Related papers: Closed-Form Power and Sample Size Calculations for…
In many hypothesis testing applications, we have mixed priors, with well-motivated informative priors for some parameters but not for others. The Bayesian methodology uses the Bayes factor and is helpful for the informative priors, as it…
Score based approaches to sampling have shown much success as a generative algorithm to produce new samples from a target density given a pool of initial samples. In this work, we consider if we have no initial samples from the target…
Gaussian time-series models are often specified through their spectral density. Such models present several computational challenges, in particular because of the non-sparse nature of the covariance matrix. We derive a fast approximation of…
Although variable selection is one of the most popular areas of modern statistical research, much of its development has taken place in the classical paradigm compared to the Bayesian counterpart. Somewhat surprisingly, both the paradigms…
A method of calculating probability values from a system of marginal constraints is presented. Previous systems for finding the probability of a single attribute have either made an independence assumption concerning the evidence or have…
We characterize the sample size required for accurate graphical model selection from non-stationary samples. The observed data is modeled as a vector-valued zero-mean Gaussian random process whose samples are uncorrelated but have different…
Sequencing technologies have revolutionised the field of molecular biology. We now have the ability to routinely capture the complete RNA profile in tissue samples. This wealth of data allows for comparative analyses of RNA levels at…
Factorial designs are frequently used in different fields of science, e.g. psychological, medical or biometric studies. Standard approaches, as the ANOVA $F$-test, make different assumptions on the distribution of the error terms, the…
Bayesian model-based reinforcement learning is a formally elegant approach to learning optimal behaviour under model uncertainty, trading off exploration and exploitation in an ideal way. Unfortunately, finding the resulting Bayes-optimal…
An ongoing "reproducibility crisis" calls into question scientific discoveries across a variety of disciplines ranging from life to social sciences. Replication studies aim to investigate the validity of findings in published research, and…
Investing efficiently in future research to improve policy decisions is an important goal. Expected Value of Sample Information (EVSI) can be used to select the specific design and sample size of a proposed study by assessing the benefit of…
Estimating the model evidence - or mariginal likelihood of the data - is a notoriously difficult task for finite and infinite mixture models and we reexamine here different Monte Carlo techniques advocated in the recent literature, as well…
It has historically been a challenge to perform Bayesian inference in a design-based survey context. The present paper develops a Bayesian model for sampling inference in the presence of inverse-probability weights. We use a hierarchical…
Metrics of model goodness-of-fit, model comparison, and model parameter estimation are the main categories of statistical problems in science. Bayesian and frequentist methods that address these questions often rely on a likelihood…
Microbiome omics data including 16S rRNA reveal intriguing dynamic associations between the human microbiome and various disease states. Drastic changes in microbiota can be associated with factors like diet, hormonal cycles, diseases, and…
My dissertation revolves around Bayesian approaches towards constrained statistical inference in the factor analysis (FA) model. Two interconnected types of restricted-model selection are considered. These types have a natural connection to…
Factor analysis is over a century old, but it is still problematic to choose the number of factors for a given data set. The scree test is popular but subjective. The best performing objective methods are recommended on the basis of…
For many important problems the quantity of interest is an unknown function of the parameters, which is a random vector with known statistics. Since the dependence of the output on this random vector is unknown, the challenge is to identify…
We use rescaled Gaussian processes as prior models for functional parameters in nonparametric statistical models. We show how the rate of contraction of the posterior distributions depends on the scaling factor. In particular, we exhibit…
We consider large-scale studies in which it is of interest to test a very large number of hypotheses, and then to estimate the effect sizes corresponding to the rejected hypotheses. For instance, this setting arises in the analysis of gene…