Estimating Mature Plays
33
numerical algorithm for its solution. The statistical treatment of the
lognormal likelihood function is explained in Appendix A.
When Kaufman proposed this discovery process model, a numerical algorithm was used to solve the likelihood function (β = 1).
Unfortunately, the algorithm is valid only when N is large (say, N > 300).
The model has been criticized by statisticians and has been ignored
by most petroleum assessment experts (who do not accept, or who are
reluctant to accept, the principle of the discovery process model because
petroleum geologists were not convinced by the example presented).
Lee and Wang (1985) solved the likelihood function (Eq. 3.5) directly
with an algorithm that can accommodate a wide range of values for
total number of pools, N (the values tested ranged from 10 to more than
2000); number of discoveries, n (the values tested ranged from 9 to about
700); and β (ranging from –1 to 100). This algorithm requires intensive computation. Nevertheless, it provides reasonable predictions, as
demonstrated by the populations tested. The successful solution of the
likelihood function opens the possibility of using the discovery process
models in petroleum resource assessments and improving their quality.
Nonparametric Discovery Process Model
A fundamental step in the probabilistic approach is to choose a prior
probability distribution that the data obeys. So far, Kaufman (1963,
1965), Lee and Wang (1985, 1990), and Meisner and Demirmen (1981)
have adopted the lognormal pool-size distribution to represent a
superpopulation. The superpopulation framework, with its lognormal
model, seems to be the most favored method, especially when the ratio
of sample size (number of discovered pools) to total number of pools in
the population is low. However, the choice of a prior probability distribution to describe pool-size distribution has been a controversial topic
for the past several decades.
In the previous sections we demonstrated how to use the lognormal discovery process model (parametric)—LDSCV—to estimate
pool-size distribution. We shall now discuss the use of a nonparametric
model that does not benefi t from a prior distribution.
A play contains N pools within the same underlying cumulative
probability distribution F. If n pools are discovered randomly from the
play, then the probability density for each pool is simply
1
i
p
n
=
(3.6)
33
numerical algorithm for its solution. The statistical treatment of the
lognormal likelihood function is explained in Appendix A.
When Kaufman proposed this discovery process model, a numerical algorithm was used to solve the likelihood function (β = 1).
Unfortunately, the algorithm is valid only when N is large (say, N > 300).
The model has been criticized by statisticians and has been ignored
by most petroleum assessment experts (who do not accept, or who are
reluctant to accept, the principle of the discovery process model because
petroleum geologists were not convinced by the example presented).
Lee and Wang (1985) solved the likelihood function (Eq. 3.5) directly
with an algorithm that can accommodate a wide range of values for
total number of pools, N (the values tested ranged from 10 to more than
2000); number of discoveries, n (the values tested ranged from 9 to about
700); and β (ranging from –1 to 100). This algorithm requires intensive computation. Nevertheless, it provides reasonable predictions, as
demonstrated by the populations tested. The successful solution of the
likelihood function opens the possibility of using the discovery process
models in petroleum resource assessments and improving their quality.
Nonparametric Discovery Process Model
A fundamental step in the probabilistic approach is to choose a prior
probability distribution that the data obeys. So far, Kaufman (1963,
1965), Lee and Wang (1985, 1990), and Meisner and Demirmen (1981)
have adopted the lognormal pool-size distribution to represent a
superpopulation. The superpopulation framework, with its lognormal
model, seems to be the most favored method, especially when the ratio
of sample size (number of discovered pools) to total number of pools in
the population is low. However, the choice of a prior probability distribution to describe pool-size distribution has been a controversial topic
for the past several decades.
In the previous sections we demonstrated how to use the lognormal discovery process model (parametric)—LDSCV—to estimate
pool-size distribution. We shall now discuss the use of a nonparametric
model that does not benefi t from a prior distribution.
A play contains N pools within the same underlying cumulative
probability distribution F. If n pools are discovered randomly from the
play, then the probability density for each pool is simply
1
i
p
n
=
(3.6)