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General Probabilistic Theories provide the most general mathematical framework for the theory of probability in an operationally natural manner, and generalize classical and quantum theories. In this article, we study state-discrimination…
We study the properties of variational Bayes approximations for exponential family models with missing values. It is shown that the iterative algorithm for obtaining the variational Bayesian estimator converges locally to the true value…
The Bayesian brain hypothesis postulates that the brain accurately operates on statistical distributions according to Bayes' theorem. The random failure of presynaptic vesicles to release neurotransmitters may allow the brain to sample from…
In statistical inference, uncertainty is unknown and all models are wrong. That is to say, a person who makes a statistical model and a prior distribution is simultaneously aware that both are fictional candidates. To study such cases,…
In a meta-analysis, it is important to specify a model that adequately describes the effect-size distribution of the underlying population of studies. The conventional normal fixed-effect and normal random-effects models assume a normal…
Bayes statistics and statistical physics have the common mathematical structure, where the log likelihood function corresponds to the random Hamiltonian. Recently, it was discovered that the asymptotic learning curves in Bayes estimation…
When we use the normal mixture model, the optimal number of the components describing the data should be determined. Testing homogeneity is good for this purpose; however, to construct its theory is challenging, since the test statistic…
This paper presents a study of the large-sample behavior of the posterior distribution of a structural parameter which is partially identified by moment inequalities. The posterior density is derived based on the limited information…
We develop a systematic procedure to approximate generalized free energy in out of equilibrium stochastic systems. The procedure only requires knowledge of the averages of macroscopic observables and uses quasi-equilibrium distribution to…
This paper discusses the asymptotic behavior of regression models under general conditions. First, we give a general inequality for the difference of the sum of square errors (SSE) of the estimated regression model and the SSE of the…
The conventional approach to Bayesian decision-theoretic experiment design involves searching over possible experiments to select a design that maximizes the expected value of a specified utility function. The expectation is over the joint…
In this paper, we consider Bayesian hypothesis testing for the balanced one-way random effects model. A special choice of the prior formulation for the ratio of variance components is shown to yield an explicit closed-form Bayes factor…
Regression adjustment is broadly applied in randomized trials under the premise that it usually improves the precision of a treatment effect estimator. However, previous work has shown that this is not always true. To further understand…
While observational data are routinely used to estimate causal effects of biomedical treatments, doing so requires special methods to adjust for observed confounding. These methods invariably rely on untestable statistical and causal…
From the sampling of data to the initialisation of parameters, randomness is ubiquitous in modern Machine Learning practice. Understanding the statistical fluctuations engendered by the different sources of randomness in prediction is…
We consider tests of hypotheses when the parameters are not identifiable under the null in semiparametric models, where regularity conditions for profile likelihood theory fail. Exponential average tests based on integrated profile…
Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…
Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…
We present an extension of local sensitivity analysis, also referred to as the perturbation approach for uncertainty quantification, to Bayesian inverse problems. More precisely, we show how moments of random variables with respect to the…
Bayesian inferences in high energy physics often use uniform prior distributions for parameters about which little or no information is available before data are collected. The resulting posterior distributions are therefore sensitive to…