Probabilities to likelihoods

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  • Biologists study living things, but what do philosophers of biology study? A cynic might say “their own navels,” but I am no cynic. A better answer is that philosophers of biology, and philosophers of science generally, study science. Ours is a second-order, not a first-order, subject. In this respect, philosophy of science is similar to history and sociology of science. A difference may be found in the fact that historians and sociologists study science as it is, whereas philosophers of science study science as it ought to be.

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  • In this lecture, we formulate the problem of linear prediction using probabilities. We also introduce the maximum likelihood estimate and show that it coincides with the least squares estimate. The goal of the lecture is for you to learn: Gaussian distributions, how to formulate the likelihood for linear regression, computing the maximum likelihood estimates for linear regression, entropy and its relation to loss, probability and learning.

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  • In m a n y applications of natural language processing it is necessary to determine the likelihood of a given word combination. For example, a speech recognizer m a y need to determine which of the two word combinations "eat a peach" and "eat a beach" is more likely. Statistical NLP methods determine the likelihood of a word combination according to its frequency in a training corpus. However, the nature of language is such that m a n y word combinations are infrequent and do not occur in a given corpus. ...

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  • A very popular approach for estimating the independent component analysis (ICA) model is maximum likelihood (ML) estimation. Maximum likelihood estimation is a fundamental method of statistical estimation; a short introduction was provided in Section 4.5. One interpretation of ML estimation is that we take those parameter values as estimates that give the highest probability for the observations. In this section, we show how to apply ML estimation to ICA estimation.

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  • Tax compliance researchers begin with the supposition that people compare the marginal benefit of noncompliance (reduced tax payments, for example) with the expected marginal costs, which account for both the likelihood of punishment and its severity. That perspective provides an approach for evaluating the effective penalties uninsured people could anticipate under an individual health mandate.

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  • Chance events are commonplace in our daily lives. Every day we face situations where the result is uncertain, and, perhaps without realizing it, we guess about the likelihood of one outcome or another. Fortunately, mastering the concepts of probability can cast new light on situations where randomness and chance appear to rule. In this fully revised second edition of Understanding Probability, the reader can learn about the world of probability in an appealing way.

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  • Unsupervised learning of linguistic structure is a difficult problem. A common approach is to define a generative model and maximize the probability of the hidden structure given the observed data. Typically, this is done using maximum-likelihood estimation (MLE) of the model parameters. We show using part-of-speech tagging that a fully Bayesian approach can greatly improve performance. Rather than estimating a single set of parameters, the Bayesian approach integrates over all possible parameter values. ...

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  • We investigate generalizations of the allsubtrees "DOP" approach to unsupervised parsing. Unsupervised DOP models assign all possible binary trees to a set of sentences and next use (a large random subset of) all subtrees from these binary trees to compute the most probable parse trees. We will test both a relative frequency estimator for unsupervised DOP and a maximum likelihood estimator which is known to be statistically consistent. We report state-ofthe-art results on English (WSJ), German (NEGRA) and Chinese (CTB) data. ...

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  • Chapter 12 - Limited dependent variable models. In this chapter, you will learn how to: Compare between different types of limited dependent variables and select the appropriate model, interpret and evaluate logit and probit models, distinguish between the binomial and multinomial cases, deal appropriately with censored and truncated dependent variables, estimate limited dependent variable models using maximum likelihood in EViews.

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  • An integrated approach among the local, State, and Federal Government provides for a logical clearinghouse for intelligence on the movement and activities of terrorist groups and the collection, interpretation, and dissemination of that information to the proper enforcement agencies. Effective planning and intelligence gathering can lessen the likelihood of a surprise emergency incident, which, improperly handled, can make or break a department and its administrators at all levels of government.

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  • ICA by Maximum Likelihood Estimation A very popular approach for estimating the independent component analysis (ICA) model is maximum likelihood (ML) estimation. Maximum likelihood estimation is a fundamental method of statistical estimation; a short introduction was provided in Section 4.5. One interpretation of ML estimation is that we take those parameter values as estimates that give the highest probability for the observations. In this section, we show how to apply ML estimation to ICA estimation.

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  • Signal detection in AWGN channels Minimum distance detector. Maximum likelihood. Average probability of symbol error. Union bound on error probability. Upper bound on error probability based on the minimum distance.ISI in the detection process due to the filtering effects of the system Overall equivalent system transfer function

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  • To understand conceptually how Bayes' theorem estimates the posttest probability of disease, it is useful to examine a nomogram version of Bayes' theorem (Fig. 3-2). In this nomogram, the accuracy of the diagnostic test in question is summarized by the likelihood ratio , which is defined as the ratio of the probability of a given test result (e.g., "positive" or "negative") in a patient with disease to the probability of that result in a patient without disease.

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  • This  survey  was  completed  via  the  internet  from  January  7  to  February  20,  2008  by  253  individuals  who  served  on  at  least  one  audit  committee  for  a  publicly  traded  company  in  2007.  Some respondents were also given the option to complete a paper and pencil survey  in  place of the online survey to increase response rate.     While conducting a probability sample with audit committee members is technically possible, it  was not feasible from a cost or time standpoint.

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  • Total public spending on lighting crime can be reduced, while keeping the mathematically expected punishment unchanged, by offsetting a cut in expenditures on catching criminals with a sufficient increase in the punish- ment to those convicted. However, risk-preferring individuals are more deterred from crime by a higher probability of conviction than by severe punishments.

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  • A probit regression model is estimated in order to analyze how firm age and size affect the likelihood of being a HGF. The analysis confirms that firm age and size affect the probability of a firm becoming any type of HGF. Larger firms are more likely to be HGFs measured in absolute numbers and less likely when HGFs are measured in relative numbers. Firm age has a significant negative impact on the likelihood of being a HGF in almost all regressions, indicating that young firms are more likely to be HGFs irrespective of how HGFs are defined. Thus, new firm...

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  • SSI continuing disability reviews (CDRs) are periodic reviews conducted to ensure recipients are still disabled according to agency rules. The frequency of these reviews is dependent on the likelihood that a recipient’s medical condition will change. Non-disability redeterminations (redeterminations) are periodic reviews that verify living arrangements, income levels, and other non-disability factors related to SSI eligibility. Similar to CDRs, the frequency of redeterminations is determined by the probability that changes affecting eligibility will occur.

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  • THE credit standing of an applicant for a personal loan is investigated intensively because it indicates, within reason- able limits, the likelihood of repayment. It should not be assumed, however, that a bank officer can foretell with cer- tainty how faithfully a borrower will meet his obligations; few applicants have economic prospects so bad that there is not some small chance of repayment, and few are so well sit- uated that there is not some possibility of delinquency or even default. The selection of borrowers must therefore rest on probabilities.

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  • We tackle the previously unaddressed problem of unsupervised determination of the optimal morphological segmentation for statistical machine translation (SMT) and propose a segmentation metric that takes into account both sides of the SMT training corpus. We formulate the objective function as the posterior probability of the training corpus according to a generative segmentation-translation model. We describe how the IBM Model-1 translation likelihood can be computed incrementally between adjacent segmentation states for efficient computation. ...

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  • Contrary to popular belief, we show that the optimal parameters for IBM Model 1 are not unique. We demonstrate that, for a large class of words, IBM Model 1 is indifferent among a continuum of ways to allocate probability mass to their translations. We study the magnitude of the variance in optimal model parameters using a linear programming approach as well as multiple random trials, and demonstrate that it results in variance in test set log-likelihood and alignment error rate.

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