Bayesian probability theory is one of the most successful frameworks to model reasoning under uncertainty. Its defining property is the interpretation of probabilities as degrees of belief in propositions about the state of the world relative to an inquiring subject. This essay examines the notion of subjectivity by dr…
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48 results for “subjective probabilities”
Testing Ambiguity and Machina Preferences Within a Quantum-theoretic Framework for Decision-makingecon.GN
Quantum framework explains human choices in ambiguity and risk.
problem Testing human choices in ambiguity and risk.
method Quantum-theoretic framework for decision-making under uncertainty.
result Quantum framework faithfully models human choices in ambiguity and risk.
Managing Derivative Exposureq-fin.PM
We present an approach to derivative exposure management based on subjective and implied probabilities. We suggest to maximize the valuation difference subject to risk constraints and propose a class of risk measures derived from the subjective distribution. We illustrate this process with specific examples for the two…
Paper develops consistent estimation of propensity scores for rare exposures.
problem Estimation of propensity score functions for rare exposures in oversampled cohorts.
method Flexible computational implementation using source population probability of exposure and observation weighting.
result Low empirical bias and variance for consistent propensity score function estimators.
We propose a probabilistic framework for pricing derivatives, which acknowledges that information and beliefs are subjective. Market prices can be translated into implied probabilities. In particular, futures imply returns for these implied probability distributions. We argue that volatility is not risk, but uncertaint…
Paper extends Bayes Theorem for interval probability estimates.
problem Real-world input probabilities are often interval estimates, not precise.
method Developed IT2 version of Bayes Theorem and a novel algorithm for encoding intervals.
result Conservative method avoids invalid output results from inconsistent input.
Portfolio Analysis Based on Markowitz Stochastic Dominance Criteria: A Behavioral Perspectiveq-fin.PM
The paper analyzes how behavioral investors make portfolio decisions using Markowitz Stochastic Dominance criteria.
problem Understanding how behavioral investors make portfolio decisions.
method Developed stochastic optimization problems and MILP models to capture subjective decision weights and probability weighting functions.
result The developed models can be used to formulate computationally tractable portfolio analysis problems.
Develops a method to make predictions more informative without sacrificing accuracy.
problem Tension between well-calibrated and bold predictions.
method Bayesian model selection-based approach for assessing calibration and maximizing boldness.
result Maximally emboldening predictions while maintaining desired level of calibration.
Maximizing Utility of Consumption Subject to a Constraint on the Probability of Lifetime Ruinq-fin.PM
In this note, we explicitly solve the problem of maximizing utility of consumption (until the minimum of bankruptcy and the time of death) with a constraint on the probability of lifetime ruin, which can be interpreted as a risk measure on the whole path of the wealth process.
The Reality Gameq-fin.GN
We introduce an evolutionary game with feedback between perception and reality, which we call the reality game. It is a game of chance in which the probabilities for different objective outcomes (e.g., heads or tails in a coin toss) depend on the amount wagered on those outcomes. By varying the `reality map', which rel…
This paper develops a dynamic equilibrium model where agents exhibit a strong form of belief heterogeneity: they disagree about zero probability events. It is shown that, somewhat surprisingly, equilibrium exists in this setting, and that the disagreement about nullsets naturally leads to equilibrium asset pricing bubb…
We propose a projected gradient dynamical system as a model for a bargaining scheme for an asset for which the two interested agents have personal valuations which do not initially coincide. The personal valuations are formed using subjective beliefs concerning the future states of the world and the reservation prices …
We determine the optimal investment strategy in a Black-Scholes financial market to minimize the so-called {\it probability of drawdown}, namely, the probability that the value of an investment portfolio reaches some fixed proportion of its maximum value to date. We assume that the portfolio is subject to a payout that…
A graph-based model aligns unaligned fMRI data across subjects efficiently.
problem Aligning fMRI data from different subjects with varying responses to stimuli.
method Develops a graph-based model to represent similarities between fMRI samples, regularizes the framework for efficient optimization, and uses kernel-based feature extraction.
result The method outperforms state-of-the-art techniques on both temporally-aligned and unaligned fMRI data.
Proposes a new method to explain model predictions for consumer recourse.
problem Current explanation methods fail to provide meaningful recourse to decision subjects.
method Develops feature responsiveness scores to highlight actionable features.
result Standard practices can undermine decision subjects by highlighting unresponsive features.
Random covers of surfacesmath.GT
Random covers of hyperbolic surfaces follow a specific probability measure.
problem Understanding the distribution of random covers of hyperbolic surfaces.
method Analyzing random covers subject to specific group isomorphism conditions.
result Asymptotic distribution of random covers according to a probability measure on moduli space of metric graphs.
Research in Econophysicscond-mat.stat-mech
This article is written for the online newspaper "The Photon" published by the Department of Physics, University of Maryland. The article describes econophysics research done in the group of Victor Yakovenko. It briefly surveys the subjects "Statistical Mechanics of Money, Income, and Wealth" and "Probability Distribut…
This paper introduces a new technique for quantifying the approximation error of a broad class of probabilistic inference programs, including ones based on both variational and Monte Carlo approaches. The key idea is to derive a subjective bound on the symmetrized KL divergence between the distribution achieved by an a…
We extend the Vasiček loan portfolio model to a setting where liabilities fluctuate randomly and asset values may be subject to systemic jump risk. We derive the probability distribution of the percentage loss of a uniform portfolio and analyze its properties. We find that the impact of liability risk is ambiguous and …
Two BO methods improve reliability optimization for rare failures.
problem Maximizing reliability of designs subject to random perturbations.
method Bayesian optimization with Thompson sampling and knowledge gradient.
result Proposed methods outperform existing techniques in extreme failure probability scenarios.
Bayesian imaging methods deliver trustworthy probabilities in some cases but struggle with uncertainty quantification.
problem Uncertainty quantification in Bayesian imaging methods.
method Monte Carlo method to explore reliability of probabilities.
result Modern Bayesian imaging techniques deliver reliable probabilities in some cases but not for uncertainty quantification.
The article reviews scoring rules for estimating and evaluating forecasts.
problem Evaluating probabilistic forecasts and estimating probability distributions.
method Mathematical foundations and characterization of scoring rules.
result Important families of scoring rules and their applications in statistics and machine learning.
Stochastic Perron's Method for the Probability of lifetime ruin problem under transaction costsmath.OC
We apply stochastic Perron's method to a singular control problem where an individual targets at a given consumption rate, invests in a risky financial market in which trading is subject to proportional transaction costs, and seeks to minimize her probability of lifetime ruin. Without relying on the dynamic programming…
In this note we prove the a pointwise ergodic theorem for functions taking values in a separable complete CAT(0)-space, analogous to Lindenstrauss' pointwise ergodic theorem for real-valued integrable functions on a probability space subject to a probability-preserving action of an amenable l.c.s.c. group, where in the…
We run experimental asset markets to investigate the emergence of excess trading and the occurrence of synchronised trading activity leading to crashes in the artificial markets. The market environment favours early investment in the risky asset and no posterior trading, i.e. a buy-and-hold strategy with a most probabl…
A lending scheme for a system of interconnected banks with probabilistic constraints of failureq-fin.MF
Optimal interbank lending scheme with probabilistic bank failure constraints.
problem Optimizing interbank lending in a network of interconnected banks with probabilistic constraints on failure.
method Derive a closed-form solution for an optimal control problem, compute systemic relevance parameters.
result General solution for interbank lending with probabilistic constraints for all banks.
A trader optimizes robust superhedging under subjective market views.
problem Optimizing robust superhedging with subjective market views.
method Dynamic programming and robust maximization under new measures.
result Existence and uniqueness of optimal investment and consumption strategies.
DynForest predicts event probabilities from longitudinal data, handling endogenous predictors.
problem Predicting individual risk using longitudinal patient history.
method Random survival forests with time-fixed features from longitudinal predictors.
result DynForest provides accurate individual event probability predictions.
Study on risk model with claims, dividends, and random probabilities.
problem Analyzing a risk model with claims, delayed claims, and randomized dividends.
method Discrete time Compound Beta-Binomial Risk Model with recursive expressions for Gerber-Shiu function.
result Recursive relations for ruin-related quantities obtained.
Proposes a new method to quantify uncertainty in neural network predictions.
problem Uncertainty in neural network predictions, especially in classification tasks.
method Explicit modeling of prediction uncertainty using subjective logic and Dirichlet distributions.
result Improved uncertainty estimation, leading to better performance on out-of-distribution queries and adversarial perturbations.
In this paper, we study the sensitivity of the spectral clustering based community detection algorithm subject to a Erdos-Renyi type random noise model. We prove phase transitions in community detectability as a function of the external edge connection probability and the noisy edge presence probability under a general…
-divergences are a general class of divergences between probability measures which include as special cases many commonly used divergences in probability, mathematical statistics and information theory such as Kullback-Leibler divergence, chi-squared divergence, squared Hellinger distance, total variation distance e…
New metric and method for sEMG-based gesture recognition under domain shifts.
problem Measuring and adapting to domain divergence in sEMG-based gesture recognition.
method Probability distribution-based metric, 2-stage autoregressive RNN architecture.
result Improved autoregressive, RNN-based architecture enhances performance.
We develop a unified approach for classification and regression support vector machines for data subject to right censoring. We provide finite sample bounds on the generalization error of the algorithm, prove risk consistency for a wide class of probability measures, and study the associated learning rates. We apply th…
A new method combines classification with population Monte Carlo for efficient ABC.
problem Inefficient particle proposals and subjectivity in ABC methods.
method Classification-PMC, blending adaptive proposals and classification.
result Classification-PMC outperforms state-of-the-art ABC methods in simulations.
Algorithm minimizes regret in adaptive control of unknown linear systems.
problem Adaptive control of unknown linear systems with quadratic costs.
method Provably polynomial time algorithm using recent developments in system estimation and robust controller synthesis.
result First algorithm with high probability guarantees of sub-linear regret.
We develop a model of tax evasion based on the Ising model. We augment the model using an appropriate enforcement mechanism that may allow policy makers to curb tax evasion. With a certain probability tax evaders are subject to an audit. If they get caught they behave honestly for a certain number of periods. Simulatin…
This paper provides a mathematical framework for understanding distribution learning models.
problem The paradox between memorization and generalization in distribution learning models.
method A unified mathematical framework to derive various distribution learning models.
result The models enjoy implicit regularization, avoiding the curse of dimensionality and resolving the paradox.
Optimizes ellipsoids for uncertainty regions in parameter estimation.
problem Learning minimal volume uncertainty ellipsoids for parameter estimation.
method Differentiable optimization approach using neural networks to approximate optimal ellipsoids.
result Approximately computed ellipsoids are smaller and more accurate than existing methods.
Given a set of experiments in which varying subsets of observed variables are subject to intervention, we consider the problem of identifiability of causal models exhibiting latent confounding. While identifiability is trivial when each experiment intervenes on a large number of variables, the situation is more complic…
Free Probability for predicting the performance of feed-forward fully connected neural networksstat.ML
New method predicts neural network performance using free probability theory.
problem Stability and performance prediction of feed-forward neural networks.
method Free Probability Theory and homotopy method for Jacobian spectral density computation.
result FPT metrics correlate highly with final test accuracies of neural networks.
Develops a method to estimate rare-event probabilities under distributional uncertainty.
problem Distributional uncertainty limits the effectiveness of rare-event simulation techniques.
method Wasserstein distributionally robust rare-event simulation (DRIS) framework.
result DRIS achieves vanishing relative error in estimating rare-event probabilities.
We present a new approach for studying the problem of optimal hedging of a European option in a finite and complete discrete-time market model. We consider partial hedging strategies that maximize the success probability or minimize the expected shortfall under a cost constraint and show that these problems can be trea…
There has been much recent interest in application of the pool-adjacent-violators (PAV) algorithm for the purpose of calibrating the probabilistic outputs of automatic pattern recognition and machine learning algorithms. Special cost functions, known as proper scoring rules form natural objective functions to judge the…
We perform a stability analysis for the utility maximization problem in a general semimartingale model where both liquid and illiquid assets (random endowments) are present. Small misspecifications of preferences (as modeled via expected utility), as well as views of the world or the market model (as modeled via subjec…
In this paper are presented methods of impact analysis on informatics system security accidents, qualitative and quantitative methods, starting with risk and informational system security definitions. It is presented the relationship between the risks of exploiting vulnerabilities of security system, security level of …
In this article, we address the question of how non-knowledge about future events that influence economic agents' decisions in choice settings has been formally represented in economic theory up to date. To position our discussion within the ongoing debate on uncertainty, we provide a brief review of historical develop…
Paper presents efficient algorithms for reconstructing noisy pooled data.
problem Reconstructing hidden states from noisy pooled data.
method Simple and efficient distributed algorithms for two noise models.
result Our algorithms reconstruct exact initial states with high probability.