AB,
The example of choosing what you believe is not realistic. No one can choose what they believe, but they can choose what evidence to consider in reaching a conclusion. We are all guilty somewhat of cherry picking the evidence we want to consider - and this is where the freedom to guide our choice kicks in.
It's true that we're all susceptible to biases when considering evidence - that's why the scientific method in particular is so heavily geared to trying to eliminate them - for example with double blind trials.
Your problem however is that what you call "evidence" is actually no such thing. When for example you can't find your car keys, pray for a bit and then then find them the narrative you tell yourself is that that's evidence for an interventionist god. To test that hypothesis however you'd need some way to eliminate the possibility that there was some other cause, or more likely it was just co-incidence. You might for example ask your wife to hide ten items around the house, pray to God to help you find them and them count the successes. Then you could repeat the experiment without the praying bit and compare the results.
The problem with
that though is that whenever people have tested claims of evidence for various gods they've always failed - the results are the same whether you pray or not. Bluntly, while you claim evidence for your particular god the reason that you've never been able to provide any of it is that there is none. It turns out that what you
call "evidence" is precisely confirmation bias, or one or more of a range of other biases.
Sorry, but there it is. Stick with personal faith claims and it's no-one's business but your own; claim
evidence for your beliefs though and you'll continue to crash and Burns.