Nthomas Baker Case

The following example demonstrates the use of probability and statistics to navigate through a genealogical bottle neck or what is sometimes called a 'brick wall'.

I take the case of the hermit Thomas Baker and to find him in the 1891 census and earlier. I could not solve this case till the release of the 1921 census in 2011.

The calculation:

First is to note the variance in the timing of Thomas' birth which is all too common an occurrence. To accommodate this we will assume his birth year as 1856±6 years.

Canada in 1891 has the population of P1891 = 4,833,239 and the census records 78,597 males with the name Thomas. This gives the frequency, in 1891 Canada of Thomas as

fThomas = 78,597/4,833,239= 0.0163.
As a check on the math so far, the number of Thomas Bakers in Canada in 1891 is estimated to be EThomas Baker = P1891 x fThomas x fBaker = 156.48. We find NThomas Baker = 115, the actual number in the 1891 census. Although the estimate is off by about 40% we don't expect much accuracy here for the choice of a boy's name will be influenced by the families culture and hence the frequency of naming. The check is only to see if we are wildly off or not. The estimate seems quite good at this point.

The probability of living in Ontario and born in Ontario in 1891 is found to be bOntario = 0.352 and the probability of being born between 1850 and 1862 is

y±6 = 763,027/P1891 = 0.158.

Thus the number of Thomas Bakers born between 1850 and 1862 and in Ontario is expected to be

E±6 Ontario = EThomas Baker x y±6 x bOntario = 156.48 x 0.158 x .352 =
This is a rather conservative estimate for we initially used the whole population of Canada to locate Thomas.

Could Thomas have come from the United States? Checking the 1900 US census gives 8 cases of Thomas Baker within the age range and born somewhere in Canada. None have mothers born in Ireland, only one is a farmer but has been in the US for 30 years and all immigrated before 1891. The chances of any being our hermit is extreme requiring a lot of strange movements for a relatively poor person. Trying to fit any of the US cases would require solving a good deal of inconsistencies and hence not very likely of satisfying the GPS. We know that it is theoretically possible for Thomas to have come from any country in the world — and to be certain we'd have to prove it with p(n>1)=0 exactly. This is impossible to do and hence we prefer a reasonably low probability so progress can be made.

The 1921 census information was critical. Without knowing where Thomas' parents were born we would have had

p(n>1)= 1.65 x