The prior term for the demographic parameters, p, expands out into its components and as a product over the Y pairs of populations (6) p = ∏ i = 1 Y p (θ A, i ) p (θ D 1, i ) p (θ D 2, i ) p (ζ D 1, i ) p (ζ D 2, i ) p (τ B, i ) p (m i ).
The prior term for the vector of divergence times for each of the Y pairs of populations, T, can be expanded as (7) p (T ) = p (t ) p (τ | t ), where τ is an ordered set of divergence-time parameters { τ1,…, τ| τ |} whose length | τ | can range from 1 to Y, and t is a vector of indices (t1,…, t Y ), where t i ∈{1,…,| τ |}.
Therefore, we do not consider the prior term in the following proof for simplicity.
As for the prior term p t), the total sample space of t is all the possible partitionings of the Y pairs of populations into 1 to Y divergence-time classes, where each partitioning consists of non-overlapping and non-empty subsets whose union is the Y pairs.
The first term is the prior term which is the classic boundary length term [25] for smooth segmentation boundaries.
For the prior terms, let p j be the frequency of the A allele at SNP j in the population, f i be the inbreeding coefficient for sample i, and z j be the probability that an individual sample for SNP j may fail entirely.
Some of these include, Panther Camp held in the Summer prior to the Fall term for incoming freshmen, where students spend a weekend in a retreat center learning all the traditional Golden Panther cheers, chants, traditions meeting other incoming students.
The model with the square term for prior cost had no considerable improvement in predictive R-square.
For this purpose, we devised a modified cost function, which includes a term for prior information (See below. Also see [ Molinelli, Korkut, Wang et al., 2013] and [ Miller et al., 2013]).
Note that if multiple prior types are used, as is the case in our scenario, Equation 5 contains one likelihood term for each prior type.
A multiple regression including the effects on the chick feeding anomaly of the log-transformed average wind speed of the present day, log-transformed wind speed the previous day, and an interaction term for present and prior wind speed, shows highly significant positive effects of both previous day's wind speed (F3,197 = 16.21, P<0.001) and the interaction term (P = 0.019).
