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I see Bayesian inference methods or probabilistic inference.

I haven't really found the definition of inference yet. Talking in terms estimation of parameters is really like method specific.

So, what is inference? Does it always mean to infer something from data. What are the approaches to inference.

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  • $\begingroup$ I believe this question is too broad and that the wikipedia page will probably be a good start: en.wikipedia.org/wiki/Inference $\endgroup$
    – tibL
    Sep 14, 2016 at 9:06
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    $\begingroup$ @tibl I think asking for a definition of inference is not too broad - though of course a complete exposition would be. $\endgroup$
    – Silverfish
    Sep 14, 2016 at 9:54
  • $\begingroup$ Statisticians study inference; probablists study implication. $\endgroup$
    – Dilip Sarwate
    Sep 14, 2016 at 13:13
  • $\begingroup$ @DilipSarwate implication means causality right, one thing implies another? $\endgroup$
    – Sie Tw
    Sep 14, 2016 at 13:17
  • $\begingroup$ I am questioning your divide between Bayesian inference and probabilistic inference which seems to suggest that Bayesian inference does not use probability at all. Frequentist statisticians use (maximum likelihood) inference to infer from the fact that a coin turned up Heads $k$ times in $n$ tosses that $p$, the probability of Heads is $\frac kn$. From the same fact, (some) Bayesian statisticians infer that $p$ is $\frac{k+1}{n+2}$. Both inferences do use notions about probability. $\endgroup$
    – Dilip Sarwate
    Sep 14, 2016 at 13:32

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Statistical inference is simply

The process of drawing conclusions about a population on the basis of measurements or observations made on a sample of individuals from the population.

as defined in Cambridge Dictionary of Statistics by B. S. Everitt. It is close to the general definition of inference, i.e. "act or process of deriving logical conclusions from premises", or "observation of patterns of facts, to see new meanings and contexts for understanding indirectly" (see also here, or here). List of all the possible approaches to statistical inference for all the possible statistical problems is unlimited.

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