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RNA-Seq data characteristically exhibits large variances, which need to be appropriately accounted for in the model. We first explore the effects of this variability on the maximum likelihood estimator (MLE) of the overdispersion parameter…
It is shown that a consistent application of Bayesian updating from a prior probability density to a posterior using evidence in the form of expectation constraints leads to exactly the same results as the application of the maximum entropy…
Bayesian neural networks (BNNs) can account for both aleatoric and epistemic uncertainty. However, in BNNs the priors are often specified over the weights which rarely reflects true prior knowledge in large and complex neural network…
In a Bayesian network, we wish to evaluate the marginal probability of a query variable, which may be conditioned on the observed values of some evidence variables. Here we first present our "border algorithm," which converts a BN into a…
Estimating the causal effect of an exposure on an outcome is an important task in many economical and biological studies. Mendelian randomization, in particular, uses genetic variants as instruments to estimate causal effects in…
Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…
It is often of interest to combine available estimates of a similar quantity from multiple data sources. When the corresponding variances of each estimate are also available, a model should take into account the uncertainty of the estimates…
Data increasingly take the form of a multi-way array, or tensor, in several biomedical domains. Such tensors are often incompletely observed. For example, we are motivated by longitudinal microbiome studies in which several timepoints are…
A flexible representation of uncertainty that remains within the standard framework of probabilistic measure theory is presented along with a study of its properties. This representation relies on a specific type of outer measure that is…
This paper extends the work of Clarke [1] on the Bayesian foundations of the biomagnetic inverse problem. It derives expressions for the expectation and variance of the a posteriori source current probability distribution given a prior…
Estimation of mutual information between (multidimensional) real-valued variables is used in analysis of complex systems, biological systems, and recently also quantum systems. This estimation is a hard problem, and universally good…
The past two decades have seen a growing interest in combining causal information, commonly represented using causal graphs, with machine learning models. Probability trees provide a simple yet powerful alternative representation of causal…
The exponential and the Lomax distributions are widely used in life testing experiments in mixture models. A mixture model of exponential distribution and Lomax distribution is proposed. Parameters of the proposed model are estimated using…
Computing the exact likelihood of data in large Bayesian networks consisting of thousands of vertices is often a difficult task. When these models contain many deterministic conditional probability tables and when the observed values are…
In this present work, we discuss the Bayesian inference for the bivariate pseudo-exponential distribution. Initially, we assume independent gamma priors and then pseudo-gamma priors for the pseudo-exponential parameters. We are primarily…
A suggestion is made for improving the Feldman Cousins method of estimating signal counts in the presence of background. The method concentrates on finding essential information about the signal and ignoring extraneous information about…
When a mathematical or computational model is used to analyse some system, it is usual that some parameters resp.\ functions or fields in the model are not known, and hence uncertain. These parametric quantities are then identified by…
A widely applicable Bayesian information criterion (Watanabe, 2013) is applicable for both regular and singular models in the model selection problem. This criterion tends to overestimate the log marginal likelihood. We identify an…
Bivariate count data arise in several different disciplines (epidemiology, marketing, sports statistics, etc., to name but a few) and the bivariate Poisson distribution which is a generalization of the Poisson distribution plays an…
Integrating data from multiple heterogeneous sources has become increasingly popular to achieve a large sample size and diverse study population. This paper reviews development in causal inference methods that combines multiple datasets…