On Probabilistic Parametric Inference
An objective operational theory of probabilistic parametric inference is formulated without invoking the so-called non-informative prior probability distributions.
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arXiv subjects
Tomaz Podobnik
Publications and source records attributed to Tomaz Podobnik.
Towards Reconciliation between Bayesian and Frequentist Reasoning
A theory of quantitative inference about the parameters of sampling distributions is constructed deductively by following very general rules, referred to as the Cox-Polya-Jaynes Desiderata. The inferences are made in terms of probability distributions that are assigned to the parameters. The Desiderata, focusing primarily on consistency of the plausible reasoning, lead to unique assignments of these probabilities in the case of sampling distributions that are invariant under Lie groups. In the scalar cases, e.g. in the case of inferring a single location or scale parameter, the requirement for logical consistency is equivalent to the requirement for calibration: the consistent probability distributions are automatically also the ones with the exact calibration and vice versa. This equivalence speaks in favour of reconciliation between the Bayesian and Frequentist schools of reasoning.
math.ST↗
On Consistent and Calibrated Inference about the Parameters of Sampling Distributions
The theory of probability, based on very general rules referred to as the Cox-Polya-Jaynes Desiderata, can be used both as a theory of random mass phenomena and as a quantitative theory of plausible inference about the parameters of sampling distributions. The existing applications of the Desiderata must be extended in order to allow for consistent inferences in the limit of complete a priori ignorance about the values of the parameters. Since the limits of consistent quantitative inference from incomplete information can clearly be established, the developed theory is necessarily an effective one. It is interesting to note that when applying the Desiderata strictly, we find no contradictions between the so-called Bayesian and frequentist schools of inductive reasoning.
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