Dependent
Populasi
Probability
Analitik
Independent
Maximum
Sampel
Simulasi
Regressor
Modelling and Simulation
One application of scientific modelling is the field of "Modelling and Simulation", generally referred
to as "M&S".
M&S has a spectrum of applications which range from concept development and analysis, through
experimentation, measurement and verification, to disposal analysis.
Projects and programs may use hundreds of different simulations, simulators and model analysis
tools.
JENIS VARIABEL
Intervening
(Mediating)
Moderator
Independent
Dependent
INTRANEOUS
EXTRANEOUS
Concomitant
Confounding
Control
Variabel tergantung adalah variabel yang tercakup dalam
hipotesis penelitian, keragamannya dipengaruhi oleh variabel
lain
Variabel bebas adalah variabel yang yang tercakup dalam
hipotesis penelitian dan berpengaruh atau mempengaruhi
variabel tergantung
Variabel antara (intervene variables) adalah variabel yang
bersifat menjadi perantara dari hubungan variabel bebas ke
variabel tergantung.
Variabel Moderator adalah variabel yang bersifat memperkuat
atau memperlemah pengaruh variabel bebas terhadap variabel
tergantung
Variabel pembaur (confounding variables) adalah suatu variabel yang
tercakup dalam hipotesis penelitian, akan tetapi muncul dalam penelitian
dan berpengaruh terhadap variabel tergantung dan pengaruh tersebut
mencampuri atau berbaur dengan variabel bebas
Variabel kendali (control variables) adalah variabel pembaur yang dapat dikendalikan
pada saat riset design. Pengendalian dapat dilakukan dengan cara eksklusi
(mengeluarkan obyek yang tidak memenuhi kriteria) dan inklusi (menjadikan obyek
yang memenuhi kriteria untuk diikutkan dalam sampel penelitian) atau dengan blocking,
yaitu membagi obyek penelitian menjadi kelompok-kelompok yang relatif homogen.
Variabel penyerta (concomitant variables) adalah suatu variabel pembaur (cofounding)
yang tidak dapat dikendalikan saat riset design. Variabel ini tidak dapat dikendalikan,
sehingga tetap menyertai (terikut) dalam proses penelitian, dengan konsekuensi harus
diamati dan pengaruh baurnya harus dieliminir atau dihilanggkan pada saat analisis
data.
MODEL & MATEMATIK: Definition
Preliminary
Formal
Expression
Goodall
Mathematical
Mapping
Rules
Maynard-Smith
Representational
Words
Predicted values
Homomorph
Model
Physical
Comparison
Symbolic
Mathematical
Simplified
Data values
Simulation
Model adalah rencana, representasi, atau deskripsi yang menjelaskan suatu objek,
sistem, atau konsep, yang seringkali berupa penyederhanaan atau idealisasi.
Bentuknya dapat berupa model fisik (maket, bentuk prototipe), model citra (gambar
rancangan, citra komputer), atau rumusan matematis.
MODEL & MATEMATIK: Relatives
Advantages
Disadvantages
Distortion
Precise
Opaqueness
Abstract
Transfer
Complexity
Replacement
Communication
Eykhoff (1974) defined a mathematical model as 'a representation of the essential
aspects of an existing system (or a system to be constructed) which presents knowledge
of that system in usable form'.
Mathematical models can take many forms, including but not limited to dynamical
systems, statistical models, differential equations, or game theoretic models.
These and other types of models can overlap, with a given model involving a variety of
abstract structures
MODEL & MATEMATIK: Families
Types
Dynamics
Compartment
Stochastic
Multivariate
Basis
Choices
A mathematical model uses
mathematical language to describe a
system.
Mathematical models are used not only in the
natural sciences and engineering disciplines (such
as physics, biology, earth science, meteorology,
and engineering) but also in the social sciences
(such as economics, psychology, sociology and
political science); physicists, engineers, computer
scientists, and economists use mathematical
models most extensively.
Network
The process of developing a mathematical model is
termed 'mathematical modelling' (also modeling).
BEBERAPA PENGERTIAN
MODEL DETERMINISTIK: Nilai-nilai yang diramal (diestimasi, diduga) dapat dihitung
secara eksak.
MODEL STOKASTIK: Model-model yang diramal (diestimasi, diduga) tergantung pada
distribusi peluang
POPULASI: Keseluruhan individu-individu (atau area, unit, lokasi dll.) yang diteliti untuk
mendapatkan kesimpulan.
SAMPEL: sejumlah tertentu individu yang diambil dari POPULASI dan dianggap nilainilai yang dihitung dari sampel dapat mewakili populasi secara keseluruhan
PARAMETER: Nilai-nilai karakteristik dari populasi
KONSTANTE, KOEFISIEAN: nilai-nilai karakteristik yang dihitung dari SAMPEL
VARIABEL DEPENDENT: Variabel yang diharapkan berubah nilainya disebabkan oleh
adanya perubahan nilai dari variabel lain
VARIABEL INDEPENDENT: variabel yang dapat menyebabkan terjadinya perubahan
VARIABEL DEPENDENT.
BEBERAPA PENGERTIAN
MODEL FITTING: Proses pemilihan parameter (konstante dan/atau
koefisien yang dapat menghasilkan nilai-nilai ramalan paling mendekati
nilai-nilai sesungguhnya
ANALYTICAL MODEL: Model yang formula-formulanya secara eksplisit
diturunkan untuk mendapatkan nilai-nilai ramalan, contohnya: MODEL
REGRESI
MODEL MULTIVARIATE
EXPERIMENTAL DESIGN
STANDARD DISTRIBUTION, etc
SIMULATION MODEL: Model yang formula-formulanya diturunkan dengan
serangkaian operasi arithmatik, misal:
Solusi persamaan diferensial
Aplikasi matrix
Penggunaan bilangan acak, dll.
DYNAMIC MODEL
MODELLING
SIMULATION
Dynamics
Equations
Computer
FORMAL
Language
ANALYSIS
Special
DYNAMO
CSMP
CSSL
General
BASIC
DYNAMIC MODEL
DIAGRAMS
SYMBOLS
RELATIONAL
LEVELS
AUXILIARY
VARIABLES
MATERIAL FLOW
PARAMETER
RATE EQUATIONS
SINK
INFORMATION FLOW
DYNAMIC MODEL:
ORIGINS
Abstraction
Equations
Steps
Computers
Hypothesis
Discriminant
Function
Simulation
Other
functions
Undestanding
Exponentials
Logistic
MATRIX MODEL
MATHEMATICS
Operations
Additions
Substraction
Multiplication
Inversion
Eigen value
Matrices
Dominant
Elements
Types
Eigen
vector
Square
Rectangular
Diagonal
Identity
Vectors
Row
Column
Scalars
MATRIX MODEL
DEVELOPMENT
Interactions
Groups
Stochastic
Size
Materials
cycles
Development stages
Markov
Models
The term matrix model may refer to one of several concepts:
In theoretical physics, a matrix model is a system (usually a quantum mechanical system) with
matrix-valued physical quantities. See, for example, Lax pair.
The "old" matrix models are relevant for string theory in two spacetime dimensions. The "new"
matrix model is a synonym for Matrix theory.
Matrix population models are used to model wildlife and human population dynamics.
The Matrix Model of substance abuse treatment was a model developed by the Matrix Institute in the
1980's to treat cocaine and methamphetamine addiction.
A concept from Algebraic logic.
STOCHASTIC MODEL
STOCHASTIC
Probabilities
History
Statistical
method
Other Models
Dynamics
Stability
A statistical model is a set of mathematical equations which describe the behavior of an
object of study in terms of random variables and their associated probability distributions. If the
model has only one equation it is called a single-equation model, whereas if it has more than one
equation, it is known as a multiple-equation model.
In mathematical terms, a statistical model is frequently thought of as a pair (Y,P) where Y is the set
of possible observations and P the set of possible probability distributions on Y. It is assumed that
there is a distinct element of P which generates the observed data.
Statistical inference enables us to make statements about which element(s) of this set are likely to
be the true one.
Spatial patern
STOCHASTIC MODEL
Distribution
Example
Pisson
Poisson
Binomial
Negative
Binomial
Negative
Binomial
Others
Test
Fitting
In statistics, spatial analysis or spatial statistics includes any of the formal techniques
which study entities using their topological, geometric, or geographic properties.
The phrase properly refers to a variety of techniques, many still in their early
development, using different analytic approaches and applied in fields as diverse as
astronomy, with its studies of the placement of galaxies in the cosmos, to chip
fabrication engineering, with its use of 'place and route' algorithms to build complex
wiring structures.
STOCHASTIC MODEL
ADDITIVE MODELS
Basic Model
Example
Error
Parameter
Orthogonal
Variance
Effects
Block
Experimental
Treatments
Analysis
Estimates
Significance
STOCHASTIC MODEL
REGRESSION
Model
Example
Error
Linear/ Nonlinear functions
Decomposition
Oxygen uptake
Equation
Theoritical
base
Reactions
Experimental
Empirical base
Assumptions
In statistics, regression analysis includes any techniques for modeling and analyzing
several variables, when the focus is on the relationship between a dependent variable
and one or more independent variables.
More specifically, regression analysis helps us understand how the typical value of the
dependent variable changes when any one of the independent variables is varied, while
the other independent variables are held fixed.
Most commonly, regression analysis estimates the conditional expectation of the dependent
variable given the independent variables — that is, the average value of the dependent
variable when the independent variables are held fixed.
Less commonly, the focus is on a quantile, or other location parameter of the conditional
distribution of the dependent variable given the independent variables. In all cases, the
estimation target is a function of the independent variables called the regression function.
In regression analysis, it is also of interest to characterize the variation of the dependent
variable around the regression function, which can be described by a probability distribution.
Regression analysis is widely used for prediction (including forecasting
of time-series data). Use of regression analysis for prediction has
substantial overlap with the field of machine learning.
Regression analysis is also used to understand which among the
independent variables are related to the dependent variable, and to
explore the forms of these relationships.
In restricted circumstances, regression analysis can be used to infer
causal relationships between the independent and dependent variables.
Underlying assumptions
Classical assumptions for regression analysis include:
The sample must be representative of the population for the inference prediction.
The error is assumed to be a random variable with a mean of zero conditional on the
explanatory variables.
The variables are error-free. If this is not so, modeling may be done using errors-invariables model techniques.
The predictors must be linearly independent, i.e. it must not be possible to express any
predictor as a linear combination of the others. See Multicollinearity.
The errors are uncorrelated, that is, the variance-covariance matrix of the errors is
diagonal and each non-zero element is the variance of the error.
The variance of the error is constant across observations (homoscedasticity). If not,
weighted least squares or other methods might be used.
These are sufficient (but not all necessary) conditions for the least-squares estimator to
possess desirable properties, in particular, these assumptions imply that the parameter
estimates will be unbiased, consistent, and efficient in the class of linear unbiased
estimators. Many of these assumptions may be relaxed in more advanced treatments.
STOCHASTIC MODEL
MARKOV
Analysis
Example
Assumptions
Analysis
Disadvantage
Transition probabilities
Advantages
Raised mire
What is a Markov Model?
Markov models are some of the most powerful tools available to engineers and
scientists for analyzing complex systems.
This analysis yields results for both the time dependent evolution of the system
and the steady state of the system.
MULTIVARIATE MODELS
METHODS
VARIATE
Variable
Dependent
Independent
Classification
Descriptive
Principal
Component
Analysis
Predictive
Discriminant
Analysis
Cluster
Analysis
Reciprocal
averaging
Canonical
Analysis
MULTIVARIATE MODEL
PRINCIPLE COMPONENT ANALYSIS
Requirement
Example
Correlation
Objectives
Environment
Organism
Eigenvalues
Regions
Eigenvectors
Principal Component Analysis (PCA) involves a mathematical procedure that transforms
a number of possibly correlated variables into a smaller number of uncorrelated
variables called principal components.
The first principal component accounts for as much of the variability in the data as
possible, and each succeeding component accounts for as much of the remaining
variability as possible.
MULTIVARIATE MODEL
CLUSTER ANALYSIS
Example
Spanning tree
Multivariate space
Demography
Rainfall regimes
Single linkage
Settlement patern
Similarity
Minimum
Distance
Cluster analysis or clustering is the assignment of a set of observations into subsets
(called clusters) so that observations in the same cluster are similar in some sense.
Clustering is a method of unsupervised learning, and a common technique for statistical
data analysis used in many fields, including machine learning, data mining, pattern
recognition, image analysis and bioinformatics.
Besides the term clustering, there are a number of terms with similar meanings,
including automatic classification, numerical taxonomy, botryology and typological
analysis.
CANONICAL
CORRELATION
MULTIVARIATE MODEL
Example
Correlation
Partitioned
Watershed
Urban area
Irrigation regions
Eigenvalues
Eigenvectors
Canonical correlation analysis (CCA) is a way of measuring the linear relationship
between two multidimensional variables.
It finds two bases, one for each variable, that are optimal with respect to correlations
and, at the same time, it finds the corresponding correlations. In other words, it finds the
two bases in which the correlation matrix between the variables is diagonal and the
correlations on the diagonal are maximized.
The dimensionality of these new bases is equal to or less than the smallest
dimensionality of the two variables.
MULTIVARIATE MODEL
Discriminant Function
Example
Discriminant
Villages
Calculation
Vehicles
Structures
Test
Discriminant function analysis involves the predicting of a categorical dependent
variable by one or more continuous or binary independent variables. It is statistically the
opposite of MANOVA.
It is useful in determining whether a set of variables is effective in predicting category
membership.
It is also a useful follow-up procedure to a MANOVA instead of doing a series of one-way
ANOVAs, for ascertaining how the groups differ on the composite of dependent
variables.
OPTIMIZATION MODEL
OPTIMIZATION
Dynamic
Meanings
Indirect
Simulation
Minimization
Experimentation
Non-Linear
Linear
Objective function
Constraints
Solution
Examples
Maximization
Optimum Transportation Routes
Optimum irrigation scheme
Optimum Regional Spacing
MODELLING PROCESS
System analysis
Processes
Introduction
Model
Bounding
Space
Time
Niche
Elements
Systems
Definition
Word Models
Impacts
Factorial
Confounding
Alternatives
Separate
Combinations
Hypotheses
Data
Modelling
Analysis
Choices
Validation
Plotting
Outliers
Test
Estimates
Conclusion
Integration
Communication
MODELLING PROCESSES
HYPOTHESES
Decision Table
Relevance
Variable
Species
Sub-systems
Processes
Relationships
Linkages
Linear
Non-Linear
Impacts
Interactive
A hypothesis (from Greek ὑπόθεσις; plural hypotheses) is a proposed explanation for an
observable phenomenon. The term derives from the Greek, ὑποτιθέναι – hypotithenai
meaning "to put under" or "to suppose." For a hypothesis to be put forward as a
scientific hypothesis, the scientific method requires that one can test it.
Scientists generally base scientific hypotheses on previous observations that cannot be
satisfactorily explained with the available scientific theories. Even though the words
"hypothesis" and "theory" are often used synonymously in common and informal usage,
a scientific hypothesis is not the same as a scientific theory – although the difference is
sometimes more one of degree than of principle.
HYPOTHESES
Hypotheses of Relevance: Mengidentifikasi dan
mendefinisikan variabel dan subsistem yang relevan dengan
permasalahan yang diteliti
Hypotheses of Processes: Menghubungkan subsistem
(atau variabel) di dalam permasalahan yang diteliti
dan mendefinisikan dampak (pengaruh) terhadap
sistem yang diteliti
Hypotheses of relationships: Merumuskan hubungan-hubungan
antar variabel dengan menggunakan formula-formula
matematik (fungsi linear, non-linear, interaksi, dll)
VALIDATION
Verification
MODELLING PROCESSES
Critical Test
Sensitivity
Analysis
Subjectives
Uncertainty
Analysis
Resources
Objectivities
Reasonableness
Experiments
Interactions
Model verification and validation (V&V) are
essential parts of the model development
process if models to be accepted and used to
support decision making
Model validation is possibly the most important step in the model building sequence. It is
also one of the most overlooked.
Often the validation of a model seems to consist of nothing more than quoting the R2
statistic from the fit (which measures the fraction of the total variability in the response
that is accounted for by the model).
ROLE OF THE COMPUTER
Roles
Introduction
Reasons
Speed
Data
Algoritm
Comparison
Speed
Implication
Techniques
Errors
Plotting
Waste
Repetition
Checking
9/10
Modelling
Data
Program
High level
Algoritms
Manual
Calculator
Computer
Language
Information
FORTRAN
BASIC
ALGOL
Machine code
Special
DYNAMO. Etc.
Development
Conclusions
Programming
ROLE OF THE COMPUTER
DATA
Machine readable
Cautions
Availability
Sampling
Format
Punched card
Exchange
Paper tape
Format
Reanalysis
Magnetic
Tape
Data banks
Disc
DATA
Data adalah kumpulan angka, fakta, fenomena atau keadaan atau lainnya,
merupakan hasil pengamatan, pengukuran, atau pencacahan dan sebagainya
…
terhadap variabel suatu obyek, …..
yang berfungsi dapat membedakan obyek yang satu dengan lainnya pada
variabel yang sama
Data adalah catatan atas kumpulan fakta.
Data merupakan bentuk jamak dari datum, berasal dari bahasa Latin yang berarti
"sesuatu yang diberikan". Dalam penggunaan sehari-hari data berarti suatu pernyataan
yang diterima secara apa adanya. Pernyataan ini adalah hasil pengukuran atau
pengamatan suatu variabel yang bentuknya dapat berupa angka, kata-kata, atau citra.
Dalam keilmuan (ilmiah), fakta dikumpulkan untuk menjadi data. Data kemudian diolah
sehingga dapat diutarakan secara jelas dan tepat sehingga dapat dimengerti oleh orang
lain yang tidak langsung mengalaminya sendiri, hal ini dinamakan deskripsi. Pemilahan
banyak data sesuai dengan persamaan atau perbedaan yang dikandungnya dinamakan
klasifikasi.
JENIS DATA
NOMINAL
• Komponen Nama (Nomos)
ORDINAL
• Komponen Nama
• Komponen Peringkat (Order)
INTERVAL
• Komponen Nama
• Komponen Peringkat (Order)
• Komponen Jarak (Interval)
• Nilai Nol tidak Mutlak
RATIO
• Komponen Nama
• Komponen Peringkat (Order)
• Komponen Jarak (Interval)
• Komponen Ratio
• Nilai Nol Mutlak
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ISBN 0-961-82517-0
Jamshid Gharajedaghi (2005) Systems Thinking: Managing Chaos and Complexity - A Platform for Designing Business
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70
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www//marno.lecture.ub.ac.id