Kim, Bryce (2017) Role of information and its processing in statistical analysis. [Preprint]
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Abstract
This paper discusses how real-life statistical analysis/inference deviates from ideal environments. More specifically, there often exist models that have equal statistical power as the actual data-generating model, given only limited information and information processing/computation capacity. This means that misspecification actually has two problems: first with misspecification around the model we wish to find, and that an actual data-generating model may never be discovered. Thus the role information - this includes data - plays on statistical inference needs to be considered more heavily than often done. A game defining pseudo-equivalent models is presented in this light. This limited information nature effectively casts a statistical analyst as a decider in decision theory facing an identical problem: trying best to form credence/belief of some events, even if it may end up not being close to objective probability. The sleeping beauty problem is used as a study case to highlight some properties of real-life statistical inference. Bayesian inference of prior updates can lead to wrong credence analysis when prior is assigned to variables/events that are not (statistical identification-wise) identifiable. A controversial idea that Bayesianism can go around identification problems in frequentist analysis is brought to more doubts. This necessitates re-defining how Kolmogorov probability theory is applied in real-life statistical inference, and what concepts need to be fundamental.
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| Item Type: | Preprint | ||||||
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| Keywords: | Kolmogorov probability theory, Bayesian inference, incomplete information inference, limited information inference, decision theory, misspecification, credence, belief, sleeping beauty problem, learning algorithms, theory of statistical inference, machine learning | ||||||
| Subjects: | Specific Sciences > Computation/Information Specific Sciences > Computer Science Specific Sciences > Economics Specific Sciences > Probability/Statistics |
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| Depositing User: | Mr. Bryce Kim | ||||||
| Date Deposited: | 21 Jul 2017 14:00 | ||||||
| Last Modified: | 21 Jul 2017 14:00 | ||||||
| Item ID: | 13244 | ||||||
| Subjects: | Specific Sciences > Computation/Information Specific Sciences > Computer Science Specific Sciences > Economics Specific Sciences > Probability/Statistics |
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| Date: | 15 July 2017 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/13244 |
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Role of information and its processing in statistical analysis. (deposited 20 Jul 2017 14:52)
- Role of information and its processing in statistical analysis. (deposited 21 Jul 2017 14:00) [Currently Displayed]
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