Related papers: Sometimes size does not matter
We introduce a mathematical framework for quantifying fine-tuning in general physical settings. In particular, we identify two distinct perspectives on fine-tuning, namely, a local and a global perspective --- and develop corresponding…
The anthropic principle is an inevitable constraint on the space of possible theories. As such it is central to determining the limits of physics. In particular, we contend that what is ultimately possible in physics is determined by…
In the mini-superspace approximation to cosmology, the canonical measure can be used to compute probabilities when a cutoff is introduced in the phase space to regularize the divergent measure. However, the region initially constrained by a…
A basic requirement for a mathematical model is often that its solution (output) shouldn't change much if the model's parameters (input) are perturbed. This is important because the exact values of parameters may not be known and one would…
The solution to fine tuning is one of the principal motivations for Beyond the Standard Model (BSM) Studies. However constraints on new physics indicate that many of these BSM models are also fine tuned (although to a much lesser extent).…
Based on the cosmological principle only, the method of describing the evolution of the Universe, called cosmography, is in fact a kinematics of cosmological expansion. The effectiveness of cosmography lies in the fact that it allows, based…
As the statistical power of imaging surveys grows, it is crucial to account for all systematic uncertainties. This is normally done by constructing a model of these uncertainties and then marginalizing over the additional model parameters.…
In cosmology, we would like to explain our observations and predict future observations from theories of the entire universe. Such cosmological theories make ontological assumptions of what entities exist and what their properties and…
We investigate a number of simple toy models to explore interesting relationships between dynamics and typicality. We start with an infinite model that has been proposed as an illustration of how non-ergodic dynamics can produce interesting…
The measure problem of cosmology is how to assign normalized probabilities to observations in a universe so large that it may have many observations occurring at many different spacetime locations. I have previously shown how the Boltzmann…
Evidence for fine-tuning of physical parameters suitable for life can perhaps be explained by almost any combination of providence, coincidence or multiverse. A multiverse usually includes parts unobservable to us, but if the theory for it…
Fine-tuning pre-trained models has been ubiquitously proven to be effective in a wide range of NLP tasks. However, fine-tuning the whole model is parameter inefficient as it always yields an entirely new model for each task. Currently, many…
Given the growth in the variety and precision of astronomical datasets of interest for cosmology, the best cosmological constraints are invariably obtained by combining data from different experiments. At the likelihood level, one…
Model selection aims to determine which theoretical models are most plausible given some data, without necessarily asking about the preferred values of the model parameters. A common model selection question is to ask when new data require…
The problem of estimating cosmological parameters such as $\Omega$ from noisy or incomplete data is an example of an inverse problem and, as such, generally requires a probablistic approach. We adopt the Bayesian interpretation of…
It is shown that the homogeneous and isotropic Universe is spatially flat in the limit which takes into account the moments of infinitely large orders of probabilistic distribution of a scale factor with respect to its mean value in the…
We present general, analytic methods for Cosmological likelihood analysis and solve the "many-parameters" problem in Cosmology. Maxima are found by Newton's Method, while marginalization over nuisance parameters, and parameter errors and…
Existing training criteria in automatic speech recognition(ASR) permit the model to freely explore more than one time alignments between the feature and label sequences. In this paper, we use entropy to measure a model's uncertainty, i.e.…
Some properties of the world are fixed by physics derived from mathematical symmetries, while others are selected from an ensemble of possibilities. Several successes and failures of ``anthropic'' reasoning in this context are reviewed in…
Probabilistic metrology attempts to improve parameter estimation by occasionally reporting an excellent estimate and the rest of the time either guessing or doing nothing at all. Here we show that probabilistic metrology can never improve…