Related papers: Doomsday: Two Flaws

Triggered by a recent interesting New Scientist article on the too frequent incorrect use of probabilistic evidence in courts, I introduce the basic concepts of probabilistic inference with a toy model, and discuss several important issues…

Selection effects in cosmology are often invoked to "explain" why some of the fundamental constant of Nature, and in particular the cosmological constant, take on the value they do in our Universe. We briefly review this probabilistic…

This chapter provides a overview of Bayesian inference, mostly emphasising that it is a universal method for summarising uncertainty and making estimates and predictions using probability statements conditional on observed data and an…

Bayesian doubly robust (DR) causal inference faces a fundamental dilemma: joint modeling of outcome and propensity score suffers from the feedback problem where outcome information contaminates propensity score estimation, while two-step…

There are two main opposing schools of statistical reasoning, Frequentist and Bayesian approaches. Until recent days, the frequentist or classical approach has dominated the scientific research, but Bayesianism has reappeared with a strong…

Missing attributes are ubiquitous in causal inference, as they are in most applied statistical work. In this paper, we consider various sets of assumptions under which causal inference is possible despite missing attributes and discuss…

A modern assessment of the classical Boltzmann-Schuetz argument for large-scale entropy fluctuations as the origin of our observable cosmological domain is given. The emphasis is put on the central implication of this picture which flatly…

Recently, several researchers have claimed that conclusions obtained from a Bayes factor (or the posterior odds) may contradict those obtained from Bayesian posterior estimation. In this short paper, we wish to point out that no such…

In this paper we provide a simple random-variable example of inconsistent information, and analyze it using three different approaches: Bayesian, quantum-like, and negative probabilities. We then show that, at least for this particular…

Latent Dirichlet allocation (LDA) obtains essential information from data by using Bayesian inference. It is applied to knowledge discovery via dimension reducing and clustering in many fields. However, its generalization error had not been…

Problems in two axiomatizations of Ja\'skowski's discussive (or discursive) logic D2 are considered. A recent axiomatization of D2 and completeness proof relative to D2's intended semantics seems to be mistaken because some formulas valid…

Criticisms of so called `subjective probability' come on the one hand from those who maintain that probability in physics has only a frequentistic interpretation, and, on the other, from those who tend to `objectivise' Bayesian theory,…

We analyse an argument of Deutsch, which purports to show that the deterministic part of classical quantum theory together with deterministic axioms of classical decision theory, together imply that a rational decision maker behaves as if…

Missing data and confounding are two problems researchers face in observational studies for comparative effectiveness. Williamson et al. (2012) recently proposed a unified approach to handle both issues concurrently using a multiply-robust…

I think we can agree that dealing with uncertainty is not easy. Probability is the main tool for dealing with uncertainty, and we know there are many probability-related puzzles and paradoxes. Here I describe a rather idiosyncratic…

In a recent paper (quant-ph/9906015), Deutsch claims to derive the "probabilistic predictions of quantum theory" from the "non-probabilistic axioms of quantum theory" and the "non-probabilistic part of classical decision theory." We show…

Bayesian inference is limited in scope because it cannot be applied in idealized contexts where none of the hypotheses under consideration is true and because it is committed to always using the likelihood as a measure of evidential…

When performing Bayesian inference, we frequently need to work with conditional probability densities. For example, the posterior function is the conditional density of the parameters given the data. Some might worry that conditional…

In the absence of a fundamental theory that precisely predicts values for observable parameters, anthropic reasoning attempts to constrain probability distributions over those parameters in order to facilitate the extraction of testable…

A fundamental question in causal inference is whether it is possible to reliably infer manipulation effects from observational data. There are a variety of senses of asymptotic reliability in the statistical literature, among which the most…