How has your local area changed due to immigration?

But then it wouldn’t be a contrary explanation to the one I’ve offered; it’s just focusing on a different aspect to it. I’ve already agreed that higher poverty in these immigrant communities is probably a significant influencing factor (though not the only one), and that higher poverty has a general correlation with littering. All I’ve done is added the logical conclusion of this: “Therefore the inclination to litter is higher in these immigrant communities”.
As I’ve said, I’m not trying to assign the difference to immigration in and of itself. I’ve assigned it to a specific pattern of immigration (e.g. immigration from particularly poor parts of the world). So the correlation you’ve observed between littering and poverty (as opposed to pure immigrant status) is something I fully expect already.
Those aren’t assumptions, they’re part of my observations (namely, observation 1).

It's not the same explanation because it makes a different assumption about the poverty (or lack thereof) of the immigrant community.

Reminder that you've blamed this community for "ruining" your city, which relies on assumptions about how the would-be British community (if it lived in the same place as these immigrants do now) would behave.

Are you claiming to know where all the immigrants in these communities come from and what littering is like in their town / city of origin?

What “different assumption”? I’m agreeing with your assumption, that there is greater poverty in the immigrant community.
I don’t think you’re saying anything contrary to what I am. You’re blaming littering on things like poverty and lack of education (which I agree with), and I’m just also explaining where the poverty and lack of education came from in this case.
Again, that’s not an “assumption”, that’s my conclusion. My four observations lead me conclude that the current immigrant community is probably littering more than the communities that would have otherwise been there had it not been for immigration. (Which could be due to higher poverty or lower education or other features of these communities).
Obviously not for every single individual, but broadly speaking (at the wider population level), yes. I know where large majorities of the immigrant communities have come from, and what those towns and cities are like.

You would need to make an assumption about the would-be British community in order to make that conclusion, that's my point. I am not making that assumption, you are. If that assumption doesn't hold then you cannot make that conclusion (not assess the probability of that conclusion).

If you don't know where everyone in these communities come from then you are again making assumptions.

I don’t understand your point here. What assumptions do you think I’m using, exactly?
Earlier you said: “It would explain all of your points if the level of poverty seen among the immigrant community is greater than that of the rest of Birmingham. That's the only assumption it would require.”
That’s also the only thing I’m assuming, as far as I can tell.

The assumption that a would-be British community, living in the places these immigrants currently live, would litter less (or suffer less poverty, etc). You require that assumption if you wish to claim that immigrants have made it worse than it would have been (i.e. they've "ruined" your city).

You're also making quite sweeping assumptions about where these immigrants have come from.

But as I said, that’s not an “assumption”. That’s my conclusion.
The four observations I gave are explained by the immigrant communities having a higher inclination to litter than the general British population (due to higher poverty and other things), which implies that there would probably be less litter if the areas were inhabited by British communities.
Again, not an assumption but an observation. I know where they have come from, broadly speaking; I’m not guessing.

It's not something you can conclude from those observations. They only tell you the relative difference between the immigrant communities and the British communities that already exist in Birmingham, not would-be British communities that would take their place. To draw your conclusion would be to assume that the would-be British communities would suffer less poverty than the immigrant communities, which isn't necessarily the case.

”Broadly speaking" is not the same thing as absolutely knowing where they come from, so this is still an assumption. For all you know some of these people could actually be British.

I’m not saying it’s necessarily the case. I’m saying it’s probably the case.
Furthermore when I say that parts of the city have been “ruined by immigration”, I’m speaking relative to the population that were there before, not some other hypothetical population that might have moved there instead.
Sure, there’s a (small IMO) chance that a British community could have moved in and ruined those areas in the same way, but in reality it was immigrant communities.
But i’m not even claiming to know where each and every individual came from. Why would I need to know that, when I’m not making claims about individuals? I’m making broad claims about a population. Broadly speaking, I know where they came from.

How are you making that assessment on the basis of probability, if not by requiring additional assumptions? Do you know the likelihoods involved? Why is the chance "small"? It doesn't matter if you are comparing against the population that was there before or the rest of Birmingham's population, the assumption is still being made.

Broadly speaking" is nevertheless still an assumption, you are making a judgement on an entire community on the basis of what is (presumably) very limited information.

It’s simply a consequence of my four observations. I can see, using several different comparisons, that these immigrant communities litter more prolifically than the average population of Birmingham / Britain, and (as per my claim that the areas have been ruined by immigration), the population that was there before. This isn’t an assumption; I can see it for myself.
I don’t understand how that is an assumption. I’m making a broad judgement about a community based on broad knowledge of that community. I would need more individualised information if I were making judgements about individuals, but I’m not doing that.

It's only a consequence from your observations if the would-be British community were sampled from the same populations you're comparing against. This is not something you're observing, it's an assumption you've made.

The assumption is that your "broad knowledge" about the community has any relevance to the judgement you're making. How many people live in the community and how many do you know (well enough) to make that judgement? Are the people littering in this community immigrants or are they British?

Not necessarily. They could be a British community that litters less than average, or about average, or more than average. But since I’ve observed that the immigrant community already litters significantly more than most British ones (in fact I’ve personally never seen a majority British community littering quite as much), it’s less likely that the would be-British community would litter even more than that.
Unless you assume that there’s some reason why the would-be British community is going to be sampled from the extreme end of the population in terms of littering.
Why wouldn’t it be relevant? They’re communities that are majority-immigrant (it’s easy enough to look up statistics on it - for example Sparkhill is less than 8% White British). And they’re also areas that suffer significantly more from littering than other areas of Birmingham.
It could be the 8% White British population that are responsible for all or most of the litter, but then you’d need a host of extra assumptions to explain why that is, in a way that coincides with the other observations I made.
Whereas my single conclusion - that these immigrant communities have a higher inclination to litter (due to poverty or whatever other reason) - already accounts for this observation without the need for more assumptions.

Whether the immigrant community litters significantly more than most British ones makes no difference. To conclude that it's therefore more likely that the would-be British community would litter just as much (or even more) requires an assumption about who / where this community would sample from.
You're assuming that the littering comes specifically from the immigrants from these communities and you're also making assumptions about where these immigrants come from (if they are immigrants at all). Being non-white doesn't automatically mean you're not British, these people could have been born and raised in Britain. Again, how many people live in these communities and how many do you know (well enough) to make these judgements about them?

It absolutely makes a difference. In order to not make an assumption, we have to say we don't know which part of the British population the would-be British community would sample from. That means they're no more likely to come from one part than another. If they're equally likely to come from any part of the population, that makes it unlikely they would come from the minority of communities that litter more, since there are far more communities that litter less.
By analogy: If you make no assumptions about the fairness of a dice, you're saying you don't know which number it is weighted towards - if any. Which means that to you, no number is any more likely to be rolled than than another. If all numbers are equally likely, that means from your perspective you're more likely to roll a number from a majority group (e.g. greater than 2) than you are to get them from a minority group (e.g. less than 2). On the other hand, if you believe that the underlined statement is false, it requires you to assume the dice is weighted towards lower numbers.
The same applies to your second point. If we make no assumptions about which individuals are littering in these communities, then each individual is equally likely to be responsible. But since there are far more immigrants compared to non-immigrants, that automatically makes it more likely that any given piece of litter was dropped by one of them. (Note: I'm saying "immigrant" just as shorthand here. What I mean is, a member of an immigrant community. It includes people who were born and raised in Britain but within these communities). Again, I'm not having to make any assumptions where any individual has come from. I don't need to know that in order to speak about the population in broad terms. In broad terms. I know where the population has come from; I don't need to assume that.

This isn't how likelihood works. The likelihood of an event occurring doesn't magically change just because you don't know what the true underlying likelihood is.

If you don't know what part of the population the would-be British community would come from then the answer is 'I don't know', not 'they are equally likely to come from any part of the population'. You can claim an event is more / less likely "to you", "from your perspective", etc, but that would simply be incorrect; you'd be misapplying probability.

The same goes for dice and the assumptions you're making about the people in the community. And, again, how many people in these communities do you actually know? Furthermore, if someone is born and raised in Britain then they aren't an immigrant.

That is exactly how Bayesian Probability works, actually. As a professional actuary, I would know.
“Bayesian probability is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification of a personal belief.”
This is why, when you flip a coin and call it in the air, we say that the probability of heads is 50%, even though physically speaking it's a matter of 100% definite fact that the coin will land on heads (or tails) based on how hard you flipped it, gravity, air resistance, weighting etc. The "50%" probability merely represents your state of not knowing which side it will land on, and having no reason to favour one or the other. To someone else, who knows how the coin is weighted, the probability might be 60%. To someone else, who has already seen how the coin landed before you have, it would be 100% or 0%.
This is also why, in ordinary language, I can say things like “You probably ate food yesterday”. To me that’s a valid statement, but to you there’s no “probably” about it; you know 100% whether you did or you didn’t; it's a matter of established fact.

That isn't how Bayesian probability works. As a professional statistician, I would know.

Not knowing what the true likelihood is does not automatically mean that all outcomes are equally likely, not even in a Bayesian framework. That would depend on what prior you choose, some priors could make certain outcomes more likely than others.

A bad application of Bayesian methods would be to choose whatever prior you like without justification. Uniform priors, which are what you're using, are generally not suitable because events in the real world are typically not all equally likely.

If you're absolutely fixed on using a uniform prior then you're obviously free to do so, nobody can stop you, but this doesn't resolve your problem. You're still making an assumption by choosing to use this prior.

That isn't how Bayesian probability works. As a professional statistician, I would know.

Not knowing what the true likelihood is does not automatically mean that all outcomes are equally likely, not even in a Bayesian framework. That would depend on what prior you choose, some priors could make certain outcomes more likely than others.

A bad application of Bayesian methods would be to choose whatever prior you like without justification. Uniform priors, which are what you're using, are generally not suitable because events in the real world are typically not all equally likely.

If you're absolutely fixed on using a uniform prior then you're obviously free to do so, nobody can stop you, but this doesn't resolve your problem. You're still making an assumption by choosing to use this prior.