Related papers: A quantum linguistic characterization of the rever…
Since the problem: "What is statistics?" is most fundamental in sceince, in order to solve this problem, there is every reason to believe that we have to start from the proposal of a worldview. Recently we proposed measurement theory (i.e.,…
Recently we proposed quantum language(or, measurement theory), which is characterized as the linguistic turn of the Copenhagen interpretation of quantum mechanics. Also, we consider that this is a kind of system theory such that it is…
The established language for statistical testing --- significance levels, power, and p-values --- is overly complicated and deceptively conclusive. Even teachers of statistics and scientists who use statistics misinterpret the results of…
The purpose of this paper is to clarify the (non-Bayesian and Bayesian) two-envelope problems in terms of quantum language (or, measurement theory), which was recently proposed as a linguistic turn of quantum mechanics (with the Copenhagen…
Quantiles can represent key operational and business metrics, but the computational challenges associated with inference has hampered their adoption in online experimentation. One-sample confidence intervals are trivial to construct;…
We address the challenge of certifying quantum behavior with single macroscopic massive particles, subject to decoherence and finite data. We propose a hypothesis testing framework that distinguishes between classical and quantum mechanics…
Suppose you are told that taking a statin will reduce your risk of a heart attack or stroke by 3% in the next ten years, or that women have better emotional intelligence than men. You may wonder how accurate the 3% is, or how confident we…
Between the two dominant schools of thought in statistics, namely, Bayesian and classical/frequentist, a main difference is that the former is grounded in the mathematically rigorous theory of probability while the latter is not. In this…
Recently, we proposed quantum language (or, measurement theory), which is characterized as the linguistic turn of the Copenhagen interpretation of quantum mechanics. We believe that this language has a great powet of description, and…
Common observations of the unpredictability of human behavior and the influence of one question on the answer to another suggest social science experiments are probabilistic and may be mutually incompatible with one another, characteristics…
Recently we proposed the linguistic interpretation of quantum mechanics (called quantum and classical measurement theory), which was characterized as a kind of metaphysical and linguistic turn of the Copenhagen interpretation. This turn…
Null hypothesis significance testing remains popular despite decades of concern about misuse and misinterpretation. We believe that much of the problem is due to language: significance testing has little to do with other meanings of the…
Testing hypotheses is an issue of primary importance in the scientific research, as well as in many other human activities. Much clarification about it can be achieved if the process of learning from data is framed in a stochastic model of…
In this investigation, we have considered two thought experiments to make a comparison between predictions of the standard and the Bohmian quantum mechanics. Concerning this, a two-particle system has been studied at two various situations…
The ability to calculate precise likelihood ratios is fundamental to many STEM areas, such as decision-making theory, biomedical science, and engineering. However, there is no assumption-free statistical methodology to achieve this. For…
Recently, we proposed measurement theory ( or. quantum language) as a linguistic turn of quantum mechanics (with the Copenhagen interpretation). This theory has a great power of scientific descriptions. In fact, we have continued asserting…
We study quantum statistical inference tasks of hypothesis testing and their canonical variations, in order to review relations between their corresponding figures of merit---measures of statistical distance---and demonstrate the crucial…
Traditional linguistic theories have largely regard language as a formal system composed of rigid rules. However, their failures in processing real language, the recent successes in statistical natural language processing, and the findings…
Alternative exact expressions are derived for the minimum error probability of a hypothesis test discriminating among $M$ quantum states. The first expression corresponds to the error probability of a binary hypothesis test with certain…
Positive and negative likelihood ratios are parameters which are used to assess and compare the effectiveness of binary diagnostic tests. Both parameters only depend on the sensitivity and specificity of the diagnostic test and are…