Posterior distributions, sampling distributions and inter-laboratory comparison data

Sampling Distributions Sampling Distributions

Sampling and Sampling Distributions

A sample is a group of objects or readings taken from a population for counting or measurement. We shall distinguish between two kinds of populations — finite populations and infinite populations. The sample must be random, meaning that all possible samples of a particular size must have equal probabilities of being chosen from the population. This will prevent bias in the sampling process. Mos...

Quantitative Comparisons between Finitary Posterior Distributions and Bayesian Posterior Distributions

Abstract. The main object of Bayesian statistical inference is the determination of posterior distributions. Sometimes these laws are given for quantities devoid of empirical value. This serious drawback vanishes when one confines oneself to considering a finite horizon framework. However, assuming infinite exchangeability gives rise to fairly tractable a posteriori quantities, which is very at...

Posterior distributions are computable from predictive distributions

As we devise more complicated prior distributions, will inference algorithms keep up? We highlight a negative result in computable probability theory by Ackerman, Freer, and Roy (2010) that shows that there exist computable priors with noncomputable posteriors. In addition to providing a brief survey of computable probability theory geared towards the A.I. and statistics community, we give a ne...

Probability and Sampling Distributions

When an experiment is conducted, such as tossing coins, rolling a die, sampling for estimating the proportion of defective units, several outcomes or events occur with certain probabilities. These events or outcomes may be regarded as a variable which takes different values and each value is associated with a probability. The values of this variable depends on chance or probability. Such a vari...