Related papers: Apocalypse Now? Reviving the Doomsday Argument
In statistical practice, whether a Bayesian or frequentist approach is used in inference depends not only on the availability of prior information but also on the attitude taken toward partial prior information, with frequentists tending to…
Our Universe is a vast, tantalizing enigma - a mystery that has aroused humankind's innate curiosity for eons. Begging questions on alien lifeforms have been thus far unfruitful, even with the bounding advancements we have embarked upon in…
This paper describes prediction methods for the number of future events from a population of units associated with an on-going time-to-event process. Examples include the prediction of warranty returns and the prediction of the number of…
The existence of a positive and possibly varying Lambda-term opens a much wider field of possibilities for the future of our Universe than it was usually thought before. Definite predictions may be made for finite (though very large)…
A wide range of stochastic processes that model the growth and decline of populations exhibit a curious dichotomy: with certainty either the population goes extinct or its size tends to infinity. There is a elegant and classical theorem…
Current observations do not rule out the possibility that the Universe might end up in an abrupt event. Different such scenarios may be explored through suitable parameterizations of the dark energy and then confronted to cosmological…
The fundamental laws and constants of our universe seem to be finely tuned for life. The various multiverse hypotheses are popular explanations for the fine tuning. This paper reviews the four main suggestions on inference in the presence…
Anthropic reasoning often begins with the premise that we should expect to find ourselves typical among all intelligent observers. However, in the infinite universe predicted by inflation, there are some civilizations which have spread…
The Simulation Argument has gained significant traction in the public arena. It has offered a hypothesis based on probabilistic analysis of its assumptions that we are likely to exist within a computer simulation. This has been derived from…
The observed value $\Lambda_{\rm obs}$ of the cosmological constant $\Lambda$ is extremely smaller than theoretical expectations, and the anthropic argument has been proposed as a solution to this problem because galaxies do not form when…
Bayesian hypothesis testing is re-examined from the perspective of an a priori assessment of the test statistic distribution under the alternative. By assessing the distribution of an observable test statistic, rather than prior parameter…
Loss-based updating, including generalized Bayes, Gibbs, and quasi-posteriors, replaces likelihoods by a user-chosen loss and produces a posterior-like distribution via exponential tilt. We give a decision-theoretic characterization that…
According to our current conception of physics, any valid physical theory is supposed to describe the objective evolution of a unique external world. However, this condition is challenged by quantum theory, which suggests that physical…
High-energy astrophysical events that cause galaxy-scale extinctions have been proposed as a way to explain or mollify the Fermi Paradox, by making the universe at earlier times more dangerous for evolving life, and reducing its present-day…
I discuss how modern cosmology illustrates under-determination of theoretical hypotheses by data, in ways that are different from most philosophical discussions. I emphasize cosmology's concern with what data could in principle be collected…
Bayesian Inference is a powerful approach to data analysis that is based almost entirely on probability theory. In this approach, probabilities model {\it uncertainty} rather than randomness or variability. This thesis is composed of a…
It is often thought that the existence of other worlds cannot be scientifically verified and therefore should be treated as philosophical speculation. In this article, I describe several methods for determining if other worlds exist, even…
Bayes' theorem incorporates distinct types of information through the likelihood and prior. Direct observations of state variables enter the likelihood and modify posterior probabilities through consistent updating. Information in terms of…
Bayesian inference --- although becoming popular in physics and chemistry --- is hampered up to now by the vagueness of its notion of prior probability. Some of its supporters argue that this vagueness is the unavoidable consequence of the…
There is no easy extension of Kaplan-Meier and Nelson-Aalen estimators to the bivariate case, and estimating bivariate survival distributions nonparametrically is associated with various non-trivial problems. The Dabrowska estimator will…