Iq option windows 7
Borchers, and L. Thomas, Introduction to Distance SamplingOxford University Press, 2001. Data Mining and Knowledge Discovery. The continuing rapid growth of on-line data and the widespread use of databases necessitate the development of techniques for extracting useful knowledge and for facilitating database access. The challenge of extracting knowledge from data is of common interest to several fields, including statistics, databases, pattern recognition, machine learning, data visualization, optimization, and high-performance computing.
The data mining process involves identifying an appropriate data set to mine or sift through to discover data content relationships. Data mining sometimes resembles the traditional scientific method of identifying a hypothesis and then testing it using an appropriate data set. Data mining tools include techniques like case-based reasoning, cluster analysis, data visualization, fuzzy query and analysis, and neural networks.
Sometimes however data mining is reminiscent of what happens when data has been collected and no significant results were found and hence an ad hoc, exploratory analysis is conducted to find a significant relationship. The combination of fast computers, cheap storage, and better communication makes it easier by the day to tease useful information out of everything from supermarket buying patterns to credit histories.
For clever marketers, that knowledge can be worth as much as the stuff real miners dig from the ground. The process thus consists of three basic stages exploration, model building or pattern definition, and validation verification. Data mining as an analytic process designed to explore large amounts of typically business or market related data in search for consistent patterns and or systematic relationships between variables, and then to validate the findings by applying the detected patterns to new subsets of data.
What distinguishes data mining from conventional statistical data analysis is that data mining is usually done for the purpose of secondary analysis aimed at finding unsuspected relationships unrelated to the purposes for which the data were originally collected. Data warehousing as a process of organizing the storage of large, multivariate data sets in a way that facilitates the retrieval of information for analytic purposes.
Data mining is now a rather vague term, but the element that is common to most definitions is predictive modeling with large data sets as used by big companies. Therefore, data mining is the extraction of hidden predictive information from large databases. It is a powerful new technology with great potential, for example, to help marketing managers preemptively define the information market of tomorrow. Data mining tools predict future trends and behaviors, allowing businesses to make proactive, knowledge-driven decisions.
The automated, prospective analyses offered by data mining move beyond the analyses of past events provided by retrospective tools. Data mining answers business questions that traditionally were too time-consuming to resolve. Data mining tools scour databases for hidden patterns, finding predictive information that experts may miss because it lies outside their expectations.
Data mining techniques can be implemented rapidly on existing software and hardware platforms across the large companies to enhance the value of existing resources, and can be integrated with new products and systems as they are brought on-line. Knowledge discovery in databases aims at tearing down the last barrier in enterprises information flow, the data analysis step. It is a label for an activity performed in a wide variety of application domains within the science and business communities, as well as for pleasure.
When implemented on high performance client-server or parallel processing computers, data mining tools can analyze massive databases while a customer or analyst takes a coffee break, then deliver answers to questions such as, Which clients are most likely to respond to my next promotional mailing, and why. The activity uses a large and heterogeneous data-set as a basis for synthesizing new and relevant knowledge.
The knowledge is new because hidden relationships within the data are explicated, and or data is combined with prior knowledge to elucidate a given problem. The term relevant is used to emphasize that knowledge discovery is a goal-driven process in which knowledge is constructed to facilitate the solution to a problem. Knowledge discovery maybe viewed as a process containing many tasks. Some of these tasks are well understood, while others depend on human judgment in an implicit matter.
Further, the process is characterized by heavy iterations between the tasks. This is very similar to many creative engineering process, e.the development of dynamic models. In this reference mechanistic, or first principles based, models are emphasized, and the tasks involved in model development are defined by. Initialize data collection and problem formulation. The initial data are collected, and some more or less precise formulation of the modeling problem is developed.
Tools selection. The software tools to support modeling and allow simulation are selected. Conceptual modeling. The system to be modeled, e.a chemical reactor, a power generator, or a marine vessel, is abstracted at first. Model representation. The essential compartments and the dominant phenomena occurring are identified and documented for later reuse. A representation of the system model is generated. Often, equations are used; however, a graphical block diagram or any other formalism may alternatively be used, depending on the modeling tools selected above.
Computer implementation. The model representation is implemented using the means provided by the modeling system of the software employed. These may range from general programming languages to equation-based modeling languages or graphical block-oriented interfaces. The model implementation is verified to really capture the intent of the modeler. No simulations for the actual problem to be solved are carried out for this purpose.
Reasonable initial values are provided or computed, the numerical solution process is debugged. The results of the simulation are validated against some reference, ideally against experimental data. The modeling process, the model, and the simulation results during validation and application of the model are documented. The model is used in some model-based process engineering problem solving task. For other model types, like neural network models where data-driven knowledge is utilized, the modeling process will be somewhat different.
Some of the tasks like the conceptual modeling phase, will vanish. Typical iq option windows 7 areas for dynamic models are control, prediction, planning, and fault detection and diagnosis. A major deficiency of today s methods is the lack of ability to utilize a wide variety of knowledge. Model application. As an example, a black-box model structure has very limited abilities to utilize first principles knowledge on a problem.
this has provided a basis for developing different hybrid schemes. Two hybrid schemes will highlight the discussion. First, it will be shown how a mechanistic model can be combined with a black-box model to represent a pH neutralization system efficiently. Second, the combination of continuous and discrete control inputs is considered, utilizing a two-tank example as case. The hybrid approach may be viewed as a means to integrate different types of knowledge, i.being able to utilize a heterogeneous knowledge base to derive a model.
Standard practice today is that almost any methods and software can treat large homogeneous data-sets. A typical example of a homogeneous data-set is time-series data from some system, e.temperature, pressure, and compositions measurements over some time frame provided by the instrumentation and control system of a chemical reactor. If textual information of a qualitative nature is provided by plant personnel, the data becomes heterogeneous.
The above discussion will form the basis for analyzing the interaction between knowledge discovery, and modeling and identification of dynamic models. In particular, we will be interested in identifying how concepts from knowledge discovery can enrich state-of-the- art within control, prediction, planning, and fault detection and diagnosis of dynamic systems.
Further Readings Marco D.Building and Managing the Meta Data Repository A Full Lifecycle GuideJohn Wiley, 2000. Thuraisingham B.Data Mining Technologies, Techniques, Tools, and TrendsCRC Press, 1998. Westphal Ch. Different approaches to handle this heterogeneous case are considered. Blaxton, Data Mining Solutions Methods and Tools for Solving Real-World ProblemsJohn Wiley, 1998.
Neural Networks Applications. The classical approaches are the feedforward neural networks, trained using back-propagation, which remain the most widespread and efficient technique to implement supervised learning. Applications include data mining, and stock market predictions. Further Readings Schurmann J.Pattern Classification A Unified View of Statistical and Neural ApproachesJohn Wiley Sons, 1996.
Bayes and Empirical Bayes Methods. Bayes and EB methods can be implemented using modern Markov chain Monte Carlo MCMC computational methods. The main steps are preprocess the data, the appropriate selection of variables, postprocessing of the results, and a final validation of the global strategy. Properly structured Bayes and EB procedures typically have good frequentist and Bayesian performance, both in theory and in practice. This in turn motivates their use in advanced high-dimensional model settings e.longitudinal data or spatio-temporal mapping modelswhere a Bayesian model implemented via MCMC often provides the only feasible approach that incorporates all relevant model features.
Smith, Bayesian TheoryWiley, 2000. Louis, Bayes and Empirical Bayes Methods for Data AnalysisChapman and Hall, 1996.Bayesian Statistical ModellingWiley, 2001. Markovian Memory Theory. Memory Theory and time series share the additive property and inside a single term there can be multiplication, but like general regression methods this does not always mean that they are all using M Theory.
One may use standard time series methods in the initial phase of modeling things, but instead proceed as follows using M Theory s Cross-Term Dimensional Analysis CTDA. Suppose that you postulate a model y af x - bg z ch u where f, g, h are some functions and x, z, u are what are usually referred to as independent variables. Notice the minus sign - to the left of b and the sign to the left of c and implicitly to the left of a, where a, b, c are positive constants.
The variable y is usually referred to as a dependent variable. According to M Theory, not only do f, g, and h influence cause y, but g influences causes f and h at least to some extent. In fact, M Theory can formulate this in terms of probable influence as well as deterministic influence. All this generalizes to the case where the functions f, g, h depend on two or more variables, e.f x, wg z, t, retc.
One can reverse this process. If it works, one has found something that mainstream regression and time series may fail to detect. If one thinks that f influences g and h and y but that h and g only influence y and not f, then express the equation of y in the above form. Of course, path analysis and Lisrel and partial least squares also claim to have causal abilities, but only in the standard regression sense of freezing so-called independent variables as givens and not in the M Theory sense which allows them to vary with y.
In fact, Bayesian probability statistics methods and M Theory methods use respectively ratios like y x and differences like y - x 1 in their equations, and in the Bayesian model x is fixed but in the M Theory model x can vary. If one looks carefully, one will notice that the Bayesian model blows up at x 0 because division by 0 is impossible, visit the The Zero Saga pagebut also near x 0 since an artificially enormous increase is introduced - precisely near rare events.
That is one of the reasons why M Theory is more successful for rare and or highly influenced influencing events, while Bayesian and mainstream methods work fairly well for frequent common and or low influence even independent and or low dependence events. Further Readings Kursunuglu B. Perlmutter, Quantum Gravity, Generalized Theory of Gravitation, and Superstring Theory-Based UnificationKluwer Academic Plenum, New York 2000.
Likelihood Methods. The decision-oriented methods treat statistics as a matter of action, rather than inference, and attempt to take utilities as well as probabilities into account in selecting actions; the inference-oriented methods treat inference as a goal apart from any action to be taken. Fisher s fiducial method is included because it is so famous, but the modern consensus is that it lacks justification. The hybrid row could be more properly labeled as hypocritical -- these methods talk some Decision talk but walk the Inference walk.
Now it is true, under certain assumptions, some distinct schools advocate highly similar calculations, and just talk about them or justify them differently. Some seem to think this is tiresome or impractical. One may disagree, for three reasons. First, how one justifies calculations goes to the heart of what the calculations actually MEAN; second, it is easier to teach things that actually make sense which is one reason that standard practice is hard to teach ; and third, methods that do coincide or nearly so for some problems may diverge sharply for others.
The difficulty with the subjective Bayesian approach is that prior knowledge is represented by a probability distribution, and this is more of a commitment than warranted under conditions of partial ignorance. Uniform or improper priors are just as bad in some respects as anything other sort of prior. Edwards, in particular, uses logarithm of normalized likelihood as a measure of support for a hypothesis. The methods in the Inference, Inverse cell all attempt to escape this difficulty by presenting alternative representations of partial ignorance.
Prior information can be included in the form of a prior support log likelihood function; a flat support represents complete prior ignorance. One place where likelihood methods would deviate sharply from standard practice is in a comparison between a sharp and a diffuse hypothesis. Consider H0 X. N 0, 100 diffuse and H1 X.
N 1, 1 standard deviation 10 times smaller. In standard methods, observing X 2 would be undiagnostic, since it is not in a sensible tail rejection interval or region for either hypothesis. But while X 2 is not inconsistent with H0, it is much better explained by H1--the likelihood ratio is about 6. 2 in favor of H1.
In Edwards methods, H1 would have higher support than H0, by the amount log 6. If these were the only two hypotheses, the Neyman-Pearson lemma would also lead one to a test based on likelihood ratio, but Edwards methods are more broadly applicable. I do not want to appear to advocate likelihood methods.
I could give a long discussion of their limitations and of alternatives that share some of their advantages but avoid their limitations. Data mining is the process of extracting knowledge from data. They are practical currently widely used in genetics and are based on a careful and profound analysis of inference. A Meta-analysis deals with a set of RESULTs to give an overall RESULT that is presumably comprehensive and valid.
But it is definitely a mistake to dismiss such methods lightly. I recall a case in physics, in which, after a phenomenon had been observed in air, emulsion data was examined. As it happens, there was no significant practical, not statistical in the theory, and also no error in the data. We really need to between the term statistically significantand the usual word significant. It is very important to distinction between statistically significant and generally significant, see Discover Magazine July, 1987The Case of Falling Nightwatchmen, by Sapolsky.
In this article, Sapolsky uses the example to point out the very important distinction between statistically significant and generally significant A diminution of velocity at impact may be statistically significant, but not of importance to the falling nightwatchman. Be careful about the word significant. It has a technical meaning, not a commonsense one. It is NOT automatically synonymous with important.
A person or group can be statistically significantly taller than the average for the population, but still not be a candidate for your basketball team. Whether the difference is substantively not merely statistically significant is dependent on the problem which is being studied. There is also graphical technique to assess robustness of meta-analysis results. We should carry out the meta-analysis dropping consecutively one study, that is if we have N studies we should do N meta-analysis using N-1 studies in each one.
After that we plot these N estimates on the y axis and compare them with a straight line that represent the overall estimate using all the studies. Topics in Meta-analysis includes Odds ratios; Relative risk; Risk difference; Effect size; Incidence rate difference and ratio; Plots and exact confidence intervals. Further Readings Glass, et al.Meta-Analysis in Social ResearchMcGraw Hill, 1987 Cooper H.Handbook of Research SynthesisRussell Sage Foundation, New York, 1994.
Industrial Data Modeling. Further Readings Montgomery D. Runger, Applied Statistics and Probability for EngineersWiley, 1998.Introduction to Probability and Statistics for Engineers and ScientistsAcademic Press, 1999. Prediction Interval. Since we don t actually know s 2we need to use t in evaluating the test statistic. The appropriate Prediction Interval for Y is.
This is similar to construction of interval for individual prediction in regression analysis. Fitting Data to a Broken Line. y a b x, for x less than or equal c y a - d c d b x, for x greater than or equal to c. A simple solution is a brute force search across the values of c. Once c is known, estimating a, b, and d is trivial through the use of indicator variables. One may use x-c as your independent variable, rather than x, for computational convenience.
Now, just fix c at a fine grid of x values in the range of your data, estimate a, b, and d, and then note what the mean squared error is. Select the value of c that minimizes the mean squared error. Unfortunately, you won t be able to get confidence intervals involving c, and the confidence intervals for the remaining parameters will be conditional on the value of c.
Further Readings For more details, see Applied Regression Analysisby Draper and Smith, Wiley 1981, Chapter 5, section 5. 4 on use of dummy variables. How to Determine if Two Regression Lines Are Parallel. Ho slope group 1 slope group 0 is equivalent to Ho b 3 0. Use t-test from variables-in-the equation table to test this hypothesis. Constrained Regression Model.
I agree that it s initially counter-intuitive see belowbut here are two reasons why it s true. The variance of the slope estimate for the constrained model is s 2 S X i 2where X i are actual X values and s 2 is estimated from the residuals. The variance of the slope estimate for the unconstrained model with intercept is s 2 S x i 2where x i are deviations from the mean, and s 2 is still estimated from the residuals. So, the constrained model can have a larger s 2 mean square error residual and standard error of estimate but a smaller standard error of the slope because the denominator is larger.
r 2 also behaves very strangely in the constrained model; by the conventional formula, it can be negative; by the formula used by most computer packages, it is generally larger than the unconstrained r 2 because it is dealing with deviations from 0, not deviations from the mean. This is because, in effect, constraining the intercept to 0 forces us to act as if the mean of X and the mean of Y both were 0.
Once you recognize that the s. of the slope isn t really a measure of overall fit, the result starts to make a lot of sense. Assume that all your X and Y are positive. If you re forced to iq option windows 7 the regression line through the origin or any other point there will be less wiggle in how you can fit the line to the data than there would be if both ends could move. Consider a bunch of points that are ALL way out, far from zero, then if you Force the regression through zero, that line will be very close to all the points, and pass through origin, with LITTLE ERROR.
And little precision, and little validity. Therefore, no-intercept model is hardly ever appropriate. Semiparametric and Non-parametric modeling. and the unknown e is interpreted as error term. The most simple model for this problem is the linear regression model, an often used generalization is the Generalized Linear Model GLM. where G is called the link function.
All these models lead to the problem of estimating a multivariate regression. Parametric regression estimation has the disadvantage, that by the parametric form certain properties of the resulting estimate are already implied. Nonparametric techniques allow diagnostics of the data without this restriction.
However, this requires large sample sizes and causes problems in graphical visualization. Semiparametric methods are a compromise between both they support a nonparametric modeling of certain features and profit from the simplicity of parametric methods. Further Readings Hдrdle W. Klinke, and B. Turlach, XploRe An Interactive Statistical Computing EnvironmentSpringer, New York, 1995.
Moderation and Mediation. Discriminant and Classification. We often need to classify individuals into two or more populations based on a set of observed discriminating variables. Methods of classification are used when discriminating variables are. quantitative and approximately normally distributed; quantitative but possibly nonnormal; categorical; or a combination of quantitative and categorical. It is important to know when and how to apply linear and quadratic discriminant analysis, nearest neighbor discriminant analysis, logistic regression, categorical modeling, classification and regression trees, and cluster analysis to solve the classification problem.
SAS has all the routines you need to for proper use of these classifications. Relevant topics are Matrix operations, Fisher s Discriminant Analysis, Nearest Neighbor Discriminant Analysis, Logistic Regression and Categorical Modeling for classification, and Cluster Analysis. For example, two related methods which are distribution free are the k-nearest neighbor classifier and the kernel density estimation approach.
In both methods, there are several problems of importance the choice of smoothing parameter s or k, and choice of appropriate metrics or selection of variables. These problems can be addressed by cross-validation methods, but this is computationally slow. An analysis of the relationship with a neural net approach LVQ should yield faster methods. Further Readings Cherkassky V, and F. Mulier, Learning from Data Concepts, Theory, and MethodsJohn Wiley Sons, 1998.
Mallick, and A. Smith, Bayesian Methods for Nonlinear Classification and RegressionWiley, 2002. Index of Similarity in Classification. A rather computationally involved for determining a similarity index I is due to Fisher, where I is the solution to the following equation. e aI e bI 1 e a b-j I. The index of similarity could be used as a distance so that the minimum distance corresponds to the maximum similarity.
Further Readings Hayek L. Buzas, Surveying Natural PopulationsColumbia University Press, NY, 1996. Generalized Linear and Logistic Models. Hre is how to obtain degree of freedom number for the 2 log-likelihood, in a logistic regression. Degrees of freedom pertain to the dimension of the vector of parameters for a given model. Suppose we know that a model ln p 1-p Bo B1x B2y B3w fits a set of data.
In this case the vector B Bo,B1, B2, B3 is an element of 4 dimensional Euclidean space, or R 4. Suppose we want to test the hypothesis Ho B3 0. We are imposing a restriction on our parameter space. The vector of parameters must be of the form B B Bo,B1, B2, 0. This vector is an element of a subspace of R 4. Namely, B4 0 or the X-axis. The likelihood ration statistic has the form.
2 log-likelihood 2 log maximum unrestricted likelihood maximum restricted likelihood 2 log maximum unrestricted likelihood -2 log maximum restricted likelihood. Which is unrestricted B vector 4-dimensions or degrees of freedom - restricted B vector 3 dimensions or degrees of freedom 1 degree of freedom which is the difference vector B B-B 0,0,0,B4 one dimensional subspace of R 4. The standard textbook is Generalized Linear Models by McCullagh and Nelder Chapman Hall, 1989.
Other SPSS Commands SAS Commands. Further Readings Harrell F, Regression Modeling Strategies With Applications to Linear Models, Logistic Regression, and Survival AnalysisSpringer Verlag, 2001. Lemeshow, Applied Logistic RegressionWiley, 2000. iq option windows 7, Multivariable Analysis A Practical Guide for CliniciansCambridge University Press, 1999. Kleinbaum D.Logistic Regression A Self-Learning TextSpringer Verlag, 1994.Logistic Regression A PrimerSage, 2000.
Survival Analysis. The methods of survival analysis are applicable not only in studies of patient survival, but also studies examining adverse events in clinical trials, time to discontinuation of treatment, duration in community care before re-hospitalisation, contraceptive and fertility studies etc. If you ve ever used regression analysis on longitudinal event data, you ve probably come up against two intractable problems. Censoring Nearly every sample contains some cases that do not experience an event.
If the dependent variable is the time of the event, what do you do with these censored cases. Time-dependent covariate Many explanatory variables like income or blood pressure change in value over time. How do you put such variables in a regression analysis. Makeshift solutions to these questions can lead to severe biases. Survival methods are explicitly designed to deal with censoring and time-dependent covariates in a statistically correct way.
Originally developed by biostatisticians, these methods have become popular in sociology, demography, psychology, economics, political science, and marketing. In Short, survival Analysis is a group of statistical methods for analysis and interpretation of survival data. Even though survival analysis can be used in a wide variety of applications e. insurance, engineering, and sociologythe main application is for analyzing clinical trials data.
Survival and hazard functions, the methods of estimating parameters and testing hypotheses that are the main part of analyses of survival data. Main topics relevant to survival data analysis are Survival and hazard functions, Types of censoring, Estimation of survival and hazard functions the Kaplan-Meier and life table estimators, Simple life tables, Peto s Logrank with trend test and hazard ratios and Wilcoxon test, can be stratifiedWei-Lachin, Comparison of survival functions The logrank and Mantel-Haenszel tests, The proportional hazards model time independent and time dependent covariates, The logistic regression model, and Methods for determining sample sizes.
In the last few years the survival analysis software available in several of the standard statistical packages has experienced a major increment in functionality, and is no longer limited to the triad of Kaplan-Meier curves, logrank tests, and simple Cox models. Further Readings Hosmer D. Lemeshow, Applied Survival Analysis Regression Modeling of Time to Event DataWiley, 1999. Swanepoel, and N. Veraverbeke, The modified bootstrap error process for Kaplan-Meier quantiles, Statistics Probability Letters58, 31-39, 2002.Survival Analysis A Self-Learning TextSpringer-Verlag, New York, 1996.Statistical Methods for Survival Data AnalysisWiley, 1992.
Grambsch, Modeling Survival Data Extending the Cox ModelSpringer 2000. This book provides thorough discussion on Cox PH model. Since the first author is also the author of the survival package in S-PLUS R, the book can be used closely with the packages in addition to SAS. Association Among Nominal Variables. Spearman s Correlation, and Kendall s tau Application. Two measures are Spearman s rank order correlation, and Kendall s tau.
Further Readings For more details see, e. Is Var1 ordered the same as Var2.Fundamental Statistics for the Behavioral Sciencesby David C. Howell, Duxbury Pr. Repeated Measures and Longitudinal Data. For those items yielding a score on a scale, the conventional t-test for correlated samples would be appropriate, or the Wilcoxon signed-ranks test.
What Is a Systematic Review. There are iq option windows 7 important questions in health care which can be informed by consulting the result of a single empirical study. Systematic reviews attempt to provide answers to such problems by identifying and appraising all available studies within the relevant focus and synthesizing their results, all according to explicit methodologies. The review process places special emphasis on assessing and maximizing the value of data, both in issues of reducing bias and minimizing random error.
The systematic review method is most suitably applied to questions of patient treatment and management, although it has also been applied to answer questions regarding the value of diagnostic test results, likely prognoses and the cost-effectiveness of health care. Information Theory. Shannon defined a measure of entropy as. that, when applied to an information source, could determine the capacity of the channel required to transmit the source as encoded binary digits.
Shannon s measure of entropy is taken as a measure of the information contained in a message. This is unlike to the portion of the message that is strictly determined hence predictable by inherent structures. Entropy as defined by Shannon is closely related to entropy as defined by physicists in statistical thermodynamics. This work was the inspiration for adopting the term entropy in information theory. Other useful measures of information include mutual information which is a measure of the correlation between two event sets.
Mutual information is defined for two events X and Y as. M X, Y H X, Y - H X - H Y. where H X, Y is the join entropy defined as. H X, Y - S p x iy i log p x iy i. Mutual information is closely related to the log-likelihood ratio test for multinomial distribution, and to Pearson s Chi-square test. The field of Information Science has since expanded to cover the full range of techniques and abstract descriptions for the storage, retrieval and transmittal of information.
Incidence and Prevalence Rates. Prevalence rate PR measures the number of cases that are present at a specified period of time. It is defined as Number of cases present at a specified period of time divides by Number of persons at risk at that specified time. These two measures are related when considering the average duration D. That is, PR IR. Note that, for example, county-specific disease incidence rates can be unstable due to small populations or low rates.
In epidemiology one can say that IR reflects probability to Become thick at given age, while the PR reflects probability to Be thick at given age. Other topics in clinical epidemiology include the use of receiver operator curves, and the sensitivity, specificity, predictive value of a test. Further Readings Kleinbaum D.
Kupper, and K. Muller, Applied Regression Analysis and Other Multivariable MethodsWadsworth Publishing Company, 1988. Miettinen O.Theoretical EpidemiologyDelmar Publishers, 1986. Software Selection. 1 Ease of learning, 2 Amount of help incorporated for the user, 3 Level of the user, 4 Number of tests and routines involved, 5 Ease of data entry, 6 Data validation and if necessary, data locking and security7 Accuracy of the tests and routines, 8 Integrated data analysis graphs and progressive reporting on analysis in one screen9 Cost.
No one software meets everyone s needs. Determine the needs first and then ask the questions relevant to the above seven criteria. Spatial Data Analysis. Many natural phenomena involve a random distribution of points in space. Biologists who observe the locations of cells of a certain type in an organ, astronomers who plot the positions of the stars, botanists who record the positions of plants of a certain species and geologists detecting the distribution of a rare mineral in rock are all observing spatial point patterns in two or three dimensions.
Such phenomena can be modelled by spatial point processes. The spatial linear model is fundamental to a number of techniques used in image processing, for example, for locating gold ore deposits, or creating maps. There are many unresolved problems in this area such as the behavior of maximum likelihood estimators and predictors, and diagnostic tools. There are strong connections between kriging predictors for the spatial linear model and spline methods of interpolation and smoothing.
The two-dimensional version of splines kriging can be used to construct deformations of the plane, which are of key importance in shape analysis. For analysis of spatially auto-correlated data in of logistic regression for example, one may use of the Moran Coefficient which is available is some statistical packages such as Spacestat. This statistic tends to be between -1 and 1, though are not restricted to this range. Values near 1 indicate similar values tend to cluster; values near -1 indicate dissimilar values tend to cluster; values near -1 n-1 indicate values tend to be randomly scattered.
Boundary Line Analysis. The main application of this analysis is in the soil electrical conductivity EC which stems from the fact that sands have a low conductivity, silts have a medium conductivity and clays have a high conductivity. Consequently, conductivity measured at low frequencies correlates strongly to soil grain size and texture. The boundary line analysis, therefore, is a method of analyzing yield with soil electrical conductivity data. This method isolates the top yielding points for each soil EC range and fits a non-linear line or equation to represent the top-performing yields within each soil EC range.
This method knifes through the cloud of EC Yield data and describes their relationship when other factors are removed or reduced. The upper boundary represents the maximum possible response to that limiting factor, e. ECand points below the boundary line represents conditions where other factors have limited the response variable.
Therefore, one may also use boundary line analysis to compare responses among species. Further Readings Kitchen N.K Sudduth, and S. Drummond, Soil Electrical Conductivity as a Crop Productivity Measure for Claypan Soils, Journal of Production Agriculture12 4607-617, 1999. Geostatistics Modeling. Further Readings Christakos G.Modern Spatiotemporal GeostatisticsOxford University Press, 2000. Box-Cox Power Transformation.
Among others the Box-Cox power transformation is often used for this purpose. trying different values of p between -3 and 3 is usually sufficient but there are MLE methods for estimating the best p. A good source on this and other transformation methods is Madansky A.Prescriptions for working StatisticiansSpringer-Verlag, 1988. For percentages or proportions such as for binomial proportionsArcsine transformations would work better.
The original idea of Arcsin p Ѕ is to establish variances as equal for all groups. The arcsin transform is derived analytically to be the variance-stabilizing and normalizing transformation. The same limit theorem also leads to the square root transform for Poisson variables such as counts and to the arc hyperbolic tangent i.Fisher s Z transform for correlation. The Arcsin Test yields a z and the 2x2 contingency test yields a chi-sq. But z 2 chi-sq, for large sample size.
A good source is Rao C.Linear Statistical Inference and Its ApplicationsWiley, 1973. How to normalize a set of data consisting of negative and positive values, and make them positive between the range 0. Define XNew X-min max-min. Box Cox power transformation is also very effective for a wide variety of nonnormality.
y transformed y l. where l ranges in practice from -3. As such it includes, inverse, square root, logarithm, etc. Note that as l approaches 0, one gets a log transformation. Multiple Comparison Tests. Multiple comparison procedures include topics such as Control of the family-Wise Error rate, The closure Principle, Hierarchical Families of Hypotheses, Single-Step and Stepwise Procedures, and P-value Adjustments.
Areas of applications include multiple comparisons among treatment means, multiple endpoints in clinical trials, multiple sub-group comparisons, etc. Nemenyi s multiple comparison test is analogous to Tukey s test, using rank sums in place of means and using n 2 k nk 1 12 Ѕ as the estimate of standard error SEwhere n is the size of each sample and k is the number of samples means.
Similarly to the Tukey test, you compare rank sum A - rank sum B SE to the studentized range for k. It is also equivalent to the Dunn Miller test which uses mean ranks and standard error k nk 1 12 Ѕ. Multilevel Statistical Modeling The two widely used software packages are MLwiN and winBUGS. They perform multilevel modeling analysis and analysis of hierarchical datasets, Markov chain Monte Carlo MCMC methodology and Bayesian approaches. Further Readings Liao T.Statistical Group ComparisonWiley, 2002.
Antedependent Modeling for Repeated Measurements. Many techniques can be used to analyze such data. Antedependence modeling is a recently developed method which models the correlation between observations at different times. Split-half Analysis. Notice that this is like factor analysis itself an exploratorynot inferential technique, i.
hypothesis testing, confidence intervals etc. simply do not apply. Alternatively, randomly split the sample in half and then do an exploratory factor analysis on Sample 1. Use those results to do a confirmatory factor analysis with Sample 2. Sequential Acceptance Sampling. Sequential acceptance sampling minimizes the number of items tested when the early results show that the batch clearly meets, or fails to meet, the required standards.
The procedure has the advantage of requiring fewer observations, on average, than fixed sample size tests for a similar degree of accuracy. Local Influence. Cook defined local influence in 1986, and made some suggestions on how to use or interpret it; various slight variations have been defined since then. But problems associated with its use have been pointed out by a number of workers since the very beginning. Variogram Analysis. A variogram summarizes the relationship between the variance of the difference in pairs of measurements and the distance of the corresponding points from each other.
Credit Scoring Consumer Credit Assessment. Accurate assessment of financial exposure is vital for continued business success. Accurate, and usable information are essential for good credit assessment in commercial decision making. The consumer credit environment is in a state of great change, driven by developments in computer technology, more demanding customers, availability of new products and increased competition. Banks and other financial institutions are coming to rely more and more on increasingly sophisticated mathematical and statistical tools.
These tools are used in a wide range of situations, including predicting default risk, estimating likely profitability, fraud detection, market segmentation, and portfolio analysis. The credit card market as an example, has changed the retail banking industry, and consumer loans. Both the tools, the behavioral scoring, and the characteristics of consumer credit data are usually the bases for a good decision. The statistical tools include linear and logistic regression, mathematical programming, trees, nearest neighbor methods, stochastic process models, statistical market segmentation, and neural networks.
These techniques are used to assess and predict consumers credit scoring. Further Readings Lewis E.Introduction to Credit ScoringFair, Isaac Co. Provides a general introduction to the issues of building a credit scoring model. Components of the Interest Rates. The pure rate This is the time value of money. A promise of 100 units next year is not worth 100 units this year. The price-premium factor If prices go up 5 each year, interest rates go up at least 5.
For example, under the Carter Administration, prices rose about 15 per year for a couple of years, interest was around 25. Same thing during the Civil War. In a deflationary period, prices may drop so this term can be negative. The risk factor A junk bond may pay a larger rate than a treasury note because of the chance of losing the principal. Banks in a poor financial condition must pay higher rates to attract depositors for the same reason. Threat of confiscation by the government leads to high rates in some countries.
Other factors are generally minor. Of course, the customer sees only the sum of these terms. These components fluctuate at different rates themselves. This makes it hard to compare interest rates across disparate time periods or economic condition. The main questions are how are these components combined to form the index. A simple sum. A weighted sum. McNemar Change Test For the yes no questions under the two conditions, set up a 2x2 contingency table McNemar s test of correlated proportions is z f01 - f10 f01 f10 Ѕ.
The same applies to other index numbers. Partial Least Squares. The method aims to identify the underlying factors, or linear combination of the X variables, which best model the Y dependent variables. Growth Curve Modeling. Sometimes we simply wish to summarize growth observations in terms of a few parameters, perhaps in order to compare individuals or groups. Many growth phenomena in nature show an S shaped pattern, with initially slow growth speeding up before slowing down to approach a limit.
These patterns can be modelled using several mathematical functions such as generalized logistic and Gompertz curves. Saturated Model Saturated Log Likelihood. Pattern recognition and Classification. What is Biostatistics. Recent advancement in human genome marks a major step in the advancement of understanding how the human body works at a molecular level.
The biomedical statistics identifies the need for computational statistical tools to meet important challenges in biomedical studies. The active areas are Clustering of very large dimensional data such as the micro-array. Clustering algorithms that support biological meaning. Network models and simulations of biological pathways.
Pathway estimation from data. Integration of multi-format and multi-type data from heterogeneous databases. Information and knowledge visualization techniques for biological systems. Further Reading Cleophas T. Zwinderman, and T. Cleophas, Statistics Applied to Clinical TrialsKluwer Academic Publishers, 2002. Shmulevich, Computational and Statistical Approaches to GenomicsKluwer Academic Publishers, 2002.
Evidential Statistics. In most cases the index is form both empirically and assigned on basis of some criterion of importance. Should this observation lead me to believe that condition C is present. Does this observation justify my acting as if condition C were present. Is this observation evidence that condition C is present. We must distinguish among these three questions in terms of the variables and principles that determine their answers.
It is already recognized that for answering the evidential question current statistical methods are seriously flawed which could be corrected by a applying the the Law of Likelihood. This law suggests how the dominant statistical paradigm can be altered so as to generate appropriate methods for objective, quantitative representation of the evidence embodied in a specific set of observations, as well as measurement and control of the probabilities that a study will produce weak or misleading evidence.
Questions of the third type, concerning the evidential interpretation of statistical data, are central to many applications of statistics in many fields.Statistical Evidence A Likelihood ParadigmChapman Hall, 1997. Further Reading Royall R. Statistical Forensic Applications. One consequence of the failure to recognize the benefits that an organized approach can bring is our failure to move evidence as a discipline into volume case analytics.
There has been an over emphasis on the formal rules of admissibility rather than the rules and principles of a methodological scientific approach. As the popularity of using DNA evidence increases, both the public and professionals increasingly regard it as the last word on a suspect s guilt or innocence. As citizens go about their daily lives, pieces of their identities are scattered in their wake.
It could as some critics warn, one day place an innocent person at the scene of a crime. The traditional methods of statistical forensic, for example, for facial reconstruction date back to the Victorian Era. Tissue depth data was collected from cadavers at a small number of landmark sites on the face. Samples were tiny, commonly numbering less than ten.
Although these data sets have been superceded recently by tissue depths collected from the living using ultrasound, the same twenty-or-so landmarks are used and samples are still small and under-representative of the general population. A number of aspects of identity--such as age, height, geographic ancestry and even sex--can only be estimated from the skull. Current research is directed at the recovery of volume tissue depth data from magnetic resonance imaging scans of the head of living individuals; and the development of simple interpolation simulation models of obesity, ageing and geographic ancestry in facial reconstruction.
Any cursory view of the literature reveals that work has centered on thinking about single cases using narrowly defined views of what evidential reasoning involves.Statistical Science in the CourtroomSpringer Verlag, 2000. Spatial Statistics. Further Readings Diggle P.The Statistical Analysis of Spatial Point PatternsAcademic Press, 1983.Spatial StatisticsWiley, 1981. What Is the Black-Sholes Model.
Further Readings Clewlow L. Strickland, Implementing Derivatives ModelsJohn Wiley Sons, 1998. What Is a Classification Tree. There are several methods of deciding when to stop. Further Reading Gastwirth J. The simplest method is to split the data into two samples. A tree is developed with one sample and tested with another. As the number of nodes used changes the mis-classification rate changes.
The mis-classification rate is calculated by fitting the tree to the test data set and increasing the number of branches one at a time. The number of nodes which minimize the mis-classification rate is chosen. Graphical Tools for High-Dimensional Classification Statistical algorithmic classification methods include techniques such as trees, forests, and neural nets.
Such methods tend to share two common traits. They can often have far greater predictive power than the classical model-based methods. And they are frequently so complex as to make interpretation very difficult, often resulting in a black box appearance. An alternative approach is using graphical tool to facilitate investigation of the inner workings of such classifiers. Additional information can be visually incorporated as to true class, predicted class, and casewise variable importance.
The A generalization of the ideas such as the data image, and the color histogram allows simultaneous examination of dozens to hundreds of variables across similar numbers of observations. Careful choice of orderings across cases and variables can clearly indicate clusters, irrelevant or redundant variables, and other features of the classifier, leading to substantial improvements in classifier interpretability.
The various programs vary in how they operate. For making splits, most programs use definition of purity. More sophisticated methods of finding the stopping rule have been developed and depend on the software package.
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