The manner in which R. Kahn presented his mathematical results on the multiplier in the Economic Journal of June, 1931, is identical to the style of presenting mathematical results used by Keynes to present his mathematical analysis starting with the A Treatise on Probability in 1921. Keynes's...

Rational Expectations is an approach to probability and expectations that was initiated by Muth in 1961. Muth's concept is based on an immense muddle and confusion in his mind about subjective and objective concepts of probability that confuses subjective probability with objective probability....

We propose a novel approach of model selection for probability estimates that can be applied in time evolving setting. The idea is that any discrepancy between different probability estimates opens a possibility to compare them by trading on a hypothetical betting market that trades...

This paper proposes a new Markov chain approach to second order weak approximation of stochastic differential equations driven by d-dimensional Brownian motion. The scheme is explicitly constructed by polynomials of Brownian motions up to second order and any discrete moment matched random...

The theory of rational expectations has no foundation in any extant theory of probability. None of the five existing theories of probability (Logical, Subjective, Classical, Propensity, and Limiting (relative) Frequency) lend any support at all to the Muthian conjecture that the subjective...

J. Muth published a paper in 1961 in Econometrica that was incoherent and inconsistent because it was based on a hybrid amalgamation of directly conflicting Subjective and Objective theories of probability. Muth's hybrid amalgamation did not exist before 1961, in 1961, or after 1961. Muth jumps...

Humans are often characterized as Bayesian reasoners. Here, we question the core Bayesian assumption that probabilities reflect degrees of belief. Across 10 studies, we find that people instead reason in a digital manner, assuming that uncertain information is either true or false when using...

We consider usual stochastic and likelihood ratio orders. It has already been proven that the comparison of two random vectors (or variables) in the sense of likelihood ratio implies their comparison in the sense of usual stochastic order. In this paper, we will prove that the reverse is also...

If we assume the Thesis that any classical Turing machine , which halts on every n-ary sequence of natural numbers as input, determines a -provable formula, whose standard interpretation is an -ary arithmetical relation (, ..., ) that holds if, and only if, halts, then standard can model the...