Related papers: Bayesian Estimation of Multinomial Cell Probabilit…
Inferring the value of a property of a large stochastic system is a difficult task when the number of samples is insufficient to reliably estimate the probability distribution. The Bayesian estimator of the property of interest requires the…
Several approaches have been proposed in the literature for clustering multivariate ordinal data. These methods typically treat missing values as absent information, rather than recognizing them as valuable for profiling population…
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 propose a Bayesian approach to estimating parameters in multiclass functional models. Unordered multinomial probit, ordered multinomial probit and multinomial logistic models are considered. We use finite random series priors based on a…
We present a new approach to the electromagnetic inverse problem that explicitly addresses the ambiguity associated with its ill-posed character. Rather than calculating a single ``best'' solution according to some criterion, our approach…
We consider the problem of performing Bayesian inference in probabilistic models where observations are accompanied by uncertainty, referred to as "uncertain evidence." We explore how to interpret uncertain evidence, and by extension the…
One of the goals of probabilistic inference is to decide whether an empirically observed distribution is compatible with a candidate Bayesian network. However, Bayesian networks with hidden variables give rise to highly non-trivial…
A spectral approach to Bayesian inference is presented. It pursues the emulation of the posterior probability density. The starting point is a series expansion of the likelihood function in terms of orthogonal polynomials. From this…
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…
Spreadsheets are ubiquitous in business with the financial sector particularly heavily reliant on the technology. It is known that the level of spreadsheet error can be high and that it is often necessary to review spreadsheets based on a…
The integration of data and knowledge from several sources is known as data fusion. When data is only available in a distributed fashion or when different sensors are used to infer a quantity of interest, data fusion becomes essential. In…
A new method for multinomial inference is proposed by representing the cell probabilities as unordered segments on the unit interval and following Dempster-Shafer (DS) theory. The resulting DS posterior is then strengthened to improve…
In Generalised Bayesian Inference (GBI), the learning rate and hyperparameters of the loss must be estimated. These inference-hyperparameters can't be estimated jointly with the other parameters, from the data, by giving them a prior.…
This paper deals with Bayesian inference of a mixture of Gaussian distributions. A novel formulation of the mixture model is introduced, which includes the prior constraint that each Gaussian component is always assigned a minimal number of…
We propose a novel Bayesian model selection technique on linear mixed-effects models to compare multiple treatments with a control. A fully Bayesian approach is implemented to estimate the marginal inclusion probabilities that provide a…
It has been shown that one can accommodate data (Bayes) and constraints (MaxEnt) in one method, the method of Maximum (relative) Entropy (ME) (Giffin 2007). In this paper we show a complex agent based example of inference with two different…
We introduce a generalized Bayesian method for multiple changepoint analysis with a loss function inspired by multinomial logistic regression. The method does not require a specification of the data-generating process and avoids restrictive…
Importance sampling algorithms are discussed in detail, with an emphasis on implicit sampling, and applied to data assimilation via particle filters. Implicit sampling makes it possible to use the data to find high-probability samples at…
Motivated by inferring cellular signaling networks using noisy flow cytometry data, we develop procedures to draw inference for Bayesian networks based on error-prone data. Two methods for inferring causal relationships between nodes in a…
This paper modifies Jaynes's axioms of plausible reasoning and derives the minimum relative entropy principle, Bayes's rule, as well as maximum likelihood from first principles. The new axioms, which I call the Optimum Information…