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More about Discovery Process Models

P.J. Lee

Jo Anne DeGraffenreid (ed.)

in Statistical Methods for Estimating Petroleum Resources

In Chapter 3 we discussed the concepts, functions, and applications of the two discovery process models LDSCV and NDSCV. In this chapter we will use various simulated populations to validate these ... More

In Chapter 3 we discussed the concepts, functions, and applications of the two discovery process models LDSCV and NDSCV. In this chapter we will use various simulated populations to validate these two models to examine whether their performance meets our expectations. In addition, lognormal assumptions are applied to Weibull and Pareto populations to assess the impact on petroleum evaluation as a result of incorrect specification of probability distributions. A mixed population of two lognormal populations and a mixed population of lognormal, Weibull, and Pareto populations were generated to test the impact of mixed populations on assessment quality. NDSCV was then applied to all these data sets to validate the performance of the models. Finally, justifications for choosing a lognormal distribution in petroleum assessments are discussed in detail. Less

Maximum Likelihood and Generalized Linear Models

Andy Hector

in The New Statistics with R: An Introduction for Biologists

This chapter revisits a regression analysis to explore the normal least squares assumption of approximately equal variance. It also considers some of the data transformations that can be used to ... More

This chapter revisits a regression analysis to explore the normal least squares assumption of approximately equal variance. It also considers some of the data transformations that can be used to achieve this. A linear regression of transformed data is compared with the generalized linear model equivalent that avoids transformation by using a link function and non-normal distributions. Generalized linear models based on maximum likelihood use a link function to model the mean (in this case a square-root link) and a variance function to model the variability (in this case the gamma distribution where the variance increases as the square of the mean). The Box–Cox family of transformations is explained in detail.Less

Generalized Linear Models

Andy Hector

in The New Statistics with R: An Introduction for Biologists

This chapter revisits a regression analysis to explore the normal least squares assumption of approximately equal variance. It also considers some of the data transformations that can be used to ... More

This chapter revisits a regression analysis to explore the normal least squares assumption of approximately equal variance. It also considers some of the data transformations that can be used to achieve this. A linear regression of transformed data is compared with a generalized linear-model equivalent that avoids transformation by using a link function and non-normal distributions. Generalized linear models based on maximum likelihood use a link function to model the mean (in this case a square-root link) and a variance function to model the variability (in this case the gamma distribution, where the variance increases as the square of the mean). The Box–Cox family of transformations is explained in detail.Less