相关论文: A Remark on the Assumptions of Bayes' Theorem
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 a Bayesian framework we prove that the optimal estimator of a conditional density is consistent.
Let $X|\mu\sim N_p(\mu,v_xI)$ and $Y|\mu\sim N_p(\mu,v_yI)$ be independent $p$-dimensional multivariate normal vectors with common unknown mean $\mu$. Based on observing $X=x$, we consider the problem of estimating the true predictive…
It is often of interest to condition on a singular event given by a random variable, e.g. $\{Y=y\}$ for a continuous random variable $Y$. Conditional measures with respect to this event are usually derived as a special case of the…
The problem of nonparametric estimation of the conditional density of a response, given a vector of explanatory variables, is classical and of prominent importance in many prediction problems since the conditional density provides a more…
Under mild conditions, it is shown the strong consistency of the Bayes estimator of the density. Moreover, the Bayes risk (for some common loss functions) of the Bayes estimator of the density (i.e. the posterior predictive density) reaches…
For a classification problem described by the joint density $P(\omega,x)$, models of $P(\omega\eq\omega'|x,x')$ (the ``Bayesian similarity measure'') have been shown to be an optimal similarity measure for nearest neighbor classification.…
We propose two nonparametric statistical tests of goodness of fit for conditional distributions: given a conditional probability density function $p(y|x)$ and a joint sample, decide whether the sample is drawn from $p(y|x)r_x(x)$ for some…
Given a finite collection of probability measures defined on subsets of a measurable space, how can we determine if they are compatible, in the sense that they can be realized as conditional distributions of a single probability measure on…
We consider a non-parametric Bayesian model for conditional densities. The model is a finite mixture of normal distributions with covariate dependent multinomial logit mixing probabilities. A prior for the number of mixture components is…
Density regression provides a flexible strategy for modeling the distribution of a response variable $Y$ given predictors $\mathbf{X}=(X_1,\ldots,X_p)$ by letting that the conditional density of $Y$ given $\mathbf{X}$ as a completely…
Two procedures for checking Bayesian models are compared using a simple test problem based on the local Hubble expansion. Over four orders of magnitude, p-values derived from a global goodness-of-fit criterion for posterior probability…
We present a structured additive regression approach to model conditional densities given scalar covariates, where only samples of the conditional distributions are observed. This links our approach to distributional regression models for…
We develop a new method for generating prediction sets that combines the flexibility of conformal methods with an estimate of the conditional distribution $P_{Y \mid X}$. Existing methods, such as conformalized quantile regression and…
Suppose we are given the conditional probability of one variable given some other variables.Normally the full joint distribution over the conditioning variablesis required to determine the probability of the conditioned variable.Under what…
We propose a non-parametric, two-sample Bayesian test for checking whether or not two data sets share a common distribution. The test makes use of data splitting ideas and does not require priors for high-dimensional parameter vectors as do…
Two Bayesian models with different sampling densities are said to be marginally equivalent if the joint distribution of observables and the parameter of interest is the same for both models. We discuss marginal equivalence in the general…
The conditional mutual information I(X;Y|Z) measures the average information that X and Y contain about each other given Z. This is an important primitive in many learning problems including conditional independence testing, graphical model…
We consider the problem of estimating the joint distribution $P$ of $n$ independent random variables within the Bayes paradigm from a non-asymptotic point of view. Assuming that $P$ admits some density $s$ with respect to a given reference…
Bayesian inference is used to estimate continuous parameter values given measured data in many fields of science. The method relies on conditional probability densities to describe information about both data and parameters, yet the notion…