SISTEM DAN PEMODELAN SISTEM oleh: smno@ub.ac.id.

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1 SISTEM DAN PEMODELAN SISTEM oleh:

2 MAKNA SUMBERDAYA ALAM “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

3 Resources use development The Comprehensive Model
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

4 FIVE GEOMETRIES IN RESOURCES USE SYSTEM
Natural resources geometry Human demand geometry NATURAL RESOURCES USE GEOMETRY Resources Degradation Geometry Natural Resources Geometry

5 SISTEM sbg suatu pendekatan 1. Filosofis 2. Prosedural 3. Alat bantu
analisis Systems thinking is the process of predicting, on the basis of anything at all, how something influences another thing. It has been defined as an approach to problem solving, by viewing "problems" as parts of an overall system, rather than reacting to present outcomes or events and potentially contributing to further development of the undesired issue or problem.

6 “Sistem”: Gugusan elemen-elemen yg saling berinteraksi dan terorganisir peri-lakunya ke arah tujuan tertentu FILOSOFI 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

7 PROSEDUR “Tahapan Pokok”: 1. Analisis Kelayakan 2. Pemodelan Abstrak
3. Disain Sistem 4. Implementasi Sistem 5. Operasi Sistem 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". Need Assesment Tahapan Pokok: - Evaluasi Outcomes

8 “digunakan dalam”: ALAT -BANTU “Model Abstrak”:
Perilaku esensialnya sama dengan dunia nyata “digunakan dalam”: 1. Perancangan / Disain Sistem 2. Menganalisis SISTEM ……………strukturnya INPUT …...…….. beragam STRUKTUR …….. fixed OUTPUT ……….. Diamati perilakunya 3. Simulasi SISTEM untuk sistem yang kompleks

9 A model is a simplified abstract view of the complex reality.
SIMULASI SISTEM: OPERASINYA “Penggunaan Komputer ”: Simulasi Komputer: Disain Sistem Strategi Pengelolaan Sistem MODEL SISTEM 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. 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. programming PROGRAM KOMPUTER

10 “Model dasar”: Model Matematik
SIMULASI SISTEM: METODOLOGI “Model dasar”: Model Matematik 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

11 MODEL KONSEP MATEMATIKA
“Pemodelan”: Serangkaian kegiatan pembuatan model MODEL: abstraksi dari suatu obyek atau situasi aktual PEMODELAN SISTEM: RUANG LINGKUP MODEL KONSEP 1. Hubungan Langsung 2. Hubungan tidak langsung 3. Keterkaitan Timbal-balik / Sebab-akibat / Fungsional 4. Peubah - peubah 5. Parameter MATEMATIKA Operasi Matematik: Formula, Tanda, Aksioma

12 JENIS-JENIS MODEL “MODEL IKONIK” : “MODEL ANALOG” : Model Fisik
“MODEL SIMBOLIK” : Simbol-simbol Matematik Angka Simbol “Persamaan” Rumus Ketidak-samaan Fungsi JENIS-JENIS MODEL “MODEL IKONIK” : Model Fisik 1. Peta-peta geografis 2. Foto, Gambar, Lukisan 3. Prototipe “MODEL ANALOG” : 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 elements, and from relationships between an element of the set and elements not a part of the relational regime.

13 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

14 FUNGSI MODEL MODEL DESKRIPTIF
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”

15 TAHAPAN PEMODELAN 1. Seleksi Konsep 2. Konstruksi Model: a. Black Box b. Structural Approach 3. Implementasi Komputer 4. Validasi (keabsahan representasi) 5. Sensitivitas 6. Stabilitas 7. Aplikasi Model 1. Asumsi Model 2. Konsistensi Internal 3. Data Input hitung parameter 4. Hubungan fungsional antar peubah-peubah 5. Uji Model vs kondisi aktual 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

16 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

17 Mengapa kita gunakan Analisis Sistem? Proses Abstraksi & Simplifikasi
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

18 Alternatives: Separate - Combination
PROSES PEMODELAN INTRODUCTION SISTEM - MODEL - PROSES Bounding - Word Model Alternatives: Separate - Combination DEFINITION Relevansi : Indikator - variabel - subsistem Proses : Linkages - Impacts Hubungan : Linear - Non-linear - interaksi Decision table: HYPOTHESES MODELLING Data : Plotting - outliers Analisis : Test - Estimation Choice : Verifikasi: Subyektif - reasonable Uji Kritis: Eksperiment - Analisis/Simulasi Sensitivity: Uncertainty - Resources - - Interaksi VALIDATION Communication Conclusions INTEGRATION

19 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 the model's original purpose and the assumptions of its validity

20 THE WHOLE SYSTEMS vs. SETS OF SUB-SYSTEMS
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

21 complexity vs. simplicity Proses Pengujian Model Hipotetik
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

22 Simbolisasi kata-kata atau istilah Pengembangan Model simbolik
WORD MODEL Masalah penelitian dideskripsikan secara verbal, dengan meng-gunakan 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

23 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).

24 HYPOTHESES Penjelasan / justifikasi Hipotesis
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 formula-formula 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

25 KONSTRUKSI MODEL Proses seleksi / uji alternatif yang ada
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

26 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

27 Validasi MODEL 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).

28 PLANNING & INTEGRATION
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 sebab- akibat (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

29 PEMODELAN KUANTITATIF : MATEMATIKA DAN STATISTIKA
MODEL STATISTIKA: FENOMENA STOKASTIK MODEL MATEMATIKA: FENOMENA DETERMINISTIK

30 WHAT IS SYSTEM MODELLING ? Sensitivity & Assumptions
Worthwhile Recognition Problems Amenable Compromise Complexity Definitions Bounding Simplification Objectives Hierarchy Identification Goals Priorities Generality Solution Family Generation Selection Modelling Inter-relationship Feed-back Stopping rules Evaluation Sensitivity & Assumptions Implementation

31 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.

32 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.

33 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.

34 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 common-sense conclusions of evolution and other basic principles of ecology.

35 MODEL & MATEMATIK: Term Modelling and Simulation
Tipe Variabel 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.

36 JENIS VARIABEL Intervening (Mediating) Moderator Control Concomitant
Independent Dependent INTRANEOUS EXTRANEOUS Confounding Control Concomitant

37 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

38 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.

39 MODEL & MATEMATIK: Definition
Preliminary Goodall Mathematical Mapping Rules Formal Expression Representational Maynard-Smith Predicted values Words Homomorph Model Comparison Physical Symbolic Mathematical Simulation Data values Simplified 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.

40 MODEL & MATEMATIK: Relatives
Advantages Disadvantages Distortion Precise Opaqueness Abstract Complexity Transfer 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

41 MODEL & MATEMATIK: Families Types
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. The process of developing a mathematical model is termed 'mathematical modelling' (also modeling). Dynamics Compartment Stochastic Multivariate Network

42 PARAMETER: Nilai-nilai karakteristik dari populasi
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 nilai-nilai 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.

43 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.

44 DYNAMIC MODEL MODELLING Equations Dynamics ANALYSIS SIMULATION
Computer FORMAL Language ANALYSIS Special General DYNAMO CSMP CSSL BASIC

45 DYNAMIC MODEL DIAGRAMS SYMBOLS SINK RELATIONAL AUXILIARY VARIABLES
LEVELS MATERIAL FLOW PARAMETER RATE EQUATIONS SINK INFORMATION FLOW

46 Discriminant Function
DYNAMIC MODEL: ORIGINS Abstraction Equations Steps Computers Hypothesis Discriminant Function Simulation Undestanding Other functions Exponentials Logistic

47 MATRIX MODEL MATHEMATICS Matrices Types Eigen value Eigen vector
Operations Matrices Elements Dominant Additions Substraction Multiplication Inversion Types Eigen vector Square Rectangular Diagonal Identity Vectors Scalars Row Column

48 MATRIX MODEL Stochastic DEVELOPMENT Interactions Groups Size
Markov Models Materials cycles Development stages 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.

49 STOCHASTIC MODEL STOCHASTIC Probabilities Statistical method
History Other Models Dynamics Statistical method 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.

50 STOCHASTIC MODEL Spatial patern Poisson Example Negative Binomial
Distribution Example Pisson Poisson Negative Binomial Binomial Negative Binomial Others Fitting Test 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.

51 STOCHASTIC MODEL Treatments ADDITIVE MODELS Analysis Variance
Basic Model Example Analysis Error Estimates Parameter Orthogonal Variance Effects Block Experimental Significance Treatments

52 Linear/ Non-linear functions
STOCHASTIC MODEL REGRESSION Model Example Equation Decomposition Error Linear/ Non-linear functions Theoritical base Oxygen uptake 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.

53 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.

54 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-in-variables 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.

55 Transition probabilities
STOCHASTIC MODEL MARKOV Analysis Example Assumptions Analysis Disadvantage Advantages Transition probabilities 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.

56 Principal Component Analysis Discriminant Analysis
MULTIVARIATE MODELS METHODS VARIATE Variable Classification Dependent Descriptive Predictive Principal Component Analysis Discriminant Analysis Independent Cluster Analysis Reciprocal averaging Canonical Analysis

57 PRINCIPLE COMPONENT ANALYSIS
MULTIVARIATE MODEL PRINCIPLE COMPONENT ANALYSIS Requirement Example Correlation Objectives Environment Organism Eigenvalues Eigenvectors Regions 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.

58 MULTIVARIATE MODEL CLUSTER ANALYSIS Multivariate space Similarity
Example Spanning tree Multivariate space Demography Rainfall regimes Similarity Minimum Single linkage Distance Settlement patern 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.

59 CANONICAL CORRELATION
MULTIVARIATE MODEL CANONICAL CORRELATION Correlation Example Partitioned Watershed Urban area Eigenvalues Eigenvectors Irrigation regions 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.

60 Discriminant Function
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.

61 OPTIMIZATION MODEL OPTIMIZATION Maximization
Dynamic Meanings Indirect Non-Linear Linear Simulation Objective function Minimization Constraints Experimentation Solution Examples Maximization Optimum Transportation Routes Optimum irrigation scheme Optimum Regional Spacing

62 MODELLING PROCESS Definition Modelling Validation Hypotheses Data
System analysis Introduction Processes Model Space Time Niche Elements Bounding Systems Definition Word Models Impacts Factorial Confounding Alternatives Separate Combinations Hypotheses Data Plotting Outliers Modelling Analysis Test Choices Estimates Validation Conclusion Integration Communication

63 MODELLING PROCESSES HYPOTHESES Decision Table Relevance Processes
Relationships Linkages Variable Linear Species Non-Linear Impacts Interactive Sub-systems 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.

64 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)

65 VALIDATION MODELLING PROCESSES
Verification Critical Test Sensitivity Analysis Subjectives Uncertainty Analysis Resources Objectivities Reason-ableness 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).

66 ROLE OF THE COMPUTER Programming Introduction Speed Algoritms Data
Roles Speed Data Algoritm Introduction Reasons Manual Calculator Computer Comparison Speed Techniques Errors Plotting Implication Repetition Checking Waste 9/10 Modelling Data FORTRAN BASIC ALGOL Program High level Algoritms Language Machine code Special DYNAMO. Etc. Information Development Conclusions Programming

67 ROLE OF THE COMPUTER DATA Machine readable Cautions Availability
Format Sampling Punched card Exchange Paper tape Format Reanalysis Magnetic Tape Data banks Disc

68 D A T A Data adalah catatan atas kumpulan fakta.
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.

69 JENIS DATA INTERVAL Komponen Nama Komponen Peringkat (Order)
Komponen Jarak (Interval) Nilai Nol tidak Mutlak NOMINAL Komponen Nama (Nomos) ORDINAL Komponen Nama Komponen Peringkat (Order) RATIO Komponen Nama Komponen Peringkat (Order) Komponen Jarak (Interval) Komponen Ratio Nilai Nol Mutlak

70 REFERENSI Russell L. Ackoff (1999) Ackoff's Best: His Classic Writings on Management. (Wiley) ISBN Russell L. Ackoff (2010) Systems Thinking for Curious Managers. (Triarchy Press). ISBN Béla H. Bánáthy (1996) Designing Social Systems in a Changing World (Contemporary Systems Thinking). (Springer) ISBN Béla H. Bánáthy (2000) Guided Evolution of Society: A Systems View (Contemporary Systems Thinking). (Springer) ISBN Ludwig von Bertalanffy ( revised) General System theory: Foundations, Development, Applications. (George Braziller) ISBN Fritjof Capra (1997) The Web of Life (HarperCollins) ISBN Peter Checkland (1981) Systems Thinking, Systems Practice. (Wiley) ISBN Peter Checkland, Jim Scholes (1990) Soft Systems Methodology in Action. (Wiley) ISBN Peter Checkland, Jim Sue Holwell (1998) Information, Systems and Information Systems. (Wiley) ISBN Peter Checkland, John Poulter (2006) Learning for Action. (Wiley) ISBN C. West Churchman ( revised) The Systems Approach. (Delacorte Press) ISBN John Gall (2003) The Systems Bible: The Beginner's Guide to Systems Large and Small. (General Systemantics Pr/Liberty) ISBN Jamshid Gharajedaghi (2005) Systems Thinking: Managing Chaos and Complexity - A Platform for Designing Business Architecture. (Butterworth-Heinemann) ISBN Charles François (ed) (1997), International Encyclopedia of Systems and Cybernetics, München: K. G. Saur. Charles L. Hutchins (1996) Systemic Thinking: Solving Complex Problems CO:PDS ISBN Bradford Keeney ( revised) Aesthetics of Change. (Guilford Press) ISBN Donella Meadows (2008) Thinking in Systems - A primer (Earthscan) ISBN John Seddon (2008) Systems Thinking in the Public Sector. (Triarchy Press). ISBN Peter M. Senge (1990) The Fifth Discipline - The Art & Practice of The Learning Organization. (Currency Doubleday) ISBN Lars Skyttner (2006) General Systems Theory: Problems, Perspective, Practice (World Scientific Publishing Company) ISBN Frederic Vester (2007) The Art of interconnected Thinking. Ideas and Tools for tackling with Complexity (MCB) ISBN Gerald M. Weinberg ( revised) An Introduction to General Systems Thinking. (Dorset House) ISBN Brian Wilson (1990) Systems: Concepts, Methodologies and Applications, 2nd ed. (Wiley) ISBN Brian Wilson (2001) Soft Systems Methodology: Conceptual Model Building and its Contribution. (Wiley) ISBN

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