Inverse Bayesian Inference Research Articles

Simulation of foraging behavior using a decision-making agent with Bayesian and inverse Bayesian inference: Temporal correlations and power laws in displacement patterns

It has been stated that in human migratory behavior, the step length series may have temporal correlation and that there is some relationship between this time dependency and the fact that the frequency distribution of step length follows a power-law distribution. Furthermore, the frequency of occurrence of the step length in some large marine organisms has been found to switch between power-law and exponential distributions, depending on the difficulty of prey acquisition. However, to date it has not been clarified how the aforementioned three phenomena arise: the positive correlation created in the step length series, the relation between the positive correlation of the step length series and the form of an individual's step length distribution, and the switching between power-law and exponential distributions depending on the abundance of prey. This study simulated foraging behavior using the Bayesian decision-making agent simultaneously performing both knowledge learning and knowledge-based inference to analyze how the aforementioned three phenomena arise. In the agent with learning and inference, past experiences were stored as hypotheses (knowledge) and they were used in current foraging behavior; at the same time, the hypothesis continued to be updated based on new experiences. The simulation results show that the agent with both learning and inference has a mechanism that simultaneously causes all the phenomena.

Can We Infer Player Behavior Tendencies from a Player’s Decision-Making Data? Integrating Theory of Mind to Player Modeling

Game AI systems need the theory of mind, which is the humanistic ability to infer others' mental models, preferences, and intent. Such systems would enable inferring players' behavior tendencies that contribute to the variations in their decision-making behaviors. To that end, in this paper, we propose the use of inverse Bayesian inference to infer behavior tendencies given a descriptive cognitive model of a player's decision making. The model embeds behavior tendencies as weight parameters in a player's decision-making. Inferences on such parameters provide intuitive interpretations about a player's cognition while making in-game decisions. We illustrate the use of inverse Bayesian inference with synthetically generated data in a game called \textit{BoomTown} developed by Gallup. We use the proposed model to infer a player's behavior tendencies for moving decisions on a game map. Our results indicate that our model is able to infer these parameters towards uncovering not only a player's decision making but also their behavior tendencies for making such decisions.

Amoebic Foraging Model of Metastatic Cancer Cells

The Lévy walk is a pattern that is often seen in the movement of living organisms; it has both ballistic and random features and is a behavior that has been recognized in various animals and unicellular organisms, such as amoebae, in recent years. We proposed an amoeba locomotion model that implements Bayesian and inverse Bayesian inference as a Lévy walk algorithm that balances exploration and exploitation, and through a comparison with general random walks, we confirmed its effectiveness. While Bayesian inference is expressed only by P(h) = P(h|d), we introduce inverse Bayesian inference expressed as P(d|h) = P(d) in a symmetry fashion. That symmetry contributes to balancing contracting and expanding the probability space. Additionally, the conditions of various environments were set, and experimental results were obtained that corresponded to changes in gait patterns with respect to changes in the conditions of actual metastatic cancer cells.

Lévy Walk in Swarm Models Based on Bayesian and Inverse Bayesian Inference

While swarming behavior is regarded as a critical phenomenon in phase transition and frequently shows the properties of a critical state such as Lévy walk, a general mechanism to explain the critical property in swarming behavior has not yet been found. Here, we address this problem with a simple swarm model, the Self-Propelled Particle (SPP) model, and propose a way to explain this critical behavior by introducing agents making decisions via the data-hypothesis interaction in Bayesian inference, namely, Bayesian and inverse Bayesian inference (BIB). We compare three SPP models, namely, the simple SPP, the SPP with Bayesian-only inference (BO) and the SPP with BIB models. We show that only the BIB model entails coexisting tornado, splash and translation behaviors, and the Lévy walk pattern.

Extended Bayesian inference incorporating symmetry bias

We start by proposing a causal induction model that incorporates symmetry bias. This model has two parameters that control the strength of symmetry bias and includes conditional probability and conventional models of causal induction as special cases. We calculated the determination coefficients between assessments by participants in eight types of causal induction experiments and the estimated values using the proposed model. The mean coefficient of determination was 0.93. Thus, it can reproduce causal induction of human judgment with high accuracy. We further propose a human-like Bayesian inference method to replace the conditional probability in Bayesian inference with the aforementioned causal induction model. In this method, two components coexist: the component of Bayesian inference, which updates the degree of confidence for each hypothesis, and the component of inverse Bayesian inference that modifies the model of each hypothesis. In other words, this method allows not only inference but also simultaneous learning. Our study demonstrates that the method addresses unsteady situations where the target of inference occasionally changes not only by making inferences based on knowledge (model) and observation data, but also by modifying the model itself.

Uncertainty of the second order

We study the stochastic dynamics of the quasispecies model with inverse Bayesian inference under environmental uncertainty. Inverse Bayesian inference is introduced through the correspondence between Bayesian inference and the replicator equation. We consider environmental uncertainty that is not modeled as the stochastic fitness called uncertainty of the second order. This is in contrast to uncertainty of the first order that can be subsumed by the stochastic fitness. The difference between these two kinds of uncertainty is discussed in the framework of categorical Bayesian probability theory. We analytically show that if the time scale of inverse Bayesian inference is sufficiently larger than that of Bayesian inference, then the quasispecies model exhibits a noise-induced transition. The theoretical result is verified by a numerical simulation.

Inverse Bayesian inference in swarming behaviour of soldier crabs.

Animals making a group sometimes approach and sometimes avoid a dense area of group mates, and that reveals the ambiguity of density preference. Although the ambiguity is not expressed by a simple deterministic local rule, it seems to be implemented by probabilistic inference that is based on Bayesian and inverse Bayesian inference. In particular, the inverse Bayesian process refers to perpetual changing of hypotheses. We here analyse a time series of swarming soldier crabs and show that they are employed to Bayesian and inverse Bayesian inference. Comparing simulation results with data of the real swarm, we show that the interpretation of the movement of soldier crabs which can be based on the inference can lead to the identification of a drastic phase shift-like transition of gathering and dispersing.This article is part of the theme issue ‘Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)’.

Validation and Uncertainty Quantification for Wall Boiling Closure Relations in Multiphase-CFD Solver

Two-fluid model-based multiphase computational fluid dynamics (MCFD) has been considered one of the most promising tools to investigate a two-phase flow and boiling system for engineering purposes. The MCFD solver requires closure relations to make the conservation equations solvable. The wall boiling closure relations, for example, provide predictions on wall superheat and heat partitioning. The accuracy of these closure relations significantly influences the predictive capability of the solver. In this paper, a study of validation and uncertainty quantification (VUQ) for the wall boiling closure relations in the MCFD solver is performed. The work has three purposes: (1) to identify influential parameters to the quantities of interest (QoIs) of the boiling system through sensitivity analysis (SA), (2) to evaluate the parameter uncertainty through Bayesian inference with the support of multiple data sets, and (3) to quantitatively measure the agreement between solver predictions and data sets. The widely used Kurul-Podowski wall boiling closure relation is studied in this paper. Several statistical methods are used, including the Morris Screening method for global SA, Markov Chain Monte Carlo for inverse Bayesian inference, and confidence interval as the validation metric. The VUQ results indicate that the current empirical correlations-based wall boiling closure relations achieved satisfactory agreement on wall superheat predictions. However, the closure relations also demonstrate intrinsic inconsistency and fail to give consistently accurate predictions for all QoIs over the well-developed nucleate boiling regime.

逆ベイズ推定を用いた意思決定プロセスのモデル化

逆ベイズ推定を用いた意思決定プロセスのモデル化

Modeling of decision-making process for moving straight using inverse Bayesian inference

Humans sometimes make unreasonable decisions when viewed in objective terms. Even in the real world, we may lose sense of direction by turning around the corner several times or mistaking the estimation of travel distance. We experimented in virtual space how we lose sense of direction under what circumstances. In the experiment, subjects viewed a three-dimensional space displayed on a computer display in the first person’s perspective and were instructed to go straight from the start to the goal position. Results showed that unreasonable selections that strayed from the centerline connecting the start and goal positions were frequently made. The change in the direction is more influential than the change in the distance, and the angle of turning also affects. Furthermore, the subject's decision – making process was modeled using Bayesian inference and inverse Bayesian inference. Comparing the two models, when the decision-making pattern suddenly changed, the model by inverse Bayesian inference could follow up faster than the Bayesian inference.

Experimental validation of Bayesian design for broadband multilayered microperforated panel absorbers

Single-layer microperforated panel (MPP) absorbers often exhibit limited absorbing bandwidth. A Bayesian inference framework (encompassing both model selection and parameter estimation) has been utilized to design broadband MPP absorbers. In this work, the broadband multilayered MPP absorbers are experimentally validated. In demonstrating ability to meet practical requirements on both high absorption and wide bandwidth, the current investigation uses a sample design scheme in the frequency range from 300 Hz to 2.4 kHz. A minimum requirement for three MPP layers and the relevant three-layer MPP parameters are derived by the two levels of Bayesian inference to meet the design scheme. MPP samples, based on the predicted design scheme, are fabricated and used to conduct normal-incidence sound absorption measurements in an impedance tube. In order to quantify the fabrication tolerance, the measured acoustic data are used to estimate the MPP parameters of the constructed absorber, using an inverse Bayesian inference method. This paper will discuss the initial MPP design, experimental validations of the designed absorption performance, as well as fabrication tolerance estimations of the MPP parameters.

Inverse Bayesian inference as a key of consciousness featuring a macroscopic quantum logical structure

To overcome the dualism between mind and matter and to implement consciousness in science, a physical entity has to be embedded with a measurement process. Although quantum mechanics have been regarded as a candidate for implementing consciousness, nature at its macroscopic level is inconsistent with quantum mechanics. We propose a measurement-oriented inference system comprising Bayesian and inverse Bayesian inferences. While Bayesian inference contracts probability space, the newly defined inverse one relaxes the space. These two inferences allow an agent to make a decision corresponding to an immediate change in their environment. They generate a particular pattern of joint probability for data and hypotheses, comprising multiple diagonal and noisy matrices. This is expressed as a nondistributive orthomodular lattice equivalent to quantum logic. We also show that an orthomodular lattice can reveal information generated by inverse syllogism as well as the solutions to the frame and symbol-grounding problems. Our model is the first to connect macroscopic cognitive processes with the mathematical structure of quantum mechanics with no additional assumptions.

Trial-by-trial modeling of electrophysiological signals during inverse Bayesian inference

Empirical support for the Bayesian brain hypothesis, although of major theoretical importance for cognitive neuroscience, is surprisingly scarce. The literature still lacks definitive functional neuroimaging evidence that neural activities code and compute Bayesian probabilities. Here, we introduce a new experimental design to relate electrophysiological measures to Bayesian inference. Specifically, an urns-and-balls paradigm was used to study neural underpinnings of probabilistic inverse inference. Event-related potentials (ERPs) were recorded from human participants who performed the urns-and-balls paradigm, and computational modeling was conducted on trial-by-trial electrophysiological signals. Five computational models were compared with respect to their capacity to predict electrophysiological measures. One Bayesian model (BAY) was compared with another Bayesian model which takes potential effects of non-linear probability weighting into account (BAYS). A predictive surprise model (TOPS) of sequential probability revisions was derived from the Bayesian models. A comparison was made with two published models of surprise (DIF [1] and OST [2]). Subsets of the trial-by-trial electrophysiological signals were differentially sensitive to model predictors: The anteriorly distributed N250 was best fit by the DIF model, the BAYS model provided the best fit to the anteriorly distributed P3a, whereas the posteriorly distributed P3b and Slow Wave were best fit by the TOPS model.