Re: [VCFtools-spec] Likelihood or probability [EXT]

[Petr D. <pd...@sa...>]

The specification is correct in what it says. They are genotype 
likelihoods, P(data|genotype). They don't scale to 1 as can be 
immediately seen in any VCF with the PL field, one of the values is 
almost always 0, for example "0,31,178".

Petr

On 09/07/2020 02:20, Jonathan Margoliash via VCFtools-spec wrote:
> Or maybe this is the point of my confusion:
>
> What constitutes the model and its parameters, and what constitutes 
> the data? If the underlying reads (or whatever sequencing data is 
> available) is used as parameters to create the model, and the 
> genotypes are the different outcomes the model assigns different 
> probabilities based on that data, then this seems to be a probability 
> function which is incorrectly being called a likelihood function. But 
> if the choice of genotype for each sample at each locus is a set of 
> parameters in the model, and the reads (or underlying sequencing data) 
> is the dataset whose probability is being estimated here, then this is 
> an appropriately named likelihood function.
>
> I don't know which interpretation is correct.
>
> Thank you,
>
> Jonathan
>
> On Wed, Jul 8, 2020 at 3:50 PM Jonathan Margoliash 
> <jma...@en... <mailto:jma...@en...>> wrote:
>
>     Hello there,
>
>     I'm trying to interpret what the GL and PL fields in the VCF spec
>     mean. They're called likelihoods. But I believe they are
>     probability functions. Can someone clarify?
>
>     My understanding (in line with this wikipedia article
>     [en.wikipedia.org]
>     <https://urldefense.proofpoint.com/v2/url?u=https-3A__en.wikipedia.org_wiki_Likelihood-5Ffunction-23Likelihood-5Ffunction-5Fof-5Fa-5Fparameterized-5Fmodel&d=DwMFaQ&c=D7ByGjS34AllFgecYw0iC6Zq7qlm8uclZFI0SqQnqBo&r=xdvdTaAZDWitAtUqWIZL0A&m=jYWtNGrhV2_93ufy8-aApWZ4gnv7EYP0PwR6AOnvbI4&s=AFghjTcK3NOfa-UY9oa1b5dEFn5sAMHy9gSYpOdl5C8&e=>)
>     is that likelihood functions are functions over different sets of
>     models with a fixed data set in mind, while in the VCF spec the GL
>     and PL fields vary over different genotypes (different data
>     outcomes), while the model that produced the VCF remains the same.
>
>     Or another way of putting it: the values of the GL field, after
>     exponentiating them to remove the log_10 scaling, should always
>     sum to 1, yes? That's a property of probability functions, not
>     likelihood functions. Or maybe I'm misunderstanding.
>
>     My guess is that the VCF spec is calling them likelihoods because
>     they're the log-scaled, even though then they should correctly be
>     called log-probabilities.
>
>     Any clarification appreciated. Thanks!
>
>     Jonathan
>
>
>
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