Tootfinder

Situated Bayes -- Feminist and Pluriversal Perspectives on Bayesian Knowledge
Juni Schindler, Goda Klumbyt\.e, Matthew Fuller
https://arxiv.org/abs/2506.09472

Situated Bayes -- Feminist and Pluriversal Perspectives on Bayesian Knowledge
This is the introduction and lead article to the Situated Bayes special issue of Computational Culture. The article introduces Bayes' Theorem and aspects of its contemporary uses, for instance in machine learning. A mathematical discussion is developed alongside a consideration of Bayes Theorem in relation to critical theories of knowledge, specifically the discussion of situated knowledge in feminist theories of science, pluriversal knowledge in decolonial theory, and critical approaches to ma…

Constrained Denoising, Empirical Bayes, and Optimal Transport
Adam Quinn Jaffe, Nikolaos Ignatiadis, Bodhisattva Sen
https://arxiv.org/abs/2506.09986 https…

Constrained Denoising, Empirical Bayes, and Optimal Transport
In the statistical problem of denoising, Bayes and empirical Bayes methods can "overshrink" their output relative to the latent variables of interest. This work is focused on constrained denoising problems which mitigate such phenomena. At the oracle level, i.e., when the latent variable distribution is assumed known, we apply tools from the theory of optimal transport to characterize the solution to (i) variance-constrained, (ii) distribution-constrained, and (iii) general-constrained denoisin…

This https://arxiv.org/abs/2411.07651 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Quasi-Bayes empirical Bayes: a sequential approach to the Poisson compound decision problem
The Poisson compound decision problem is a long-standing problem in statistics, where empirical Bayes methodologies are commonly used to estimate Poisson's means in static or batch domains. In this paper, we study the Poisson compound decision problem in a streaming or online domain. Adopting a quasi-Bayesian approach, referred to as Newton's algorithm, we obtain a sequential estimate that is easy to evaluate, computationally efficient, and maintain a constant per-observation computational cost…

Exoplaneteers Keep Overestimating Sigma Significances
David Kipping, Bj\"orn Benneke
https://arxiv.org/abs/2506.05392 https://ar…

Exoplaneteers Keep Overestimating Sigma Significances
Astronomers, and in particular exoplaneteers, have a curious habit of expressing Bayes factors as frequentist sigma values. This is of course completely unnecessary and arguably rather ill-advised. Regardless, the practice is common - especially in the detection claims of chemical species within exoplanet atmospheres. The current canonical conversion strategy stems from a statistics paper from Sellke et al. (2001), who derived an upper bound on the Bayes factor between the test and null hypothe…

Statistical Limits for Finite-Rank Tensor Estimation
Riccardo Rossetti, Galen Reeves
https://arxiv.org/abs/2506.06749 https://arxiv.o…

Statistical Limits for Finite-Rank Tensor Estimation
This paper provides a unified framework for analyzing tensor estimation problems that allow for nonlinear observations, heteroskedastic noise, and covariate information. We study a general class of high-dimensional models where each observation depends on the interactions among a finite number of unknown parameters. Our main results provide asymptotically exact formulas for the mutual information (equivalently, the free energy) as well as the minimum mean-squared error in the Bayes-optimal sett…

This https://arxiv.org/abs/2505.24502 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Predictability of quantum observables: Applications in QKD and top quarks
We quantify and optimize the predictability of local observables in bipartite quantum systems by employing the Bayes risk and the inference variance, two measures rooted in statistical learning theory. Specifically, we minimized these quantities when the prediction is improved by an additional quantum system, providing analytical expressions for arbitrary two-qubit states, and showcasing a connection with Einstein-Podolsky-Rosen steering criteria. Then, we embed our Bayes risk minimization into…

The relation of bias with risk in empirically constrained inferences
Dalton A R Sakthivadivel
https://arxiv.org/abs/2507.03699 https://

The relation of bias with risk in empirically constrained inferences
We give some results relating asymptotic characterisations of maximum entropy probability measures to characterisations of Bayes optimal classifiers. Our main theorems show that maximum entropy is a universally Bayes optimal decision rule given constraints on one's knowledge about some observed data in terms of an expected loss. We will extend this result to the case of uncertainty in the observations of expected losses by generalising Sanov's theorem to distributions of constraint values.

Equilibrium Computation in First-Price Auctions with Correlated Priors
Aris Filos-Ratsikas, Yiannis Giannakopoulos, Alexandros Hollender, Charalampos Kokkalis
https://arxiv.org/abs/2506.05322

Equilibrium Computation in First-Price Auctions with Correlated Priors
We consider the computational complexity of computing Bayes-Nash equilibria in first-price auctions, where the bidders' values for the item are drawn from a general (possibly correlated) joint distribution. We show that when the values and the bidding space are discrete, determining the existence of a pure Bayes-Nash equilibrium is NP-hard. This is the first hardness result in the literature of the problem that does not rely on assumptions of subjectivity of the priors, or convoluted tie-breaki…

Replaced article(s) found for stat.ME. https://arxiv.org/list/stat.ME/new
[1/1]:
- Non-conjugate variational Bayes for pseudo-likelihood mixed effect models
Cristian Castiglione, Mauro Bernardi

Paracomplete Probabilities
Sankha S. Basu, Esha Jain
https://arxiv.org/abs/2507.04312 https://arxiv.org/pdf/2507.04312

Paracomplete Probabilities
This paper presents an advance in the direction of working with probabilities in a paracomplete setting using Logics of Formal Undeterminedness (LFUs). The undeterminedness is interpreted here as missing evidence. A theorem of total paracomplete probability and a paracomplete Bayes' rule have been proved using this setup. We end with a definition of a paracomplete probability space illustrating a way to define probabilities on sets in the presence of undeterminedness.

Estimation of An Infinite Dimensional Transition Probability Matrix Using a Generalized Hierarchical Stick-Breaking Process
Agamani Saha, Souvik Roy
https://arxiv.org/abs/2507.07433

Estimation of An Infinite Dimensional Transition Probability Matrix Using a Generalized Hierarchical Stick-Breaking Process
Markov chains provide a foundational framework for modeling sequential stochastic processes, with the transition probability matrix characterizing the dynamics of state evolution. While classical estimation methods such as maximum likelihood and empirical Bayes approaches are effective in finite-state settings, they become inadequate in applications involving countably infinite or dynamically expanding state spaces, which frequently arise in domains such as natural language processing, populati…

Bayes linear estimator in the general linear model
Hirai Mukasa
https://arxiv.org/abs/2506.21192 https://arxiv.org/pdf/2506.21192

Bayes linear estimator in the general linear model
Bayes linear estimators are derived by minimizing the Bayes risk with respect to the squared loss function. Non-unbiased estimators such as an ordinary ridge estimator, a typical shrinkage estimator, and a fractional rank estimator are either Bayes linear estimators or their limit points. First, we prove that Bayes linear estimators are linearly complete, but not necessarily linearly sufficient. Second, we derive a necessary and sufficient condition under which two Bayes linear estimators coinc…

Minimax and Bayes Optimal Best-arm Identification: Adaptive Experimental Design for Treatment Choice
Masahiro Kato
https://arxiv.org/abs/2506.24007 https:/…

Minimax and Bayes Optimal Best-arm Identification: Adaptive Experimental Design for Treatment Choice
This study investigates adaptive experimental design for treatment choice, also known as fixed-budget best-arm identification. We consider an adaptive procedure consisting of a treatment-allocation phase followed by a treatment-choice phase, and we design an adaptive experiment for this setup to efficiently identify the best treatment arm, defined as the one with the highest expected outcome. In our designed experiment, the treatment-allocation phase consists of two stages. The first stage is a…

Linear Discriminant Analysis with Gradient Optimization on Covariance Inverse
Cencheng Shen, Yuexiao Dong
https://arxiv.org/abs/2506.06845 https://

Linear Discriminant Analysis with Gradient Optimization on Covariance Inverse
Linear discriminant analysis (LDA) is a fundamental method in statistical pattern recognition and classification, achieving Bayes optimality under Gaussian assumptions. However, it is well-known that classical LDA may struggle in high-dimensional settings due to instability in covariance estimation. In this work, we propose LDA with gradient optimization (LDA-GO), a new approach that directly optimizes the inverse covariance matrix via gradient descent. The algorithm parametrizes the inverse co…

Max Entropy Moment Kalman Filter for Polynomial Systems with Arbitrary Noise
Sangli Teng, Harry Zhang, David Jin, Ashkan Jasour, Ram Vasudevan, Maani Ghaffari, Luca Carlone
https://arxiv.org/abs/2506.00838

Max Entropy Moment Kalman Filter for Polynomial Systems with Arbitrary Noise
Designing optimal Bayes filters for nonlinear non-Gaussian systems is a challenging task. The main difficulties are: 1) representing complex beliefs, 2) handling non-Gaussian noise, and 3) marginalizing past states. To address these challenges, we focus on polynomial systems and propose the Max Entropy Moment Kalman Filter (MEM-KF). To address 1), we represent arbitrary beliefs by a Moment-Constrained Max-Entropy Distribution (MED). The MED can asymptotically approximate almost any distribution…

Savage-Dickey density ratio estimation with normalizing flows for Bayesian model comparison
Kiyam Lin, Alicja Polanska, Davide Piras, Alessio Spurio Mancini, Jason D. McEwen
https://arxiv.org/abs/2506.04339

Savage-Dickey density ratio estimation with normalizing flows for Bayesian model comparison
A core motivation of science is to evaluate which scientific model best explains observed data. Bayesian model comparison provides a principled statistical approach to comparing scientific models and has found widespread application within cosmology and astrophysics. Calculating the Bayesian evidence is computationally challenging, especially as we continue to explore increasingly more complex models. The Savage-Dickey density ratio (SDDR) provides a method to calculate the Bayes factor (eviden…

This https://arxiv.org/abs/2401.14283 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Information Leakage Detection through Approximate Bayes-optimal Prediction
In today's data-driven world, the proliferation of publicly available information raises security concerns due to the information leakage (IL) problem. IL involves unintentionally exposing sensitive information to unauthorized parties via observable system information. Conventional statistical approaches rely on estimating mutual information (MI) between observable and secret information for detecting ILs, face challenges of the curse of dimensionality, convergence, computational complexity, an…

🔍 Wie wir aus Erfahrung lernen können: Thomas Bayes und die Diagnose von Erkrankungen in der Medizin
Risiko & Wahrscheinlichkeit: Die Schlüssel zu besseren Gesundheitsentscheidungen! 🩺 Wir erklären, wie Statistik & Medizin zusammenpassen.
⏲ Uhrzeit: 17:00-24:00 Uhr
🗓️ Datum: 21.06.2025
🧑‍🔬 Veranstalter: CIDAS Campus-Institut Data Science
📍 Veranstaltungsort: @…

Predictability of quantum observables: Applications in QKD and top quarks
Dennis I. Mart\'inez-Moreno, Miguel Castillo-Celeita, Diego G. Bussandri
https://arxiv.org/abs/2505.24502

Predictability of quantum observables: Applications in QKD and top quarks
We quantify and optimize the predictability of local observables in bipartite quantum systems by employing the Bayes risk and the inference variance, two measures rooted in statistical learning theory. Specifically, we minimized these quantities when the prediction is improved by an additional quantum system, providing analytical expressions for arbitrary two-qubit states, and showcasing a connection with Einstein-Podolsky-Rosen steering criteria. Then, we embed our Bayes risk minimization into…

Learning to Coordinate Bidders in Non-Truthful Auctions
Hu Fu, Tao Lin
https://arxiv.org/abs/2507.02801 https://arxiv.org/pdf/2507.02…

Learning to Coordinate Bidders in Non-Truthful Auctions
In non-truthful auctions such as first-price and all-pay auctions, the independent strategic behaviors of bidders, with the corresponding equilibrium notion -- Bayes Nash equilibria -- are notoriously difficult to characterize and can cause undesirable outcomes. An alternative approach to designing better auction systems is to coordinate the bidders: let a mediator make incentive-compatible recommendations of correlated bidding strategies to the bidders, namely, implementing a Bayes correlated …

This https://arxiv.org/abs/2502.10527 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csDS_…

Algorithms and Hardness for Estimating Statistical Similarity
We introduce and study the computational problem of determining statistical similarity between probability distributions. For distributions $P$ and $Q$ over a finite sample space, their statistical similarity is defined as $S_{\mathrm{stat}}(P, Q) := \sum_x \min(P(x), Q(x))$. Despite its fundamental nature as a measure of similarity between distributions, capturing essential concepts such as Bayes error in prediction and hypothesis testing, this computational problem has not been previously exp…

Bayesian Analysis of Non-extensive Parameters in Au-Au Collisions
Randy Dobler, Juliana O. Costa, Marcelo D. Alloy, D\'ebora P. Menezes
https://arxiv.org/abs/2507.01646

Bayesian Analysis of Non-extensive Parameters in Au-Au Collisions
In this work, a Bayesian statistical framework is employed to analyze particle yield ratios in Au-Au collisions, utilizing Non-Extensive Statistics (NES). Through Markov Chain Monte Carlo (MCMC) sampling, we systematically estimate key parameters, including the non-extensive factor $q$, temperature $T$, and chemical potential $μ$. Our analysis confirms previous findings highlighting the suitability and robustness of Bayesian methods in describing heavy-ion collision data. A subsequent Bayes fa…

This https://arxiv.org/abs/2311.10685 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qfi…

High-Throughput Asset Pricing
We apply empirical Bayes (EB) to mine data on 136,000 long-short strategies constructed from accounting ratios, past returns, and ticker symbols. This ``high-throughput asset pricing'' matches the out-of-sample performance of top journals while eliminating look-ahead bias. Naively mining for the largest Sharpe ratios leads to similar performance, consistent with our theoretical results, though EB uniquely provides unbiased predictions with transparent intuition. Predictability is concentrated i…

Putting Skill as Nearly Indistinguishable from Noise: An Empirical Bayes Analysis of PGA Tour Performance
Ryan S. Brill, Abraham J. Wyner
https://arxiv.org/abs/2506.21822

Putting Skill as Nearly Indistinguishable from Noise: An Empirical Bayes Analysis of PGA Tour Performance
We revisit a foundational question in golf analytics: how important are the core components of performance--driving, approach play, and putting--in explaining success on the PGA Tour? Building on Mark Broadie's strokes gained analyses, we use an empirical Bayes approach to estimate latent golfer skill and assess statistical significance using a multiple testing procedure that controls the false discovery rate. While tee-to-green skill shows clear and substantial differences across players, putt…

In our #ISE2025 lecture last Wednesday, we learned how in n-gram language models via Markov assumption and maximum likelihood estimation we can predict the probability of the occurrence of a word given a specific context (i.e. n words previous in the sequence of words).
#NLP

Multilevel Decomposition of Generalized Entropy Measures Using Constrained Bayes Estimation: An Application to Japanese Regional Data
Yuki Kawakubo, Kazuhiko Kakamu
https://arxiv.org/abs/2506.21213

Multilevel Decomposition of Generalized Entropy Measures Using Constrained Bayes Estimation: An Application to Japanese Regional Data
We propose a method for multilevel decomposition of generalized entropy (GE) measures that explicitly accounts for nested population structures such as national, regional, and subregional levels. Standard approaches that estimate GE separately at each level do not guarantee compatibility with multilevel decomposition. Our method constrains lower-level GE estimates to match higher-level benchmarks while preserving hierarchical relationships across layers. We apply the method to Japanese income d…

This https://arxiv.org/abs/2210.03905 has been replaced.
link: https://scholar.google.com/scholar?q=a

Empirical Bayes Selection for Value Maximization
We study the problem of selecting the best $m$ units from a set of $n$ as $m / n \to α\in (0, 1)$, where noisy, heteroskedastic measurements of the units' true values are available and the decision-maker wishes to maximize the aggregate true value of the units selected. Given a parametric prior distribution, the empirical Bayes decision rule incurs $O_p(n^{-1})$ regret relative to the Bayesian oracle that knows the true prior. More generally, if the error in the estimated prior is of order $O_…

Bayesian Knowledge Transfer for a Kalman Fixed-Lag Interval Smoother
Ond\v{r}ej Skalsk\'y, Jakub Dokoupil
https://arxiv.org/abs/2506.14572 https://

Bayesian Knowledge Transfer for a Kalman Fixed-Lag Interval Smoother
A Bayesian knowledge transfer mechanism that leverages external information to improve the performance of the Kalman fixed-lag interval smoother (FLIS) is proposed. Exact knowledge of the external observation model is assumed to be missing, which hinders the direct application of Bayes' rule in traditional transfer learning approaches. This limitation is overcome by the fully probabilistic design, conditioning the targeted task of state estimation on external information. To mitigate the negati…

The power of mediators: Price of anarchy and stability in Bayesian games with submodular social welfare
Kaito Fujii
https://arxiv.org/abs/2506.02655 https:…

The power of mediators: Price of anarchy and stability in Bayesian games with submodular social welfare
This paper investigates the role of mediators in Bayesian games by examining their impact on social welfare through the price of anarchy (PoA) and price of stability (PoS). Mediators can communicate with players to guide them toward equilibria of varying quality, and different communication protocols lead to a variety of equilibrium concepts collectively known as Bayes (coarse) correlated equilibria. To analyze these equilibrium concepts, we consider a general class of Bayesian games with submo…

Large-Scale Estimation under Unknown Heteroskedasticity
Sheng Chao Ho
https://arxiv.org/abs/2507.02293 https://arxiv.org/pdf/2507.022…

Large-Scale Estimation under Unknown Heteroskedasticity
This paper studies nonparametric empirical Bayes methods in a heterogeneous parameters framework that features unknown means and variances. We provide extended Tweedie's formulae that express the (infeasible) optimal estimators of heterogeneous parameters, such as unit-specific means or quantiles, in terms of the density of certain sufficient statistics. These are used to propose feasible versions with nearly parametric regret bounds of the order of $(\log n)^κ/ n$. The estimators are employed…

Interim correlated rationalizability in large games
Lukasz Balbus, Michael Greinecker, Kevin Reffett, Lukasz Wozny
https://arxiv.org/abs/2506.18426 https:/…

Interim correlated rationalizability in large games
We provide general theoretical foundations for modeling strategic uncertainty in large distributional Bayesian games with general type spaces, using a version of interim correlated rationalizability. We then focus on the case in which payoff functions are supermodular in actions, as is common in the literature on global games. This structure allows us to identify extremal interim correlated rationalizable solutions with extremal interim Bayes-Nash equilibria. Notably, no order structure on type…

Variational Learning Finds Flatter Solutions at the Edge of Stability
Avrajit Ghosh, Bai Cong, Rio Yokota, Saiprasad Ravishankar, Rongrong Wang, Molei Tao, Mohammad Emtiyaz Khan, Thomas M\"ollenhoff
https://arxiv.org/abs/2506.12903

Variational Learning Finds Flatter Solutions at the Edge of Stability
Variational Learning (VL) has recently gained popularity for training deep neural networks and is competitive to standard learning methods. Part of its empirical success can be explained by theories such as PAC-Bayes bounds, minimum description length and marginal likelihood, but there are few tools to unravel the implicit regularization in play. Here, we analyze the implicit regularization of VL through the Edge of Stability (EoS) framework. EoS has previously been used to show that gradient d…

Comparison of $R_h=ct$ and $\Lambda$CDM using DESI DR1 measurements
Kunj Panchal, Shantanu Desai
https://arxiv.org/abs/2506.18445 https://

Comparison of $R_h=ct$ and $Λ$CDM using DESI DR1 measurements
We use DESI DR1 BAO measurements of the ratio of tranvserse comoving distance to Hubble distance in order to test the compatibility of $R_h=ct$ over flat $Λ$CDM. For this purpose, we used Bayesian model selection to evaluate the efficacy of these models given the observed data. When we consider the BAO measurements up to redshift of 1.3, both models are equally favored. However, when we consider the Lyman-$α$ QSO measurement at redshift of 2.33, we find Bayes factors of greater than 100 for f…

A Bayesian approach to modelling spectrometer data chromaticity corrected using beam factors -- II. Model priors and posterior odds
Peter H. Sims, Judd D. Bowman, Steven G. Murray, John P. Barrett, Rigel C. Cappallo, Colin J. Lonsdale, Nivedita Mahesh, Raul A. Monsalve, Alan E. E. Rogers, Titu Samson, Akshatha K. Vydula
https://…

A Bayesian approach to modelling spectrometer data chromaticity corrected using beam factors -- II. Model priors and posterior odds
The reliable detection of the global 21-cm signal, a key tracer of Cosmic Dawn and the Epoch of Reionization, requires meticulous data modelling and robust statistical frameworks for model validation and comparison. In Paper I of this series, we presented the Beam-Factor-based Chromaticity Correction (BFCC) model for spectrometer data processed using BFCC to suppress instrumentally induced spectral structure. We demonstrated that the BFCC model, with complexity calibrated by Bayes factor-based …

Replaced article(s) found for cs.GT. https://arxiv.org/list/cs.GT/new
[1/1]:
- Bayes correlated equilibria, no-regret dynamics in Bayesian games, and the price of anarchy
Kaito Fujii

Generalized Labeled Multi-Bernoulli Filters and Multitarget-Correlation Models
Ronald Mahler
https://arxiv.org/abs/2506.02772 https://

Generalized Labeled Multi-Bernoulli Filters and Multitarget-Correlation Models
The generalized labeled multi-Bernoulli (GLMB) filter is a theoretically rigorous Bayes-optimal multitarget tracking algorithm with computationally tractable implementations, based on labeled random finite set (LRFS) theory. It presumes that multitarget populations can be approximated using GLMB multitarget probability density functions (p.d.f.'s), which consist of weighted hypotheses regarding the current target-states. A special case of the GLMB p.d.f.-the LMB p.d.f.-presumes that the targets…

Comparing Misspecified Models with Big Data: A Variational Bayesian Perspective
Yong Li, Sushanta K. Mallick, Tao Zeng, Junxing Zhang
https://arxiv.org/abs/2507.00763

Comparing Misspecified Models with Big Data: A Variational Bayesian Perspective
Optimal data detection in massive multiple-input multiple-output (MIMO) systems often requires prohibitively high computational complexity. A variety of detection algorithms have been proposed in the literature, offering different trade-offs between complexity and detection performance. In recent years, Variational Bayes (VB) has emerged as a widely used method for addressing statistical inference in the context of massive data. This study focuses on misspecified models and examines the risk fu…

Optimal Estimation of Two-Way Effects under Limited Mobility
Xu Cheng, Sheng Chao Ho, Frank Schorfheide
https://arxiv.org/abs/2506.21987 https://

Optimal Estimation of Two-Way Effects under Limited Mobility
We propose an empirical Bayes estimator for two-way effects in linked data sets based on a novel prior that leverages patterns of assortative matching observed in the data. To capture limited mobility we model the bipartite graph associated with the matched data in an asymptotic framework where its Laplacian matrix has small eigenvalues that converge to zero. The prior hyperparameters that control the shrinkage are determined by minimizing an unbiased risk estimate. We show the proposed empiric…

Local empirical Bayes correction for Bayesian modeling
Yoshiko Hayashi
https://arxiv.org/abs/2506.11424 https://arxiv.org/pdf/2506.11…

Local empirical Bayes correction for Bayesian modeling
The James-Stein estimator has attracted much interest as a shrinkage estimator that yields better estimates than the maximum likelihood estimator. The James-Stein estimator is also very useful as an argument in favor of empirical Bayesian methods. However, for problems involving large-scale data, such as differential gene expression data, the distribution is considered a mixture distribution with different means that cannot be considered sufficiently close. Therefore, it is not appropriate to a…

Replaced article(s) found for stat.CO. https://arxiv.org/list/stat.CO/new
[1/1]:
- Closed-form approximations of the two-sample Pearson Bayes factor
Thomas J. Faulkenberry

Replaced article(s) found for math.ST. https://arxiv.org/list/math.ST/new
[1/1]:
Empirical Bayes large-scale multiple testing for high-dimensional binary outcome data

Joint Quantile Shrinkage: A State-Space Approach toward Non-Crossing Bayesian Quantile Models
David Kohns, Tibor Szendrei
https://arxiv.org/abs/2506.13257 …

Joint Quantile Shrinkage: A State-Space Approach toward Non-Crossing Bayesian Quantile Models
Crossing of fitted conditional quantiles is a prevalent problem for quantile regression models. We propose a new Bayesian modelling framework that penalises multiple quantile regression functions toward the desired non-crossing space. We achieve this by estimating multiple quantiles jointly with a prior on variation across quantiles, a fused shrinkage prior with quantile adaptivity. The posterior is derived from a decision-theoretic general Bayes perspective, whose form yields a natural state-s…