ArbitraryPrior

class ArbitraryPrior

Enacts a prior probability density distribution on the generation of the most recent common ancestor (MRCA) between extant hereditary stratigraphic columns that is arbitrary, but computationally efficient.

The prior expectation for MRCA generation is taken as equal probability within each interval between ranks with common strata retained by both extant columns up through the first retained disparity between the columns.

Prior probability density is assumed uniformly distributed within each interval between coincident retained ranks. So, conditioning on the assumption that the true generation of the MRCA occurs within a particular interval, the prior expected value for the MRCA generation will be the midpoint of the interval.

This prior is simple to compute, but may not meaningfully reflect the a reasonable pre-expectation for the MRCA generation. Importantly, the enacted prior expectation will depend directly on the instrumentation used (i.e., the distribution of coincident retained strata induced by the chosen stratum retention policy). For example, a wide interval between coincident retained ranks and a short interval between coincident retained ranks will be assigned equal prior probability, resulting in greater per-generation prior probability within the small window than within a wide window.

This prior policy guarantees the maximum likelihood estimate to fall between the last retained commonality and the first retained disparity of two extant columns. Because each interval between coincident retained ranks has equal prior probability, the likelihood of the true MRCA falling within preceding intervals strictly decreases with qualification by spurious differentia collisions (i.e., common retained strata). This property makes maximum likelihood estimation under this prior especially efficient.

__init__()

Methods

CalcIntervalConditionedMean(begin_rank: int, end_rank: int) → float

Calculate the centriod of prior probability mass within an interval of possible MRCA generations.

Parameters

begin_rankint

The starting rank of the interval, inclusive.

end_rankint

The ending rank of the interval, exclusive.

Returns

float

The prior expected generation of MRCA conditioned on the assumption that the MRCA falls within the given interval.

CalcIntervalProbabilityProxy(begin_rank: int, end_rank: int) → float

Characterize the prior probability of the MRCA generation falling within an interval range.

Parameters

begin_rankint

The starting rank of the interval, inclusive.

end_rankint

The ending rank of the interval, exclusive.

Returns

float

The proxy statistic, proportional to the true estimated interval probability of the MRCA value by a fixed (but unspecified) constant proportion.

SampleIntervalConditionedValue(begin_rank: int, end_rank: int) → int

Sample a generation of the MRCA conditioned on the assumption that the MRCA falls within the given interval.

Parameters

begin_rankint

The starting rank of the interval, inclusive.

end_rankint

The ending rank of the interval, exclusive.

Returns

int

A sampled generation of the MRCA, conditioned on the assumption that the MRCA falls within the given interval.