Miklós Kásler - Zoltán Szentirmay (szerk.): Identifying the Árpád Dynasty Skeletons Interred in the Matthias Church. Applying data from historical, archaeological, anthropological, radiological, morphological, radiocarbon dating and genetic research (Budapest, 2021)

Investigated bone samples and methods

Let us denote by p(w; v; k) the population frequency of the allele for the

w-th locus (w = 1; 2; ::7);

v-th allele (v = 1 for maternal, v = 2 for paternal allele); k-th person (k = 1;2; 10).

For practical reasons, the frequency of missing data is set to 1. For example p(3; 2; 4) = 0:052; it is

the population frequency of the third locus of the fourth persons paternal allele.

Neglog likelihood: In our analysis the basic concept is the logarithm of the likelihood of the whole sample. To avoid negative numbers, we multiply the log likelihood by (-1 ), and refer the number as NL (negative log-likelihood). If all of the alleles were independent, then NL = 216.330451 In the general case

m 2 n

NL = - 52 log(p(w’ fc))w=lv=l k=l

Thanks to the negative multiplier, any improvement in NL refers to a better family structure of the investigated persons. It may occur that for some structure NL is larger than the above cornerstone number, and such a situation tells us that the structure is out of question. We shall seek the appropriate family structure by trial and error method for the number of all possible structure is astronomically large. We do not present all of the details in our research, but it will be motivated solely on corresponding NL numbers.

In relation to father, grandfather and uncles NL=205.639\

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