priors
Classes to specify prior expectation for the distribution of MRCA generation between hereditary stratigraphic columns, to assist in estimating the phylogenetic relationship of hereditary stratigraphic columns.
Classes
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. |
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Enacts a prior expectation that the generation of the most recent common ancestor (MRCA) between extant hereditary stratigraphic columns becomes exponentialy less likely with increasing antiquity. |
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Enacts a prior expectation that the generation of the most recent common ancestor (MRCA) between extant hereditary stratigraphic columns becomes exponentialy less likely with increasing antiquity. |
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Enacts a prior expectation that the generation of the most recent common ancestor (MRCA) is equally likely to occur at any generation since genesis. |
- 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.
- CalcIntervalConditionedMean(begin_rank: int, end_rank: int) float[source]
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[source]
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[source]
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.
- class GeometricPrior
Enacts a prior expectation that the generation of the most recent common ancestor (MRCA) between extant hereditary stratigraphic columns becomes exponentialy less likely with increasing antiquity.
This prior calculates the exact, discrete geometric distribution of time to MRCA expected under the Wright-Fisher model [1].
Populations. In Mathematical Statistical Physics (pp. 489-545). Elsevier. https://doi.org/10.1016/S0924-8099(06)80048-X
Notes
A static factory function to init an instance with a growth factor calculated from contextual information like population size and the number of generations elapsed since genesis should be made available in the future.
See Also
- GeometricPrior
A continuous approximation of this prior.
- CalcIntervalConditionedMean(begin_rank: int, end_rank: int) float[source]
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[source]
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[source]
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.
- class ExponentialPrior
Enacts a prior expectation that the generation of the most recent common ancestor (MRCA) between extant hereditary stratigraphic columns becomes exponentialy less likely with increasing antiquity.
This prior provides a continuous approximation of the geometric distribution of time to MRCA expected under the Wright-Fisher model [1].
Populations. In Mathematical Statistical Physics (pp. 489-545). Elsevier. https://doi.org/10.1016/S0924-8099(06)80048-X
Notes
A static factory function to init an instance with a growth factor calculated from contextual information like population size and the number of generations elapsed since genesis should be made available in the future.
See Also
- GeometricPrior
An exact, discrete analog of this prior.
- CalcIntervalConditionedMean(begin_rank: int, end_rank: int) float[source]
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[source]
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[source]
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.
- class UniformPrior
Enacts a prior expectation that the generation of the most recent common ancestor (MRCA) is equally likely to occur at any generation since genesis.
See Also
- GeometricPrior
An exact, discrete analog of this prior.
- CalcIntervalConditionedMean(begin_rank: int, end_rank: int) float[source]
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[source]
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[source]
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.