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The notion of belief likelihood function of repeated trials is introduced, whenever the uncertainty for individual trials is encoded by a belief measure (a finite random set). This generalises the traditional likelihood function, and…
The belief that numbers offer a single, objective description of reality overlooks a crucial truth: data does not speak for itself. Every dataset results from choices-what to measure, how, when, and with whom-which inevitably reflect…
In this article we demonstrate how algorithmic probability theory is applied to situations that involve uncertainty. When people are unsure of their model of reality, then the outcome they observe will cause them to update their beliefs. We…
A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction, disjunction, inverse, and conditional fallacies, as well as unpacking effects and partitioning effects. Quantum…
Data separation is a well-studied phenomenon that can cause problems in the estimation and inference from binary response models. Complete or quasi-complete separation occurs when there is a combination of regressors in the model whose…
As artificial intelligence and machine learning tools become more accessible, and scientists face new obstacles to data collection (e.g. rising costs, declining survey response rates), researchers increasingly use predictions from…
Counterfactual reasoning -- envisioning hypothetical scenarios, or possible worlds, where some circumstances are different from what (f)actually occurred (counter-to-fact) -- is ubiquitous in human cognition. Conventionally,…
Well known Simpson's paradox is puzzling and surprising for many, especially for the empirical researchers and users of statistics. However there is no surprise as far as mathematical details are concerned. A lot more is written about the…
The two most important algorithms in artificial intelligence are backpropagation and belief propagation. In spite of their importance, the connection between them is poorly characterized. We show that when an input to backpropagation is…
Observational data about human behavior is often heterogeneous, i.e., generated by subgroups within the population under study that vary in size and behavior. Heterogeneity predisposes analysis to Simpson's paradox, whereby the trends…
Confounding seriously impairs our ability to learn about causal relations from observational data. Confounding can be defined as a statistical association between two variables due to inputs from a common source (the confounder). For…
The sure thing principle and the law of total probability are basic laws in classic probability theory. A disjunction fallacy leads to the violation of these two classical probability laws. In this paper, a new quantum dynamic belief…
We investigate how Simpson's paradox affects analysis of trends in social data. According to the paradox, the trends observed in data that has been aggregated over an entire population may be different from, and even opposite to, those of…
This paper describes Simpson's paradox, and explains its serious implications for randomised control trials. In particular, we show that for any number of variables we can simulate the result of a controlled trial which uniformly points to…
We present a novel variant of decision making based on the mathematical theory of separable Hilbert spaces. This mathematical structure captures the effect of superposition of composite prospects, including many incorporated intentions,…
Confirmation bias is a cognitive bias that adversely affects management decisions, and mathematical modelling is an aid to its detailed understanding. Bias in opinion update about the value of a parameter is modelled here assuming that…
In a probability-based reasoning system, Bayes' theorem and its variations are often used to revise the system's beliefs. However, if the explicit conditions and the implicit conditions of probability assignments `me properly distinguished,…
Many writers have observed that default logics appear to contain the "lottery paradox" of probability theory. This arises when a default "proof by contradiction" lets us conclude that a typical X is not a Y where Y is an unusual subclass of…
The study of belief change has been an active area in philosophy and AI. In recent years two special cases of belief change, belief revision and belief update, have been studied in detail. Roughly, revision treats a surprising observation…
The issue of confidence factors in Knowledge Based Systems has become increasingly important and Dempster-Shafer (DS) theory has become increasingly popular as a basis for these factors. This paper discusses the need for an empirical…