Re: A statistician would argue ....
".... that there is life elsewhere in the Universe."
First problem is to define life.
The second is to work out what steps have to be undergone to create the sub-systems it needs in a pre-biotic situation.
The next is to bring those subsystems them together. Not only do they have to have come about in the same place but also at the same time. It's no use, for example, if an energy handling system comes about after all the amino acid/nucleotide stuff has developed but fallen apart because something destructive has happened to the components.
They have to come together in a way that enables them to function together.
They also have to survive whatever changes that befall their planet including what they evolve into; the development of green plants, for instance, was a big threat to earlier life forms because it released free oxygen for the first ime, which is very poisonous to life that can't cope with that.
Although life as we know it is very good at perpetuating the otherwise improbable it is, itself, extremely unlikely.
As far as I can see the traditional statistical argument has been there are a lot of suitably sized planets (whatever suitably sized might mean) in the habitable zone and we know life started here on Earth (so how can might it be?) so there must be lots out there and where are they? Well, we know of one: here, us. Without looking at the individual requirements, estimating their likelihood (not easy, I'd have thought) and combining them there isn't a realistic assessment of how likely it is that eliminates observer bias.