# Mathematical logic and statistics

1. Oct 31, 2012

### Cinitiator

Let's say that a treatment A has been proven to have an impact on the levels of B with a given confidence interval.
Let's also say that we know that the treatment C causes the treatment A to be imposed on our sample.
Before the testing on the effects of C has been done, which statistical models allow one to estimate the effects of the C treatment before hypothesis testing given these conditions? And the magnitude of the said effects, their likelihood, etc.? Is such an application of rationalism even appropriate in science?

Last edited: Oct 31, 2012
2. Oct 31, 2012

### chiro

Hey Cinitiator.

There are examples of logic known as Probabilistic Logic that allow one to construct logical inference and deduction from statements that are probabilistic.

I think that this is more than appropriate for science since statistics really is at the heart of making decisions about evidence of data and how they can contribute (at least only in part) to causal connections between variables and variation in the context of a particular process.

As you probably are aware, we can measure interaction terms and the magnitude of those relative to the other affects and also relative to the total amount of variation that both the data and the model yield.

But when it comes to likelihood, you still have to decide whether you will force a population model on this (as is done in MLE) or whether to use some sort of general empirical distribution or similar construct.

The thing is that when it comes to likelihood, you will at some point have to make an assumption and usually (but not always) this translates into forcing a specific characteristic to have some underlying distribution (like a Normal, Chi-square, whatever).

So now the issues becomes: how valid is this likelihood? How do we actually establish said validity? What is the basis for this validity both mathematically and otherwise rationally?

So now you're getting back into really deep statistical and logical issues because you have to decide whether the model actually has use with regards to its accuracy, and not only that, you need to be able to give some justification for this in a rational sense as opposed to a mathematical simplification.

It's not going to be a trivial problem.