...The article, "Bayesian Inference and Contractualist Justification on Interstate 95", written by Arthur Isak Applbaum sheds light on philosophic controversial issue of racial profiling. (1) Applbaum argues that the use of racial generalizations can be justified if the statistical inference is accurate. He describes three types of cases that police might use group-based selection criteria: group-based patrol, group-based enforcement, and group-based identification. The later one states that police will select unidentified people who fit the group-based description for a known violation from public for scrutiny. For example, if a thief is a tall redhead woman, then police try to stop all the tall redhead women to find that thief. (2) He argues that, under this type, accurate profiling can make police more effective and people who are selected only bear a minor cost. The author claims that if the statistical generalization is accurate, then the net gain from searching strategies would be huge from profiling. For the benefits side, profiling helps police largely reduce their searching work and makes the efforts more effective. For the costs side, the selected people may only bear few minutes questioning and that is not a big deal for rational persons except particular circumstances. Thus, the net gain from profiling, compared to search all the people, is largely positive. Hence, the use of racial profiling can be justified in this case. (3) Although the profiling can help police complete...
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...Wilbert A. McClay Email1: mcclay.w@husky.neu.edu Email2: wilmcclay@gmail.com Homeland Security Radiographic Image Analysis Project Image Analysis of Radiographic Scans for Detection of Threats in Cargo Containers Motivation The current standard methods for examining containers that pose a potential terrorist threat involve Department of Homeland Security (DHS) officers generally conducting either non-intrusive or physical inspections. The non-intrusive inspection (NII) involves use of X-ray or gamma ray scanners to generate an image of the contents, which DHS officers review for anomalies. DHS officers also scan cargo using radiation detection devices. When an irregularity is identified, officers may physically examine all or a portion of the container’s contents (see Figure 1 below). [pic] Figure 1: Cargo container being examined by portable VACIS system. Problem Importance The methods implemented will enable the identification and evaluation of cargo radiographic images having an extremely widespread and powerful impact for Homeland Security. Project Description Radiographic imaging has become an important tool for screening cargo containers for potential nuclear or radiological threats. We are investigating methods to extract features from these images that effectively characterize the contents and when combined with other measurements and information could indicate whether or not a threat is present. Analysis...
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...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 loop, Metropolis-Hastings algorithm, measurement error, missing data. 1. Introduction Road traffic management is becoming increasingly reliant on the availability of real-time traffic flow data. In Melbourne, for example, SCATS (Sydney Coordinated Adaptive Traffic System) makes use of such data to optimize signals over the road network. Similar schemes operate in many other cities throughout...
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...topicmodels: An R Package for Fitting Topic Models Bettina Grun ¨ Johannes Kepler Universit¨t Linz a Kurt Hornik WU Wirtschaftsuniversit¨t Wien a Abstract This article is a (slightly) modified and shortened version of Gr¨n and Hornik (2011), u published in the Journal of Statistical Software. Topic models allow the probabilistic modeling of term frequency occurrences in documents. The fitted model can be used to estimate the similarity between documents as well as between a set of specified keywords using an additional layer of latent variables which are referred to as topics. The R package topicmodels provides basic infrastructure for fitting topic models based on data structures from the text mining package tm. The package includes interfaces to two algorithms for fitting topic models: the variational expectation-maximization algorithm provided by David M. Blei and co-authors and an algorithm using Gibbs sampling by Xuan-Hieu Phan and co-authors. Keywords: Gibbs sampling, R, text analysis, topic model, variational EM. 1. Introduction In machine learning and natural language processing topic models are generative models which provide a probabilistic framework for the term frequency occurrences in documents in a given corpus. Using only the term frequencies assumes that the information in which order the words occur in a document is negligible. This assumption is also referred to as the exchangeability assumption for the words in a document and this assumption leads...
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...classification for given problem is posed with serious challenge as on one side the data set is highly imbalanced in favour of B+E against B(So we have to avoid over fitting for generalization) & on the other side wrong classification can have serious consequences in diplomatic relationship between nations. So Our thrust has been to choose between various methods , one with sound justification towards our results & showing how was it better than others . Based on comparative study of various methods we have finally chosen Biased Minimax Probability Machine [1] & we would be proving superiority of our methods over SVM classifier with different parameters which we tried. Besides authors [1] have shown superiority of BMPM over DT, Naive Bayesian Classifier, K-nn classification, & other under/over Sampling methods. Methodology of BMPM: For two class Classification: Let Family {x}, {y} with mean vector & Covariance matrices {x, ∑x }, {y, ∑y} belong to class1 & class2 respectively. Let α be the worst-case accuracy for future data points from family of {x}, and β be the worst-case accuracy for future data points from family of {y}. Depending upon severity of the false positive & true positive rates α, β(Policy variables) it tries to find a maximal hyper plane to separate the two classes [pic] [pic] We can also have Non Linear Classifier by mapping the feature space into suitable higher dimension. The above optimization is changed according to needs, so we would be doing...
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...probabilistic model for which a graph denotes the conditional dependence structure between random variables. They are commonly used in probability theory, statistics—particularly Bayesian statistics—and machine learning. An example of a graphical model. Each arrow indicates a dependency. In this example: D depends on A, D depends on B, D depends on C, C depends on B, and C depends on D. Contents [hide] 1 Types of graphical models 1.1 Bayesian network 1.2 Markov random field 1.3 Other types 2 Applications 3 See also 4 Notes 5 References and further reading 5.1 Books and book chapters 5.2 Journal articles 5.3 Other Types of graphical models[edit] Generally, probabilistic graphical models use a graph-based representation as the foundation for encoding a complete distribution over a multi-dimensional space and a graph that is a compact or factorized representation of a set of independences that hold in the specific distribution. Two branches of graphical representations of distributions are commonly used, namely, Bayesian networks and Markov networks. Both families encompass the properties of factorization and independences, but they differ in the set of independences they can encode and the factorization of the distribution that they induce.[1] Bayesian network[edit] Main article: Bayesian network If the network structure of the model is a directed acyclic graph, the model represents a factorization of the joint probability of all random variables. More precisely...
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...Unit 2 DB Subjective Probability “ A probability derived from an individual's personal judgment about whether a specific outcome is likely to occur. Subjective probabilities contain no formal calculations and only reflect the subject's opinions and past experience.” (investopedia.com, 2013) There are three elements of a probability which combine to equal a result. There is the experiment ,the sample space and the event (Editorial board, 2012). In this case the class is the experiment because the process of attempting it will result in a grade which could vary from an A to F. The different grades that can be achieved in the class are the sample space. The event or outcome is the grade that will be received at the end of the experiment. I would like to achieve an “A” in this class but due to my lack of experience in statistical analysis, my hesitation towards advanced mathematics, and the length of time it takes for me to complete my course work a C in this class may be my best result. I have a 1/9 chance or probability to receive an “A” in the data range presented to me which is (A,A-,B,B-,C,C-,D,D- AND F). By the grades that have been posted I would say that the other students have a much better chance of receiving a better grade than mine. I have personally use subjective probability in my security guard business in bidding on contracts based on the clients involved , the rates that I charge versus the rates other companies charge and the amount of work involved...
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...Decision of Uncertainty Darylisha Jones QNT/561 February 14, 2011 Paul Thomasman Decision of Uncertainty Introduction Decision: Extending automobile warranties or not? It comes a time when one has to make that decision of extending an automobile warranty when it has expired. Because auto warranties provide well needed protection, it does not come cheap be any means. Therefore, the decision to be made is the price of purchasing a warranty over the cost of repairs without a warranty. An extended warranty supplies the ability of possessing coverage of an automobile. It supplies coverage for repairs, parts, rentals, and even labor at a warranty rate rather paying out- of -pocket for every issue. Research In order to make the correct decision, I will research information on purchasing extended warranty of a 2005 Chevrolet Impala. In one year my warranty of my vehicle will expire, and I will have to decide on purchasing an extended warranty to protect my vehicle. After researching the effects of not extending a warranty can result in high auto repair bills. An average cost of an engine repair without protection for an Impala is $2,000. Therefore, information of whether or not major repairs are needed for this vehicle must be taken into consideration. After gaining information from many auto repair shops of their experience of servicing vehicles, it is wise to acquire extending a warranty. The chances of auto repairs being needed within five years on my vehicle...
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...The market value of the firm is then the value of its net financial assets plus the value of its capital assets (less any other liabilitiesUnder non-ideal conditions, it may be difficult to write down a complete set of states of nature and associated cash flows. Even if these can be written down, difficulties remain because objective state probabilities are not available. This is perhaps the most fundamental difficulty, since these probabilities must be subjectively estimated. Also an interest rate is not necessarily given. All of these difficulties lead to reliability problems of lack of representational faithfulness and possible bias. The expected present value calculation can still be made, but it is an estimate because the probabilities and other values that go into it are estimates. The expected value of a single roll of a fair die is: x 1 (1 2 3 4 5 6) 3.5 6 b. First, you would have to write down a set of possible states of nature for the die. One simple possibility would be to define: State 1: die is fair State 2: die is not fair. Then, subjective probabilities of each state need to be assessed, based on any prior information you have. For example, if the person supplying you with the die looks suspicious, you might assess the probability of state 2 as 0.50, say. A problem with this approach, however, is that to calculate the expected value of a single roll, you need an expected value conditional on state 2, and this expected value...
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...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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...Decision on Uncertainty QNT/561 Decision on Uncertainty Decisions are made every day by individuals. These decisions are made armed with knowledge regarding the outcome of a decision or made with uncertainty of the outcome. Probability is tool of measurement used to determine the likelihood of an occurrence during an event. Because 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...
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...[pic] FACULTY OF LAW AND BUSINESS School of Business North Sydney Campus Semester 2, 2014 STAT102: BUSINESS DATA ANALYSIS Probability Trees A survey of STAT102 students reveals that among the students that attain CR or better grades, 60% of them attended both lectures and tutorials. Among the students that attain PASS or FAILURE, only 20% of them attended both lectures and tutorials. Not attending both lectures and tutorials and with self-study, a student feels that the chance of attaining CR or better grades is quite low, 10%. The student is willing to attend both lectures and tutorials only if the efforts would increase the probability of achieving CR or better grades to 20% or more. Please use the following notations for the various states: C = CR or better grades CC = PASS or FAILURE L = Attend both lectures and tutorials LC = Do not attend both lectures and tutorials Required Should the student attend both lectures and tutorials? Please justify your answer with the posterior probability (prior probabilities are revised after the decision to attend both lectures and tutorials). The prior probability (probabilities determined prior to the decision of attending both lectures and tutorials) of attaining CR or better grades is P(C) = 0.1 P(CC) = 0.9 Complement rule Conditional probabilities are P(L(C) = 0.6 (for a student that have achieved a CR or better grade, the...
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...In researching the needs for Abbon Laboratories in regards to their email server, I researched Naïve Bayesian Filters. Bayesian spam filtering; is a statistical technique of e-mail filtering. It makes use of a naive Bayes classifier to identify spam e-mail. The Bayesian classifiers work by associating the use of tokens (typically words, phrases, etc), with spam and non-spam e-mails and then using Bayesian inference to calculate a probability that an email is or is not spam. Bayesian spam filtering is considered to be a powerful procedure for dealing with spam, that can be tailored to the email needs of individual users, and gives low false positive spam detection rates that are generally acceptable to users. The process of Bayesian spam filtering works in the way of distinguishing particular words which have a higher probability of occurring in spam email. This filter however, doesn’t know these probabilities in advance, and must be first trained so it can build them up. In order to train the filter, the user must first manually indicate whether a new email is spam or not. For all the words in each training email, the filter will adjust the probabilities that each word will appear in spam or legitimate email in its database. After training the system, the word probabilities are used to compute the probability that an email with a particular set of words in it belongs to a particular category. Each word in the email contributes to the email’s spam probability, or only...
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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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...THE EFFECT OF SAVINGS RATE IN CANADA The impact of savings rate in an economic has become a very conflicting issue in research and among economist all over the world. This may be due to the importance of savings generally to the economic growth and development of any nation. However, the structure of every economy cannot be generalised by a particular economics’ variation because various countries have different social security and pension schemes, and different tax systems, all of which have an effect on disposable income. In addition, the age of a country’s population, the availability and ease of credit, the overall wealth, and cultural and social factors within a country all affect savings rates within a particular country. Therefore, this paper seeks to find the effect of savings in the Canadian economy. Household saving is defined as the difference between a household’s disposable incomes mainly wages received, revenue of the self-employed and net property income and its consumption (expenditures on goods and services). The household savings rate is calculated by dividing household savings by household disposable income. A negative savings rate indicates that a household spends more than it receives as regular income and finances some of the expenditure through credit (increasing debt), through gains arising from the sale of assets (financial or non-financial), or by running down cash and deposits. Since the early-to-mid-1990s, savings rates have been stable in some...
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