Decision Analysis. Carlos A. Santos Silva June 5 th, 2009
|
|
- Antony Skinner
- 5 years ago
- Views:
Transcription
1 Decision Analysis Carlos A. Santos Silva June 5 th, 2009
2 What is decision analysis? Often, there is more than one possible solution: Decision depends on the criteria Decision often must be made in uncertain environments: Making decisions with or without experimentation Decision analysis: decision making in face of great uncertainty; rational decision when the outcomes are uncertain due to randomness in nature It is different from Game Theory, where decision is done assuming competitive environments Decision Making Without experimentation With experimentation
3 Example Company owns a tract of land that may contain oil. Contracted geologist reports that chance of oil is 1 in 4. Another oil company offers for the land. Cost of drilling is If oil is found, expected revenue is (expected profit is ). Alternative Status of land Oil Payoff Dry Drill for oil Sell the land Chance of status 1 in 4 3 in 4
4 Decision making without experimentation Decision maker needs to choose one of possible decision alternatives. There are several states of nature (due to random factors). Each combination of a decision alternative and state of nature results in a known payoff, which is one entry of a payoff table. Payoff table is used to find an optimal alternative for the decision making according to a criterion. Probabilities for states of nature provided by prior distribution are prior probabilities.
5 Maximin payoff criterion Maximin payoff criterion: For each possible decision alternative, find the minimum payoff over all states. Next, find the maximum of these minimum payoffs. Choose the alternative whose minimum payoff gives this maximum. Choose selling!!! Best guarantee of payoff: pessimistic viewpoint. Alternative State of nature Oil Dry Minimum 1. Drill for oil Sell the land Maximin value Prior probability
6 Maximum likelihood criterion Maximum likelihood criterion: Identify most likely state of nature. For this state of nature, find the decision alternative with the maximum payoff. Choose this decision alternative Choose selling!!! Most likely state: ignores important information and low-probability big payoff. Alternative State of nature Oil Dry 1. Drill for oil Sell the land Maximum in this column Prior probability Most likely
7 Bayes decision rule Bayes decision rule: Using prior probabilities, calculate the expected value of payoff for each decision alternative. Choose the decision alternative with the maximum expected payoff. For the prototype example: E[Payoff (drill)] = 0.25(700) ( 100) = 100. E[Payoff (sell)] = 0.25(90) (90) = 90. Choose drilling!!! Incorporates all available information (payoffs and prior probabilities). What if probabilities are wrong?
8 Sensitivity analysis with Bayes rules Prior probabilities can be questionable. True probabilities of having oil are 0.15 to 0.35 (so, probabilities for dry land are from 0.65 to 0.85). p = prior probability of oil. Example: expected payoff from drilling for any p: E[Payoff (drill)] = 700p 100(1 p) = 800p 100. In figure, the crossover point is where the decision changes from one alternative to another: E[Payoff (drill)] = E[Payoff (sell)] 800p 100 = 90 p =
9 Decision Making with Experimentation Improved estimates are called posterior probabilities. Example: a detailed seismic survey costs USS: unfavorable seismic soundings: oil is fairly unlikely. FSS: favorable seismic soundings: oil is fairly likely. Based on part experience, the following probabilities are given: P(USS State=Oil) = 0.4; P(FSS State=Oil) = = 0.6. P(USS State=Dry) = 0.8; P(FSS State=Dry) = = 0.2. From probability theory, the Bayes theorem can be obtained: P(State = state i Finding = finding j) = = n k= 1 P(Finding = finding j State = state i) P(State = state i) P(Finding = finding j State = state k ) P(State = state k )
10 Probability Tree Diagram
11 Optimal Policy Using Bayes decision rule, the optimal policy of optimizing payoff is given by: Finding from seismic survey Optimal alternative Expected payoff excluding cost of survey Expected payoff including cost of survey USS Sell the land FSS Drill for oil Is it worth spending 30 to conduct the experimentation?
12 Value of Experimentation Before performing an experimentation, determine its potential value. Two methods: 1. Expected value of perfect information it is assumed that all uncertainty is removed. Provides an upper bound on potential value of experiment. 2. Expected value of information is the actual improvement in expected payoff.
13 Expected value of perfect information State of nature Alternative Oil Dry 1. Drill for oil Sell the land Maximum payoff Prior probability Expected payoff with perfect information = 0.25(700) (90) = Expected value of perfect information (EVPI) is: EVPI = expected payoff with perfect information expected payoff without experimentation Example: EVPI = = As exceeds 30, the seismic survey should be done
14 Expected value of information Requires expected payoff with experimentation: Expected payoff with experimentation= Example: j P(Finding = finding j) E[payoff Finding = finding j] see probability tree diagram, where: P(USS) = 0.7, P(FSS) = 0.3. Expected payoff (excluding cost of survey) was obtained in optimal policy: E(Payoff Finding = USS) = 90, E(Payoff Finding = FSS) = 300. So, expected payoff with experimentation is Expected payoff with experimentation = 0.7(90) + 0.3(300) = 153. Expected value of experimentation (EVE) is: EVE = expected payoff with experimentation expected payoff without experimentation (EVE = = 53) As 53 exceeds 30, the seismic survey should be done
15 Decision tree with analysis (see class 7)
16 Optimal policy for prototype example The decision tree results in the following decisions: Do the seismic survey. If the result is unfavorable, sell the land. If the result is favorable, drill for oil. The expected payoff (including the cost of the seismic survey) is 123 ( ). Same result as obtained with experimentation For any decision tree, the backward induction procedure always will lead to the optimal policy
17 NOW WHAT?
18 So far we learned Operations Research arrive at optimal or near optimal solutions to complex problems using Mathematical modeling, Statistics, Algorithms Linear and Nonlinear Programming Dynamic Programming Metaheuristics Multiobjective Optimization Decision Analysis Prescribing the recommended action using Statistics, Decision Trees
19 Is this enough? Modeling optimization problems (cost functions and constraints) Sometimes it is difficult to have a mathematic description of what we want We need new tools to help us describe the reality Modeling systems Sometimes it is difficult to describe a system using mathematical expressions It is necessary to build a model only using data Soft Computing Computer techniques that tolerant of imprecision, uncertainty, partial truth, and approximation Fuzzy Systems Neural Networks
20 Soft Computing (slides from Prof. João Sousa) Carlos A. Santos Silva June 5 th, 2009
21 FUZZY SYSTEMS
22 Precision vs. Relevancy A 1500 kg mass is approaching your your head head at 45,3m/s. at 45.3 m/sec. OUT!! LOOK OUT!
23 Probability vs. Possibility Event u: Hans ate X eggs for breakfast. Probability distribution: P X (u) Possibility distribution: π X (u) u P X (u) π X (u)
24 Introduction Imprecision or vagueness in natural language does not imply a loss of accuracy or meaningfulness! Proposed in 1965 by Lotfi Zadeh Fuzzy Sets, Information Control, 8, pp How to describe very complex systems? Allow some degree of uncertainty in their description! How to deal mathematically with uncertainty? Using probabilistic theory (stochastic). Using the theory of fuzzy sets (nonstochastic). Applications Modeling, control, optimization and decision making
25 Classical set (binary logic) Example: set of old people A = {age age 70} 1 A age [years]
26 Logic propositions Nick is old... true or false? Nick s age: age Nick = 70, µ A (70) = 1 (true) age Nick = 69.9, µ A (69.9) = 0 (false) age Nick = 90, µ A (90) = 1 (true) A age [years]
27 Fuzzy set Graded membership, element belongs to a set to a certain degree. The world is not only black and white, yes or no,..the world is not binary 1 A Membership membership grade de age [years]
28 Fuzzy proposition Nick is old... degree of truth age Nick = 70, µ A (70) = 0.5 age Nick = 69.9, µ A (69.9) = 0.49 age Nick = 90, µ A (90) = 1 1 A Membership grade membership grade age [years]
29 Types of membership functions (a) Triangular MF (b) Trapezoidal MF (c) Gaussian MF (d) Generalized Bell MF
30 Linguistic values describe variables Membership membershi ip grade 1 young middle-age old young middle age old infan t age [years]
31 Fuzzy if-then rules Fuzzy propositions x is A, y is B Linguistic (Mamdani) fuzzy if-then rule If x is A then y is B (or A B) Antecedent or premise: x is A Consequent or conclusion: y is B
32 Fuzzy Inference System Data base Knowledge database Rule base If Xis then Yis input fuzzification inference defuzzification output
33 Example How white is the hair depending on the age?
34 Premises
35 Conclusions
36 Rules
37 If you are 33. You have 47,4% of white hair
38 CONTROL
39 Example: Liquid level in a tank If level is low then increase valve opening If level is OK then maintain valve opening If level is high then decrease valve opening h R João Miguel da Costa Sousa / Alexandra Moutinho 39
40 Fired fuzzy rules
41 Aggregation and defuzzifucation
42 CLUSTERING
43 Example of linguistic model Ifincomeis Lowthentaxis Low Ifincomeis Highthentaxis High
44 Fuzzy c-means example 1
45 Fuzzy c-means example MF 0.5 MF Y 0 0 X Y 0 0 X MF Y 0 0 X
46 DECISION ANALYSIS
47 Example A person is driving a car on a cold winter day down a road. Suddenly, a dog jumps in front of the car. The driver can decide between two actions: 1. he can break hard applying full power to the brakes, or 2. he can brake soft knowing that the car cannot come to a stop before a collision with the animal. What should the driver do? Θ ={slippery road, not slippery road} A={brake soft, brake hard}
48 Decision tree brake soft hit dog slightly D 1 brake hard slipandhittree D 2 roadisnotslippery brake soft hit dog slightly D 3 brake hard do not hit anything D 4 Θ states alternatives A solution set κ consequences Ξ D preference ordering
49 OPTIMIZATION
50 Fuzzy goal Goal: Product concentration should be about 80%. 1 membership gr rade 0.5 About80%
51 Fuzzy constraint Constraint: Product concentration should be not substantially higher than 75%. 1 membership grad de 0.5 Not substantially higherthan75%
52 Optimal fuzzy decision Fuzzy decision F should satisfy decision goals G as well as decision constraints membership grade x m FuzzyDecisionµ D Symmetric model Maximizing decision using min: a* = arg max µ ( a) µ ( a) a A G C
53 NEURAL NETWORKS
54 Neural networks Motivation: Humans are able to process complex tasks efficiently (perception, pattern recognition, reasoning, etc.). Ability to learn from examples. Adaptability and fault tolerance. Engineering applications: Nonlinear approximation and classification. Learning (adaptation) from data: black-box modeling. Very-Large-Scale Integration implementation.
55 Biological neuron Soma: body of the neuron. Dendrites: receptors (inputs) of the neuron. Axon: output of neuron; connected to dendrites of other neurons via synapses. Synapses: transfer of information between neurons (electrochemical signals).
56 Neural networks Biological neural networks Neuron switching time: s Number of neurons: 10 billion Connections per neuron (synapses): 10,000 Face recognition time: 0.1 s Artificial neural networks Weighted connections amongst units Highly parallel, distributed process Emphasis on tuning weights automatically Use when Biological neural network Soma Dendrite Artificial neural network Neuron Input Input and output are high-dimensional, mathematical form of system is unknown and interpretability of identified model is unimportant Applications Axon Synapse Pattern recognition, Classification, Prediction, Modeling Output Weight
57 Artificial Network x 1 4 x x x 9 Layer 1 Layer 2 Layer 3 (Input) (Hidden) (Output)
58 Artificial neuron x 1 x 2... w 2 Neuron y x n w n x i : i-th input of the neuron w i : synaptic strengh (weight) for x i y = σ (Σw i x i ): output signal
59 Types of neurons McCulloch and Pits (1943) Threshold θ: n y= sign wixi θ i= 1 Other types of activation functions (net= Σw i x i ) , if 0 step net y = 0, if net< 0 y linear = y + sigmoid 1 net 1 e = net
60 FORECAST
61 Example
DECISION ANALYSIS. Decision often must be made in uncertain environments. Examples:
DECISION ANALYSIS Introduction Decision often must be made in uncertain environments. Examples: Manufacturer introducing a new product in the marketplace. Government contractor bidding on a new contract.
More informationDECISION ANALYSIS. (Hillier & Lieberman Introduction to Operations Research, 8 th edition)
DECISION ANALYSIS (Hillier & Lieberman Introduction to Operations Research, 8 th edition) Introduction Decision often must be made in uncertain environments Examples: Manufacturer introducing a new product
More informationTIm 206 Lecture notes Decision Analysis
TIm 206 Lecture notes Decision Analysis Instructor: Kevin Ross 2005 Scribes: Geoff Ryder, Chris George, Lewis N 2010 Scribe: Aaron Michelony 1 Decision Analysis: A Framework for Rational Decision- Making
More informationUnderstanding neural networks
Machine Learning Neural Networks Understanding neural networks An Artificial Neural Network (ANN) models the relationship between a set of input signals and an output signal using a model derived from
More informationChapter 13 Decision Analysis
Problem Formulation Chapter 13 Decision Analysis Decision Making without Probabilities Decision Making with Probabilities Risk Analysis and Sensitivity Analysis Decision Analysis with Sample Information
More informationDecision Making Models
Decision Making Models Prof. Yongwon Seo (seoyw@cau.ac.kr) College of Business Administration, CAU Decision Theory Decision theory problems are characterized by the following: A list of alternatives. A
More informationForecasting stock market return using ANFIS: the case of Tehran Stock Exchange
Available online at http://www.ijashss.com International Journal of Advanced Studies in Humanities and Social Science Volume 1, Issue 5, 2013: 452-459 Forecasting stock market return using ANFIS: the case
More informationAlternate Models for Forecasting Hedge Fund Returns
University of Rhode Island DigitalCommons@URI Senior Honors Projects Honors Program at the University of Rhode Island 2011 Alternate Models for Forecasting Hedge Fund Returns Michael A. Holden Michael
More informationCost Overrun Assessment Model in Fuzzy Environment
American Journal of Engineering Research (AJER) e-issn : 2320-0847 p-issn : 2320-0936 Volume-03, Issue-07, pp-44-53 www.ajer.org Research Paper Open Access Cost Overrun Assessment Model in Fuzzy Environment
More informationA Taxonomy of Decision Models
Decision Trees and Influence Diagrams Prof. Carlos Bana e Costa Lecture topics: Decision trees and influence diagrams Value of information and control A case study: Drilling for oil References: Clemen,
More informationStock Trading Following Stock Price Index Movement Classification Using Machine Learning Techniques
Stock Trading Following Stock Price Index Movement Classification Using Machine Learning Techniques 6.1 Introduction Trading in stock market is one of the most popular channels of financial investments.
More informationSubject : Computer Science. Paper: Machine Learning. Module: Decision Theory and Bayesian Decision Theory. Module No: CS/ML/10.
e-pg Pathshala Subject : Computer Science Paper: Machine Learning Module: Decision Theory and Bayesian Decision Theory Module No: CS/ML/0 Quadrant I e-text Welcome to the e-pg Pathshala Lecture Series
More informationCauses of Poor Decisions
Lecture 7: Decision Analysis Decision process Decision tree analysis The Decision Process Specify objectives and the criteria for making a choice Develop alternatives Analyze and compare alternatives Select
More informationModule 15 July 28, 2014
Module 15 July 28, 2014 General Approach to Decision Making Many Uses: Capacity Planning Product/Service Design Equipment Selection Location Planning Others Typically Used for Decisions Characterized by
More informationDecision Analysis under Uncertainty. Christopher Grigoriou Executive MBA/HEC Lausanne
Decision Analysis under Uncertainty Christopher Grigoriou Executive MBA/HEC Lausanne 2007-2008 2008 Introduction Examples of decision making under uncertainty in the business world; => Trade-off between
More informationSCHOOL OF BUSINESS, ECONOMICS AND MANAGEMENT. BF360 Operations Research
SCHOOL OF BUSINESS, ECONOMICS AND MANAGEMENT BF360 Operations Research Unit 5 Moses Mwale e-mail: moses.mwale@ictar.ac.zm BF360 Operations Research Contents Unit 5: Decision Analysis 3 5.1 Components
More informationAgenda. Lecture 2. Decision Analysis. Key Characteristics. Terminology. Structuring Decision Problems
Agenda Lecture 2 Theory >Introduction to Making > Making Without Probabilities > Making With Probabilities >Expected Value of Perfect Information >Next Class 1 2 Analysis >Techniques used to make decisions
More informationUNIT 5 DECISION MAKING
UNIT 5 DECISION MAKING This unit: UNDER UNCERTAINTY Discusses the techniques to deal with uncertainties 1 INTRODUCTION Few decisions in construction industry are made with certainty. Need to look at: The
More informationChapter 7: Estimation Sections
1 / 40 Chapter 7: Estimation Sections 7.1 Statistical Inference Bayesian Methods: Chapter 7 7.2 Prior and Posterior Distributions 7.3 Conjugate Prior Distributions 7.4 Bayes Estimators Frequentist Methods:
More informationChapter 3. Decision Analysis. Learning Objectives
Chapter 3 Decision Analysis To accompany Quantitative Analysis for Management, Eleventh Edition, by Render, Stair, and Hanna Power Point slides created by Brian Peterson Learning Objectives After completing
More informationRole of soft computing techniques in predicting stock market direction
REVIEWS Role of soft computing techniques in predicting stock market direction Panchal Amitkumar Mansukhbhai 1, Dr. Jayeshkumar Madhubhai Patel 2 1. Ph.D Research Scholar, Gujarat Technological University,
More informationThe Course So Far. Atomic agent: uninformed, informed, local Specific KR languages
The Course So Far Traditional AI: Deterministic single agent domains Atomic agent: uninformed, informed, local Specific KR languages Constraint Satisfaction Logic and Satisfiability STRIPS for Classical
More informationDecision Making. DKSharma
Decision Making DKSharma Decision making Learning Objectives: To make the students understand the concepts of Decision making Decision making environment; Decision making under certainty; Decision making
More informationA B C D E F 1 PAYOFF TABLE 2. States of Nature
Chapter Decision Analysis Problem Formulation Decision Making without Probabilities Decision Making with Probabilities Risk Analysis and Sensitivity Analysis Decision Analysis with Sample Information Computing
More informationPrediction of Stock Closing Price by Hybrid Deep Neural Network
Available online www.ejaet.com European Journal of Advances in Engineering and Technology, 2018, 5(4): 282-287 Research Article ISSN: 2394-658X Prediction of Stock Closing Price by Hybrid Deep Neural Network
More informationPrediction of Fine in Accidents using Fuzzy Rule Based Model
Prediction of Fine in Accidents using Fuzzy Rule Based Model Jaya Pal 1, Vandana Bhattacherjee 2 1,2 Department of Computer Science & Engg., Birla Institute of Technology, Ranchi, India 1 jayapal@bitmesra.ac.in
More informationPredicting Economic Recession using Data Mining Techniques
Predicting Economic Recession using Data Mining Techniques Authors Naveed Ahmed Kartheek Atluri Tapan Patwardhan Meghana Viswanath Predicting Economic Recession using Data Mining Techniques Page 1 Abstract
More informationJohan Oscar Ong, ST, MT
Decision Analysis Johan Oscar Ong, ST, MT Analytical Decision Making Can Help Managers to: Gain deeper insight into the nature of business relationships Find better ways to assess values in such relationships;
More informationFull file at CHAPTER 3 Decision Analysis
CHAPTER 3 Decision Analysis TRUE/FALSE 3.1 Expected Monetary Value (EMV) is the average or expected monetary outcome of a decision if it can be repeated a large number of times. 3.2 Expected Monetary Value
More informationNeuro Fuzzy based Stock Market Prediction System
Neuro Fuzzy based Stock Market Prediction System M. Gunasekaran, S. Anitha, S. Kavipriya, Asst Professor, Dept of MCA, III MCA, Dept Of MCA, III MCA, Dept of MCA, Park College of Engg& tech, Park College
More informationDecision Analysis CHAPTER LEARNING OBJECTIVES CHAPTER OUTLINE. After completing this chapter, students will be able to:
CHAPTER 3 Decision Analysis LEARNING OBJECTIVES After completing this chapter, students will be able to: 1. List the steps of the decision-making process. 2. Describe the types of decision-making environments.
More informationA Hybrid Expert System for IT Security Risk Assessment
A Hybrid Expert System for IT Security Risk Assessment Andrew L.S. Gordon, Ivan Belik, Shahram Rahimi 1, Department of Computer Science, Mailcode 4511 Southern Illinois University, Carbondale, IL, USA
More informationChapter 7: Estimation Sections
1 / 31 : Estimation Sections 7.1 Statistical Inference Bayesian Methods: 7.2 Prior and Posterior Distributions 7.3 Conjugate Prior Distributions 7.4 Bayes Estimators Frequentist Methods: 7.5 Maximum Likelihood
More informationDecision Analysis Models
Decision Analysis Models 1 Outline Decision Analysis Models Decision Making Under Ignorance and Risk Expected Value of Perfect Information Decision Trees Incorporating New Information Expected Value of
More information2017 Predictive Analytics Symposium
2017 Predictive Analytics Symposium Session 31, Beyond Crisp Logic--Welcome to the Fuzzy Real World! Presenter: Geoffrey R. Hileman, FSA, MAAA SOA Antitrust Compliance Guidelines SOA Presentation Disclaimer
More informationThe Fuzzy-Bayes Decision Rule
Academic Web Journal of Business Management Volume 1 issue 1 pp 001-006 December, 2016 2016 Accepted 18 th November, 2016 Research paper The Fuzzy-Bayes Decision Rule Houju Hori Jr. and Yukio Matsumoto
More informationA_A0008: FUZZY MODELLING APPROACH FOR PREDICTING GOLD PRICE BASED ON RATE OF RETURN
Section A - Mathematics / Statistics / Computer Science 13 A_A0008: FUZZY MODELLING APPROACH FOR PREDICTING GOLD PRICE BASED ON RATE OF RETURN Piyathida Towwun,* Watcharin Klongdee Risk and Insurance Research
More information56:171 Operations Research Midterm Examination Solutions PART ONE
56:171 Operations Research Midterm Examination Solutions Fall 1997 Write your name on the first page, and initial the other pages. Answer both questions of Part One, and 4 (out of 5) problems from Part
More informationOptimal Investment for Worst-Case Crash Scenarios
Optimal Investment for Worst-Case Crash Scenarios A Martingale Approach Frank Thomas Seifried Department of Mathematics, University of Kaiserslautern June 23, 2010 (Bachelier 2010) Worst-Case Portfolio
More informationDecision Theory Using Probabilities, MV, EMV, EVPI and Other Techniques
1 Decision Theory Using Probabilities, MV, EMV, EVPI and Other Techniques Thompson Lumber is looking at marketing a new product storage sheds. Mr. Thompson has identified three decision options (alternatives)
More informationInformation aggregation for timing decision making.
MPRA Munich Personal RePEc Archive Information aggregation for timing decision making. Esteban Colla De-Robertis Universidad Panamericana - Campus México, Escuela de Ciencias Económicas y Empresariales
More information56:171 Operations Research Midterm Examination October 28, 1997 PART ONE
56:171 Operations Research Midterm Examination October 28, 1997 Write your name on the first page, and initial the other pages. Answer both questions of Part One, and 4 (out of 5) problems from Part Two.
More informationLog-Robust Portfolio Management
Log-Robust Portfolio Management Dr. Aurélie Thiele Lehigh University Joint work with Elcin Cetinkaya and Ban Kawas Research partially supported by the National Science Foundation Grant CMMI-0757983 Dr.
More informationThe Course So Far. Decision Making in Deterministic Domains. Decision Making in Uncertain Domains. Next: Decision Making in Uncertain Domains
The Course So Far Decision Making in Deterministic Domains search planning Decision Making in Uncertain Domains Uncertainty: adversarial Minimax Next: Decision Making in Uncertain Domains Uncertainty:
More informationD I S C O N T I N U O U S DEMAND FUNCTIONS: ESTIMATION AND PRICING. Rotterdam May 24, 2018
D I S C O N T I N U O U S DEMAND FUNCTIONS: ESTIMATION AND PRICING Arnoud V. den Boer University of Amsterdam N. Bora Keskin Duke University Rotterdam May 24, 2018 Dynamic pricing and learning: Learning
More informationOptimizing the Hurwicz criterion in decision trees with imprecise probabilities
Optimizing the Hurwicz criterion in decision trees with imprecise probabilities Gildas Jeantet and Olivier Spanjaard LIP6 - UPMC 104 avenue du Président Kennedy 75016 Paris, France {gildas.jeantet,olivier.spanjaard}@lip6.fr
More informationStochastic Approximation Algorithms and Applications
Harold J. Kushner G. George Yin Stochastic Approximation Algorithms and Applications With 24 Figures Springer Contents Preface and Introduction xiii 1 Introduction: Applications and Issues 1 1.0 Outline
More informationProbabilistic Meshless Methods for Bayesian Inverse Problems. Jon Cockayne July 8, 2016
Probabilistic Meshless Methods for Bayesian Inverse Problems Jon Cockayne July 8, 2016 1 Co-Authors Chris Oates Tim Sullivan Mark Girolami 2 What is PN? Many problems in mathematics have no analytical
More informationPattern Recognition by Neural Network Ensemble
IT691 2009 1 Pattern Recognition by Neural Network Ensemble Joseph Cestra, Babu Johnson, Nikolaos Kartalis, Rasul Mehrab, Robb Zucker Pace University Abstract This is an investigation of artificial neural
More informationInterval estimation. September 29, Outline Basic ideas Sampling variation and CLT Interval estimation using X More general problems
Interval estimation September 29, 2017 STAT 151 Class 7 Slide 1 Outline of Topics 1 Basic ideas 2 Sampling variation and CLT 3 Interval estimation using X 4 More general problems STAT 151 Class 7 Slide
More informationInternational Journal of Advance Engineering and Research Development. Stock Market Prediction Using Neural Networks
Scientific Journal of Impact Factor (SJIF): 3.134 International Journal of Advance Engineering and Research Development Volume 2, Issue 12, December -2015 Stock Market Prediction Using Neural Networks
More informationInvesting through Economic Cycles with Ensemble Machine Learning Algorithms
Investing through Economic Cycles with Ensemble Machine Learning Algorithms Thomas Raffinot Silex Investment Partners Big Data in Finance Conference Thomas Raffinot (Silex-IP) Economic Cycles-Machine Learning
More informationLecture 7: Bayesian approach to MAB - Gittins index
Advanced Topics in Machine Learning and Algorithmic Game Theory Lecture 7: Bayesian approach to MAB - Gittins index Lecturer: Yishay Mansour Scribe: Mariano Schain 7.1 Introduction In the Bayesian approach
More informationLecture 12: Introduction to reasoning under uncertainty. Actions and Consequences
Lecture 12: Introduction to reasoning under uncertainty Preferences Utility functions Maximizing expected utility Value of information Bandit problems and the exploration-exploitation trade-off COMP-424,
More informationPhD Qualifier Examination
PhD Qualifier Examination Department of Agricultural Economics May 29, 2015 Instructions This exam consists of six questions. You must answer all questions. If you need an assumption to complete a question,
More informationStock Market Prediction Based on Fundamentalist Analysis with Fuzzy- Neural Networks
Stock Market Prediction Based on Fundamentalist Analysis with Fuzzy- Neural Networks RENATO DE C. T. RAPOSO 1 AND ADRIANO J. DE O. CRUZ 2 Nú cleo de Computação Eletrô nica, Instituto de Matemá tica, Federal
More informationChapter 18 Student Lecture Notes 18-1
Chapter 18 Student Lecture Notes 18-1 Business Statistics: A Decision-Making Approach 6 th Edition Chapter 18 Introduction to Decision Analysis 5 Prentice-Hall, Inc. Chap 18-1 Chapter Goals After completing
More informationEvaluating Strategic Forecasters. Rahul Deb with Mallesh Pai (Rice) and Maher Said (NYU Stern) Becker Friedman Theory Conference III July 22, 2017
Evaluating Strategic Forecasters Rahul Deb with Mallesh Pai (Rice) and Maher Said (NYU Stern) Becker Friedman Theory Conference III July 22, 2017 Motivation Forecasters are sought after in a variety of
More informationSTANDARDISATION OF RISK ASSESSMENT PROCESS BY MODIFYING THE RISK MATRIX
STANDARDISATION OF RISK ASSESSMENT PROCESS BY MODIFYING THE RISK MATRIX C. S.SatishKumar 1, Dr S. Shrihari 2 1,2 Department of Civil Engineering National institute of technology Karnataka (India) ABSTRACT
More information56:171 Operations Research Midterm Examination Solutions PART ONE
56:171 Operations Research Midterm Examination Solutions Fall 1997 Answer both questions of Part One, and 4 (out of 5) problems from Part Two. Possible Part One: 1. True/False 15 2. Sensitivity analysis
More informationFuzzy logic application in the evaluation of the Solvency Capital Requirement (SCR) in life insurance
Fuzzy logic application in the evaluation of the Solvency Capital Requirement (SCR) in life insurance Abder OULIDI 1-2 Frédéric ALEXIS 3 Frédéric HENGE 4 Gildas ROBERT 4 1 Institut de Mathématiques Appliquées
More informationLecture 17: More on Markov Decision Processes. Reinforcement learning
Lecture 17: More on Markov Decision Processes. Reinforcement learning Learning a model: maximum likelihood Learning a value function directly Monte Carlo Temporal-difference (TD) learning COMP-424, Lecture
More informationPERT 12 Quantitative Tools (1)
PERT 12 Quantitative Tools (1) Proses keputusan dalam operasi Fundamental Decisin Making, Tabel keputusan. Konsep Linear Programming Problem Formulasi Linear Programming Problem Penyelesaian Metode Grafis
More informationManagerial Economics Uncertainty
Managerial Economics Uncertainty Aalto University School of Science Department of Industrial Engineering and Management January 10 26, 2017 Dr. Arto Kovanen, Ph.D. Visiting Lecturer Uncertainty general
More informationNonlinear Manifold Learning for Financial Markets Integration
Nonlinear Manifold Learning for Financial Markets Integration George Tzagkarakis 1 & Thomas Dionysopoulos 1,2 1 EONOS Investment Technologies, Paris (FR) 2 Dalton Strategic Partnership, London (UK) Nice,
More informationFuzzy Inference Modeling Methodology for the Simulation of Population Growth
The International Arab Journal of Information Technology, Vol. 2, No. 1, January 2005 75 Fuzzy Inference Modeling Methodology for the Simulation of Population Growth Hassan Diab and Jean Saade Department
More informationDecision Making. D.K.Sharma
Decision Making D.K.Sharma 1 Decision making Learning Objectives: To make the students understand the concepts of Decision making Decision making environment; Decision making under certainty; Decision
More informationDecision Making. BUS 735: Business Decision Making and Research. Learn how to conduct regression analysis with a dummy independent variable.
Making BUS 735: Business Making and Research 1 Goals of this section Specific goals: Learn how to conduct regression analysis with a dummy independent variable. Learning objectives: LO5: Be able to use
More informationSequential Decision Making
Sequential Decision Making Dynamic programming Christos Dimitrakakis Intelligent Autonomous Systems, IvI, University of Amsterdam, The Netherlands March 18, 2008 Introduction Some examples Dynamic programming
More informationTop-down particle filtering for Bayesian decision trees
Top-down particle filtering for Bayesian decision trees Balaji Lakshminarayanan 1, Daniel M. Roy 2 and Yee Whye Teh 3 1. Gatsby Unit, UCL, 2. University of Cambridge and 3. University of Oxford Outline
More informationFinal Examination CS540: Introduction to Artificial Intelligence
Final Examination CS540: Introduction to Artificial Intelligence December 2008 LAST NAME: FIRST NAME: Problem Score Max Score 1 15 2 15 3 10 4 20 5 10 6 20 7 10 Total 100 Question 1. [15] Probabilistic
More informationFeedback Effect and Capital Structure
Feedback Effect and Capital Structure Minh Vo Metropolitan State University Abstract This paper develops a model of financing with informational feedback effect that jointly determines a firm s capital
More informationIran s Stock Market Prediction By Neural Networks and GA
Iran s Stock Market Prediction By Neural Networks and GA Mahmood Khatibi MS. in Control Engineering mahmood.khatibi@gmail.com Habib Rajabi Mashhadi Associate Professor h_mashhadi@ferdowsi.um.ac.ir Electrical
More informationIntroduction LEARNING OBJECTIVES. The Six Steps in Decision Making. Thompson Lumber Company. Thompson Lumber Company
Valua%on and pricing (November 5, 2013) Lecture 4 Decision making (part 1) Olivier J. de Jong, LL.M., MM., MBA, CFD, CFFA, AA www.olivierdejong.com LEARNING OBJECTIVES 1. List the steps of the decision-making
More informationDetermination of Insurance Policy Using a hybrid model of AHP, Fuzzy Logic, and Delphi Technique: A Case Study
Determination of Insurance Policy Using a hybrid model of AHP, Fuzzy Logic, and Delphi Technique: A Case Study CHIN-SHENG HUANG, YU-JU LIN 2, CHE-CHERN LIN 3 : Department and Graduate Institute of Finance,
More informationCA200 Quantitative Analysis for Business Decisions. File name: CA200_Section_03B_DecisionTheory
CA200 Quantitative Analysis for Business Decisions File name: CA200_Section_03B_DecisionTheory Table of Contents 3. Decision theory... 3 3.1 Elements of a decision problem (See 3A )... 3 3.2 Decision making
More informationFinding Equilibria in Games of No Chance
Finding Equilibria in Games of No Chance Kristoffer Arnsfelt Hansen, Peter Bro Miltersen, and Troels Bjerre Sørensen Department of Computer Science, University of Aarhus, Denmark {arnsfelt,bromille,trold}@daimi.au.dk
More informationLending Club Loan Portfolio Optimization Fred Robson (frobson), Chris Lucas (cflucas)
CS22 Artificial Intelligence Stanford University Autumn 26-27 Lending Club Loan Portfolio Optimization Fred Robson (frobson), Chris Lucas (cflucas) Overview Lending Club is an online peer-to-peer lending
More informationCSC 411: Lecture 08: Generative Models for Classification
CSC 411: Lecture 08: Generative Models for Classification Richard Zemel, Raquel Urtasun and Sanja Fidler University of Toronto Zemel, Urtasun, Fidler (UofT) CSC 411: 08-Generative Models 1 / 23 Today Classification
More informationDecision making under uncertainty
Decision making under uncertainty 1 Outline 1. Components of decision making 2. Criteria for decision making 3. Utility theory 4. Decision trees 5. Posterior probabilities using Bayes rule 6. The Monty
More informationChapter 2 Uncertainty Analysis and Sampling Techniques
Chapter 2 Uncertainty Analysis and Sampling Techniques The probabilistic or stochastic modeling (Fig. 2.) iterative loop in the stochastic optimization procedure (Fig..4 in Chap. ) involves:. Specifying
More informationBudget Management In GSP (2018)
Budget Management In GSP (2018) Yahoo! March 18, 2018 Miguel March 18, 2018 1 / 26 Today s Presentation: Budget Management Strategies in Repeated auctions, Balseiro, Kim, and Mahdian, WWW2017 Learning
More informationComparative Study between Linear and Graphical Methods in Solving Optimization Problems
Comparative Study between Linear and Graphical Methods in Solving Optimization Problems Mona M Abd El-Kareem Abstract The main target of this paper is to establish a comparative study between the performance
More informationBusiness Strategies in Credit Rating and the Control of Misclassification Costs in Neural Network Predictions
Association for Information Systems AIS Electronic Library (AISeL) AMCIS 2001 Proceedings Americas Conference on Information Systems (AMCIS) December 2001 Business Strategies in Credit Rating and the Control
More informationMonitoring - revisited
Monitoring - revisited Anders Ringgaard Kristensen Slide 1 Outline Filtering techniques applied to monitoring of daily gain in slaughter pigs: Introduction Basic monitoring Shewart control charts DLM and
More informationResearch Article Portfolio Optimization of Equity Mutual Funds Malaysian Case Study
Fuzzy Systems Volume 2010, Article ID 879453, 7 pages doi:10.1155/2010/879453 Research Article Portfolio Optimization of Equity Mutual Funds Malaysian Case Study Adem Kılıçman 1 and Jaisree Sivalingam
More informationInternational Journal of Computer Engineering and Applications, Volume XII, Issue II, Feb. 18, ISSN
International Journal of Computer Engineering and Applications, Volume XII, Issue II, Feb. 18, www.ijcea.com ISSN 31-3469 AN INVESTIGATION OF FINANCIAL TIME SERIES PREDICTION USING BACK PROPAGATION NEURAL
More informationProject Management Certificate Program
Project Management Certificate Program Risk Management Terry Skaggs ( Denver class) skaggst@centurytel.net 719-783-0880 Lee Varra-Nelson (Fort Collins class) lvarranelson@q.com 970-407-9744 or 970-215-4949
More informationBSc (Hons) Software Engineering BSc (Hons) Computer Science with Network Security
BSc (Hons) Software Engineering BSc (Hons) Computer Science with Network Security Cohorts BCNS/ 06 / Full Time & BSE/ 06 / Full Time Resit Examinations for 2008-2009 / Semester 1 Examinations for 2008-2009
More informationMS-E2114 Investment Science Lecture 4: Applied interest rate analysis
MS-E2114 Investment Science Lecture 4: Applied interest rate analysis A. Salo, T. Seeve Systems Analysis Laboratory Department of System Analysis and Mathematics Aalto University, School of Science Overview
More informationMarkov Decision Processes
Markov Decision Processes Robert Platt Northeastern University Some images and slides are used from: 1. CS188 UC Berkeley 2. AIMA 3. Chris Amato Stochastic domains So far, we have studied search Can use
More informationEconomics 101A (Lecture 25) Stefano DellaVigna
Economics 101A (Lecture 25) Stefano DellaVigna April 29, 2014 Outline 1. Hidden Action (Moral Hazard) II 2. The Takeover Game 3. Hidden Type (Adverse Selection) 4. Evidence of Hidden Type and Hidden Action
More informationDecision Analysis. Chapter Topics
Decision Analysis Chapter Topics Components of Decision Making Decision Making without Probabilities Decision Making with Probabilities Decision Analysis with Additional Information Utility Decision Analysis
More informationAn Improved Approach for Business & Market Intelligence using Artificial Neural Network
Available Online at www.ijcsmc.com International Journal of Computer Science and Mobile Computing A Monthly Journal of Computer Science and Information Technology ISSN 2320 088X IMPACT FACTOR: 5.258 IJCSMC,
More informationNumerical Methods for Pricing Energy Derivatives, including Swing Options, in the Presence of Jumps
Numerical Methods for Pricing Energy Derivatives, including Swing Options, in the Presence of Jumps, Senior Quantitative Analyst Motivation: Swing Options An electricity or gas SUPPLIER needs to be capable,
More information1. A is a decision support tool that uses a tree-like graph or model of decisions and their possible consequences, including chance event outcomes,
1. A is a decision support tool that uses a tree-like graph or model of decisions and their possible consequences, including chance event outcomes, resource costs, and utility. A) Decision tree B) Graphs
More informationApplication of Triangular Fuzzy AHP Approach for Flood Risk Evaluation. MSV PRASAD GITAM University India. Introduction
Application of Triangular Fuzzy AHP Approach for Flood Risk Evaluation MSV PRASAD GITAM University India Introduction Rationale & significance : The objective of this paper is to develop a hierarchical
More informationComputational Finance. Computational Finance p. 1
Computational Finance Computational Finance p. 1 Outline Binomial model: option pricing and optimal investment Monte Carlo techniques for pricing of options pricing of non-standard options improving accuracy
More informationEngineering Risk Benefit Analysis
Engineering Risk Benefit Analysis 1.155, 2.943, 3.577, 6.938, 10.816, 13.621, 16.862, 22.82, ES.72, ES.721 A 1. The Multistage ecision Model George E. Apostolakis Massachusetts Institute of Technology
More informationCredit risk early warning system using fuzzy expert systems
Central European Conference on Information and Intelligent Systems, 2014 Credit risk early warning system using fuzzy expert systems Igor Kaluđer" Goran Klepac, PhD Context Recent financial crisis revealed
More information