...Decision: To purchase or not purchase rental car insurance In December of 2011, I will be traveling to Salem, Oregon to celebrate Christmas with my family. I have decided to stay for Christmas in Salem, Oregon for a week. The total trip is exactly a 1000 mile down the Interstate 5 highway each way from Oceanside, California to Salem, Oregon, and vice versa with a total of 2000 miles round trip. However, the expenses identified with air travel versus driving, I made my final decision to drive to Salem, Oregon, in a rental vehicle and not my car. Enterprise Rental is the one company that I choose that has a good rental plan at $9.99 a day for a weekend rate of three days. Because I am an excellent client with the company. Enterprise Rental has extended the weekend rate of three days to four days as an award of my loyalty as a client to the company for many years. Any extra days after the four days, the company will charge the $15.99 per day of the standard rate. This eliminates the taxes and insurance included with the daily rate. Taxes are naturally $3.00 dollars per day and will eliminate for this purpose of my decision. However, the insurance has no deductible per occurrence at $12.99 per day, which is included in this decision (Mankiw, G., 2003). My privately owned vehicle has an insurance policy that covers both comprehensive and collision claims and brings in a $500.00 deductible per occurrence. To make a final decision in purchasing the rental companies insurance...
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...Reasoning Under Uncertainty Most tasks requiring intelligent behavior have some degree of uncertainty associated with them. The type of uncertainty that can occur in knowledge-based systems may be caused by problems with the data. For example: 1. Data might be missing or unavailable 1. Data might be present but unreliable or ambiguous due to measurement errors. 1. The representation of the data may be imprecise or inconsistent. 1. Data may just be user’s best guess. 1. Data may be based on defaults and the defaults may have exceptions. The uncertainty may also be caused by the represented knowledge since it might 1. Represent best guesses of the experts that are based on plausible or statistical associations they have observed. 1. Not be appropriate in all situations (e.g., may have indeterminate applicability) Given these numerous sources of errors, most knowledge-based systems require the incorporation of some form of uncertainty management. When implementing some uncertainty scheme we must be concerned with three issues: 1. How to represent uncertain data 2. How to combine two or more pieces of uncertain data 3. How to draw inference using uncertain data We will introduce three ways of handling uncertainty: Probabilistic reasoning. Certainty factors Dempster-Shafer Theory 1. Classical Probability The oldest and best defined...
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...IJCSI International Journal of Computer Science Issues, Vol. 8, Issue 4, No 1, July 2011 ISSN (Online): 1694-0814 www.IJCSI.org 374 Dynamic User Interface Based on Cognitive Approach in Web Based Learning L.Jayasimman1, A.Nisha Jebaseeli 2, Dr.E.George Dharma Prakashraj 3 and J.Charles 4 1 Computer Application, Anna University, J J College of Eng. And Tech. Trichy, Tamilnadu, India 2 Computer Science, Bharathidasan University, BDU Constituent College Trichy, Tamilnadu, India 3 Computer Science and Engineering, Bharathidasan University Trichy, Tamilnadu, India 4 Computer Science, Bharathidasan University, Arignar Anna Govt. College Trichy, Tamilnadu, India With bandwidth increasing at a constant pace, technology in education has become an important part for delivery of educational content to students. Online learning in various forms is gaining popularity but lacks the adaptability required to hold the learners attention due to its rigid structure. Though animation and powerful graphics enhance the learning content, delivery of content according to learners need is yet to become a reality. It is not possible to build a l earning system that can satisfy every learner as some people respond best when they see basic facts on a clean page, others when they have a lot of charts and graphs at their fingertips. To overcome these shortcomings the content delivery itself can be made dynamic based on the learner's need. In this paper we propose a novel method...
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...Modelling Football Data By Renzo Galea A Dissertation Submitted in Partial Fulfilment of the Requirements For the Degree of Bachelor of Science (Honours) Statistics and Operations Research as main area DEPARTMENT OF STATISTICS AND OPERATIONS RESEARCH FACULTY OF SCIENCE UNIVERSITY OF MALTA MAY 2011 Declaration of Authorship I, Renzo Galea 25889G, declare that this dissertation entitled: “Modelling Football Data”, and the work presented in it is my own. I confirm that: (1) This work is carried out under the auspices of the Department of Statistics and Operations Research as part fulfillment of the requirements of the Bachelor of Science (Hons.) course. (2) Where any part of this dissertation has previously been submitted for a degree or any other qualification at this university or any other institution, this has been clearly stated. (3) Where I have used or consulted the published work of others, this is always clearly attributed. (4) Where I have quoted from the works of others, the source is always given. With the exception of such quotations, this dissertation is entirely my own work. (5) I have acknowledged all sources used for the purpose of this work. Signature: _______________________ Date: _______________________ Abstract Renzo Galea, B.Sc. (Hons.) Department of Statistics & Operations Research May 2011 University of Malta The main goal of this dissertation is to investigate the Bayesian modelling performance for ...
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...Dove Valentine Mailing Campaign Course Name: Business Analytics Using Data Mining Submitted by: (Student names) Group Members (8A) Harneet Chawla Ankit Sobti Kanika Miglani Varghese Cherian Saad Khan Note: Considering our client is an FMCG, each technique mentioned below has been explained in detail ensuring thorough/easy understanding. Business Analytics Using Data Mining – Final Project Valentine Coupon Scheme Executive summary Business problem We have been hired by our client, a reputed FMCG conglomerate, Unilever as data mining consultants. Our client has a range of products in the Personal Care Category that comprises of soaps etc. One of the brands that our client happens to own is the Dove brand of soap. For the first time the client is formulating a Valentine mai-in-coupon scheme to be rolled out in the month of February (next year). The scheme has the following business objectives: 1) Understand the customer profile of those customers who buy Dove soap. 2) Based on the customer profile understanding, predict for next year, new customers who are most likely to buy Dove. 3) Send out a mail-in-discount coupon to those respective customers of Hypermarket. 4) Client will be conducting a promotional campaign for which it will be incurring substantial costs thus it wants to ensure that next year when the campaign is rolled out, the coupons are sent out to customers who are most likely to avail them. 5) Client wants to increase customer loyalty towards Dove soap, considering...
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...Outline 4 Probability – the chance that an uncertain event will occur (always between 0 and 1) Impossible Event – an event that has no chance of occurring (probability = 0) Certain Event – an event that is sure to occur (probability = 1) Assessing Probability probability of occurrence= probability of occurrence based on a combination of an individual’s past experience, personal opinion, and analysis of a particular situation Events Simple event An event described by a single characteristic Joint event An event described by two or more characteristics Complement of an event A , All events that are not part of event A The Sample Space is the collection of all possible events Simple Probability refers to the probability of a simple event. Joint Probability refers to the probability of an occurrence of two or more events. ex. P(Jan. and Wed.) Mutually exclusive events is the Events that cannot occur simultaneously Example: Randomly choosing a day from 2010 A = day in January; B = day in February Events A and B are mutually exclusive Collectively exhaustive events One of the events must occur the set of events covers the entire sample space Computing Joint and Marginal Probabilities The probability of a joint event, A and B: Computing a marginal (or simple) probability: Probability is the numerical measure of the likelihood that an event will occur The probability of any event must be between...
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...A Statistical Perspective on Data Mining Ranjan Maitra∗ Abstract Technological advances have led to new and automated data collection methods. Datasets once at a premium are often plentiful nowadays and sometimes indeed massive. A new breed of challenges are thus presented – primary among them is the need for methodology to analyze such masses of data with a view to understanding complex phenomena and relationships. Such capability is provided by data mining which combines core statistical techniques with those from machine intelligence. This article reviews the current state of the discipline from a statistician’s perspective, illustrates issues with real-life examples, discusses the connections with statistics, the differences, the failings and the challenges ahead. 1 Introduction The information age has been matched by an explosion of data. This surfeit has been a result of modern, improved and, in many cases, automated methods for both data collection and storage. For instance, many stores tag their items with a product-specific bar code, which is scanned in when the corresponding item is bought. This automatically creates a gigantic repository of information on products and product combinations sold. Similar databases are also created by automated book-keeping, digital communication tools or by remote sensing satellites, and aided by the availability of affordable and effective storage mechanisms – magnetic tapes, data warehouses and so on. This has created a situation...
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...Assignment 3 – Classification Note: Show all your work. Problem 1 (25 points) Consider the following dataset: ID | A1 | A2 | A3 | Class | 1 | Low | Mild | East | Yes | 2 | Low | Hot | West | No | 3 | Medium | Mild | East | No | 4 | Low | Mild | East | Yes | 5 | High | Mild | East | Yes | 6 | Medium | Hot | West | No | 7 | High | Hot | West | Yes | 8 | Low | Cool | West | No | 9 | Medium | Cool | East | Yes | 10 | High | Cool | East | No | 11 | Medium | Mild | West | Yes | 12 | Medium | Cool | West | No | 13 | Medium | Hot | West | Yes | 14 | high | Hot | East | Yes | Suppose we have a new tuple X = (A1 = Medium, A2 = Cool, A3 = East). Predict the class label of X using Naïve Bayesian classification. You need show all your work. Problem 2 (25 points) Consider the following dataset D. ID | A1 | A2 | A3 | Class | 1 | Low | Mild | East | Yes | 2 | Low | Hot | West | No | 3 | Medium | Mild | East | No | 4 | Low | Mild | West | Yes | 5 | High | Cool | East | Yes | 6 | Low | Hot | West | No | 7 | High | Hot | West | Yes | 8 | Low | Cool | West | No | 9 | Medium | Cool | East | Yes | 10 | High | Hot | East | No | 11 | Medium | Mild | East | Yes | 12 | Medium | Cool | West | No | 13 | High | Hot | West | Yes | 14 | High | Hot | East | Yes | (1) Compute the Info of the whole dataset D. (2) Compute the information gain for each of A1, A2, and A3, and determine the splitting attribute (or the best split attribute)...
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...2012 [APSSRA 2012, May 25, 2012 ] Bayesian Updating in Structural Reliability Daniel Straub Engineering Risk Analysis Group TU München Ever increasing amounts of information are available Sensor data Satelite data Spatial measurements on structures Advanced simulation Sources: Frey et al. (in print); Gehlen et al. (2010); Michalski et al (2011); Schuhmacher et al. (2011) 2 1 01.06.2012 1973: 3 Probabilistic Updating of Flaw Information Tang (1973) • Imperfect information through inspection modeled by probability-ofdetection: 4 2 01.06.2012 Probabilistic Updating of Flaw Information Tang (1973) 5 Updating models and reliability computations with (indirect) information • Bayes‘ rule: ∝ 6 3 01.06.2012 How to compute the reliability of a geotechnical site conditional on deformation monitoring outcomes? -> Integrate Bayesian updating in structural reliability methods 7 Prior model in structural reliability • Failure domain: Ω 0 • Probability of failure: Pr ∈Ω d 8 4 01.06.2012 Information in structural reliability • Inequality information: Ω 0 • Conditional probability of failure: Pr | Pr ∩ Pr ∈ Ω ∩Ω ∈Ω d d 9 Information in structural reliability • Equality information: Ω 0 • Conditional probability of failure: Pr | Pr ∩ Pr 0 0 ? 10 5 01.06.2012 In statistics, information is expressed as likelihood function • Likelihood function...
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...Credibility Theory Lecture Solutions – Week 1 1.1 Let A be the event that a student is an actuarial student. C be the event that a student is a Credibility Theory student. P(C) = 0.02 ⇒ P( C ) = 0.98 P(A | C) = 0.98 P(A | C ) = 0.07 P( A | C ) P(C ) P ( A | C ) P(C ) + P( A | C ) P(C ) P (C | A) = = 0.98 × 0.02 0.98 × 0.02 + 0.07 × 0.98 = 0.0196 0.0882 = 0.2222 = 22% 1.2 Let A1 = “The science department is a heavy polluter”. A2 = “The science department is a light polluter”. A3 = “The science department is not a polluter”. B = “The waterways are visibly polluted”. P(A1) = 0.1; P(A2) = 0.2; P(A3) = 0.7. P(B |A1) = 0.9; P(B |A2) = 0.6; P(B |A3) = 0.3. P(B) = P(B |A1)P(A1) + P(B |A2)P(A2) + P(B |A3)P(A3) = 0.9*0.1 + 0.6*0.2 + 0.3*0.7 = 0.42 P ( A1 | B) = P( B | A1 ) P( A1 ) 0.9 × 0.1 = = 0.21 P( B) 0.42 P ( A2 | B) = P( B | A2 ) P( A2 ) 0.6 × 0.2 = = 0.29 P( B) 0.42 P( A3 | B) = P( B | A3 ) P( A3 ) 0.3 × 0.7 = = 0.5 P( B) 0.42 1.3 The Bayesian model is: p ~ U(0,1) and (X|p) ~ Bin(n,p). Thus, f(p) = 1, 0 ≤ p ≤ 1 and ⎛n⎞ f(x|p) = ⎜ ⎟ p x (1 − p) n − x . ⎝x⎠ ⎛n⎞ x n −x ⎜ ⎟ p (1 − p) x f(p|x) = ⎝ ⎠ 1⎛ n ⎞ x n −x ∫0 ⎜ x ⎟ p (1 − p) dp ⎝ ⎠ = p x (1 − p) n − x 1 ∫p 0 Recall: 1 ∫p 0 α−1 x (1 − p) n − x dp (1 − p)β−1 dp = Γ(α)Γ(β) Γ(α + β) Therefore, f(p|x) = Γ(n + 2) p x (1 − p) n − x , Γ(x + 1)Γ(n − x +...
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...“niche” versus “change-of-pace” brands Albert C. Bemmaor, December 23, 2011 March 30, 2012 October 12, 2012 The use of the “REIBST2_vaa.xls” data file is restricted to the course MKGM31203 (Q1, 2012-2013) at ESSEC Business School. “Niche” brands can be defined as brands that benefit from an abnormally high repeat rate whereas “change-of-pace” brands can be defined as brands with an abnormally low repeat rate for a given penetration level. Key notions Here are some basic notions you need be familiar with prior to carrying out this exercise: (i) (ii) (iii) (iv) (v) (vi) (vii) What a “variable” is. What a mean (expected value) is and how to compute it; What the notion of independence between two events means and how to test for it; What a correlation between two variables is and how to measure it; What a market share is and how to interpret it; What a penetration is and how to interpret it; What the duplication between two brands is and how to interpret it. Analysis as a scientific process Analyzing data consists of a three-step procedure: (i) (ii) (iii) Defining expectations: What do you expect to find and why? If you have “no idea” about your expectations, you need to develop these ideas by discussing with colleagues, “experts”, reading textbooks and/or using other supporting material; Running the analysis; Comparing your expectations with the findings. Do they match? Did you obtain any surprising result? If so, what are their implications...
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...Parañaque City A Term Paper Presented to: Edmar Orata Probability by: Jirolyn Fabro Miguel Angelo Rosales March 15, 2012 I - Introduction II - Interpretations III - Etymology IV - History V - Applications 1. Weather Forecasting 2. Batting Average 3. Winning the Lottery 4. VI - Discussion VII - I-Introduction Probability is the ratio of the number of ways an event can occur to the number of possible outcomes. Probability is expressed as a fraction or decimal from 0 to 1. Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we are not certain.[1] The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The certainty we adopt can be described in terms of a numerical measure and this number, between 0 and 1, we call probability. [2] The higher the probability of an event, the more certain we are that the event will occur. Thus, probability in an applied sense is a measure of the likeliness that a (random) event will occur. The concept has been given an axiomatic mathematical derivation in probability theory, which is used widely in such areas of study as mathematics, statistics, finance, gambling, science, artificial intelligence/machine learning and philosophy to, for example, draw inferences about the likeliness of events. Probability is used to...
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...of CRM project. (Reinartz, Kraft & Hoyer, 2004). The present paper discusses statistical interpretation of research data to find whether CRM project is worth pursuing given the strength of firm’s project management capability along with market evaluation of CRM implementation. Market analysis shows that 47% of the company finds that inadaptability of the end-user with CRM applications put the project in jeopardy(Coltman and Devinney, 2007). Data is analyzed for implementation of CRM through different vendors for companies of all range from less than $750K to over $10M. It consists of implementation statistics over the past 10 years. To analyze research data, Bayes’ theorem is selected as the probability model that was close to implementation of CRM project. Statistics and Probability Tutorial(n.d.) states that Bayes’ theorem looks appropriate in the context as it provides logical inference to calculate the degree of confidence based on already gathered evidence. Statistical result of data reflects that the probability of project being failed by a project management methodology is 47%. Conditional probability calculation shows that if there is established project management methodology in the firm there was a 16% chance the project would fail. The CRM research analyst additionally stated that even though a project management is not adequate, failure is not always imminent. Failure also...
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...Journal of Data Science 2(2004), 231-244 Estimating Vehicle Speed from Traffic Count and Occupancy Data Martin L. Hazelton University of Western Australia Abstract: Automatic vehicle detectors are now common on road systems across the world. Many of these detectors are based on single inductive loops, from which data on traffic volumes (i.e. vehicle counts) and occupancy (i.e. proportion of time during which the loop is occupied) are available for 20 or 30 second observational periods. However, for the purposes of traffic management it is frequently useful to have data on (mean) vehicle speeds, but this is not directly available from single loop detectors. While detector occupancy is related in a simple fashion to vehicle speed and length, the latter variable is not measured on the vehicles that pass. In this paper a new method for speed estimation from traffic count and occupancy data is proposed. By assuming a simple random walk model for successive vehicle speeds an MCMC approach to speed estimation can be applied, in which missing vehicle lengths are sampled from an exogenous data set. Unlike earlier estimation methods, measurement error in occupancy data is explicitly modelled. The proposed methodology is applied to traffic flow data from Interstate 5 near Seattle, during a weekday morning. The efficacy of the estimation scheme is examined by comparing the estimates with independently collected vehicle speed data. The results are encouraging. Key words: Bayesian inference, inductance...
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...people are often challenged with uncertainty when making a decision the probability concept is important in the decision making process. Statistics are used for probability analysis of events that cannot be controlled. Many decisions are often made with a significant lack of knowledge and probability helps to determine the unknown. Further, when comparing several alternatives it is often difficult to make a decision regarding which alternative to choose. Making a decision is very similar to a gamble. To determine the consequence of a decision the value of an outcome and its probability must be calculated. Bayes' theorem (also known as Bayes' rule) is a useful tool for calculating conditional probabilities (Stat Trek, 2013). In applying Bayes’ theorem one must recognize the types of problems that only can be used. The following conditions must exist in considering Bayes’ theorem (Stat Trek, 2013): ■ The sample space is partitioned into a set of mutually exclusive events { A1, A2, . . . , An }. ■ Within the sample space, there exists an event B, for which P(B) > 0. ■ The analytical goal is to compute a conditional probability of the form: P( Ak | B ). ■ You know at least one of the two sets of probabilities described below. • P( Ak ∩ B ) for each Ak • P( Ak ) and P( B | Ak ) for each Ak For example, Bob is building a deck tomorrow. The weather person has predicted that it will snow. Historical weather data indicates that it snows only twice each year. When it actually...
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