The value of cost-free uncertain evidence

We explore the question of whether cost-free uncertain evidence is worth waiting for in advance of making a decision. A classical result in Bayesian decision theory, known as the value of evidence theorem, says that, under certain conditions, when you update your credences by conditionalizing on some cost-free and certain evidence, the subjective expected utility of obtaining this evidence is never less than the subjective expected utility of not obtaining it. We extend this result to a type of update method, a variant of Judea Pearl’s virtual conditionalization, where uncertain evidence is represented as a set of likelihood ratios. Moreover, we argue that focusing on this method rather than on the widely accepted Jeffrey conditionalization enables us to show that, under a fairly plausible assumption, gathering uncertain evidence not only maximizes expected pragmatic utility, but also minimizes expected epistemic disutility (inaccuracy).

Standard of proof in common law: Mathematical explication and probative value of statistical data

As a result of recent amendments to the procedural legislation of Ukraine, one may observe a tendency in judicial practice to differentiate the standards of proof depending on the type of litigation. Thus, in commercial litigation the so-called standard of “probability of evidence” applies, while in criminal proceedings – “beyond a reasonable doubt” standard applies. The purpose of this study was to find the rational justification for the differentiation of the standards of proof applied in civil (commercial) and criminal cases and to explain how the same fact is considered proven for the purposes of civil lawsuit and not proven for the purposes of criminal charge. The study is based on the methodology of Bayesian decision theory. The paper demonstrated how the principles of Bayesian decision theory can be applied to judicial fact-finding. According to Bayesian theory, the standard of proof applied depends on the ratio of the false positive error disutility to false negative error disutility. Since both types of error have the same disutility in a civil litigation, the threshold value of conviction is 50+ percent. In a criminal case, on the other hand, the disutility of false positive error considerably exceeds the disutility of the false negative one, and therefore the threshold value of conviction shall be much higher, amounting to 90 percent. Bayesian decision theory is premised on probabilistic assessments. And since the concept of probability has many meanings, the results of the application of Bayesian theory to judicial fact-finding can be interpreted in a variety of ways. When dealing with statistical evidence, it is crucial to distinguish between subjective and objective probability. Statistics indicate objective probability, while the standard of proof refers to subjective probability. Yet, in some cases, especially when statistical data is the only available evidence, the subjective probability may be roughly equivalent to the objective probability. In such cases, statistics cannot be ignored

Machines Imitating Human Thinking Using Bayesian Learning and Bootstrap

In the field of cognitive science, much research has been conducted on the diverse applications of artificial intelligence (AI). One important area of study is machines imitating human thinking. Although there are various approaches to development of thinking machines, we assume that human thinking is not always optimal in this paper. Sometimes, humans are driven by emotions to make decisions that are not optimal. Recently, deep learning has been dominating most machine learning tasks in AI. In the area of optimal decisions involving AI, many traditional machine learning methods are rapidly being replaced by deep learning. Therefore, because of deep learning, we can expect the faster growth of AI technology such as AlphaGo in optimal decision-making. However, humans sometimes think and act not optimally but emotionally. In this paper, we propose a method for building thinking machines imitating humans using Bayesian decision theory and learning. Bayesian statistics involves a learning process based on prior and posterior aspects. The prior represents an initial belief in a specific domain. This is updated to posterior through the likelihood of observed data. The posterior refers to the updated belief based on observations. When the observed data are newly added, the current posterior is used as a new prior for the updated posterior. Bayesian learning such as this also provides an optimal decision; thus, this is not well-suited to the modeling of thinking machines. Therefore, we study a new Bayesian approach to developing thinking machines using Bayesian decision theory. In our research, we do not use a single optimal value expected by the posterior; instead, we generate random values from the last updated posterior to be used for thinking machines that imitate human thinking.

APPLICATION OF MULTI-TRAIT BAYESIAN DECISION THEORY FOR PARENTAL GENOMIC SELECTION

In all breeding programs, the decision about which individuals to select and intermate to form the next selection cycle is crucial. The improvement of genetic stocks requires considering multiple traits simultaneously, given that economic value and net genetic merits depend on many traits; therefore, with the advance of computational and statistical tools and genomic selection (GS), researchers are focusing on multi-trait selection. Selection of the best individuals is difficult, especially in traits that are antagonistically correlated, where improvement in one trait might imply a reduction in other(s). There are approaches that facilitate multi-trait selection, and recently a Bayesian decision theory (BDT) has been proposed. Parental selection using BDT has the potential to be effective in multi-trait selection given that it summarizes all relevant quantitative genetic concepts such as heritability, response to selection and the structure of dependence between traits (correlation). In this study, we applied BDT to provide a treatment for the complexity of multi-trait parental selection using three multivariate loss functions (LF), Kullback-Leibler (KL), Energy Score, and Multivariate Asymmetric Loss (MALF), to select the best performing parents for the next breeding cycle in two extensive real wheat data sets. Results show that the high ranking lines in genomic estimated breeding value (GEBV) for certain traits did not always have low values for PEL. For both data sets, the KL loss function gave similar importance to all traits including grain yield. In contrast, the Energy Score and MALF gave better performance in 3 of 4 traits that were different than grain yield. The BDT approach should help breeders to decide based not only on the GEBV per se of the parent to be selected, but also on the level of uncertainty according to the Bayesian paradigm.