Related papers: Boltzmann-Informed Probabilities
Probabilistic forecasts are essential for various downstream applications such as business development, traffic planning, and electrical grid balancing. Many of these probabilistic forecasts are performed on time series data that contain…
Conventional game theory assumes that players are perfectly rational. In a realistic situation, however, players are rarely perfectly rational. This bounded rationality is one of the main reasons why the predictions of Nash equilibrium in…
We consider a constrained hierarchical opinion dynamics in the case of leaders' competition and with complete information among leaders. Each leaders' group tries to drive the followers' opinion towards a desired state accordingly to a…
Reinforcement learning systems are often concerned with balancing exploration of untested actions against exploitation of actions that are known to be good. The benefit of exploration can be estimated using the classical notion of Value of…
We study the value of stochastic predictions in online optimal control with random disturbances. Prior work provides performance guarantees based on prediction error but ignores the stochastic dependence between predictions and…
We develop a theory of estimation when in addition to a sample of $n$ observed outcomes the underlying probabilities of the observed outcomes are known, as is typically the case in the context of numerical simulation modeling, e.g. in…
Results in contact sports like Rugby are mainly interpreted in terms of the ability and/or luck of teams. But this neglects the important role of the {\em motivation} of players, reflected in the effort exerted in the game. Here we present…
Maximum Likelihood Estimation (MLE) is the bread and butter of system inference for stochastic systems. In some generality, MLE will converge to the correct model in the infinite data limit. In the context of physical approaches to system…
We establish fundamental connections between utility theories of wealth from the economic sciences and information-theoretic quantities. In particular, we introduce operational tasks based on betting where both gambler and bookmaker have…
Standard maximum likelihood estimation cannot be applied to discrete energy-based models in the general case because the computation of exact model probabilities is intractable. Recent research has seen the proposal of several new…
We define quantum-like probabilistic behaviour as behaviour which is impossible to describe by using the classical probability model. We discuss the conjecture that cognitive behaviour is quantum-like. There is presented the scheme for an…
In recent years, probabilistic forecasts techniques were proposed in research as well as in applications to integrate volatile renewable energy resources into the electrical grid. These techniques allow decision makers to take the…
There is a third way of implementing probability models and practicing. This is to answer questions put in terms of observables. This eliminates frequentist hypothesis testing and Bayes factors and it also eliminates parameter estimation.…
The probability distribution function for thermodynamics and econophysics is obtained by solving an equilibrium equation. This approach is different from the common one of optimizing the entropy of the system or obtaining the state of…
We derive an analytical approximation for making quantitative predictions for ecological communities as a function of the mean intensity of the inter-specific competition and the species richness. This method, with only a fraction of the…
As a dedicated follower of sports statistics and with the MLB season beginning in late March, I set out to predict how many wins each team would accumulate by the end of the 162 game season. The goal was to build a simulation framework…
Prediction-powered inference (PPI) is a recent framework for valid statistical inference with partially labeled data, combining model-based predictions on a large unlabeled set with bias correction from a smaller labeled subset. Building on…
The handling of probabilities in the form of uncertainty or partial information is an essential task for LLMs in many settings and applications. A common approach to evaluate an LLM's probabilistic reasoning capabilities is to assess its…
Multiplicative random processes in (not necessaryly equilibrium or steady state) stochastic systems with many degrees of freedom lead to Boltzmann distributions when the dynamics is expressed in terms of the logarithm of the normalized…
We compare probabilistic predictions of extreme temperature anomalies issued by two different forecast schemes. One is a dynamical physical weather model, the other a simple data model. We recall the concept of skill scores in order to…