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is listed in sequence for best understanding.
Parameter An
unobservable quantity that defines a probability distribution,
such as the mean of a normal distribution.
Belief The
subjective assessment of uncertainty. In the Bayesian paradigm,
quantified by probability. In the statistical domain.
Probability A
quantity such that impossible assigns 0, certainty assigns 1, and
interdediate levels of certainty assign numbers between. The probability
of mutually exclusive events is the sum of the probbilities of
the component events. The semantics of probability are frequentist
or subjective.
Frequentist
probability The interpretation that a probability represents
a long-run frequency of an event. Thus, the statement, "The
probabiity of the coin coming up heads is 0.5" means that
50% of coin tosses are heads. The statement, "Your probability
of having cancer is 50%" cannot be made, since a particular
patient cannot be repeated.
Subjectivist
probability The interpretation that a probability represents
the subjective belief of the spaker. Thus, the statement, "The
probabiity of the coin coming up heads is 0.5" means that
I am 50% certain that the coin will come up heads. The statement, "Your
probability of having cancer is 50%," means that the speaker
is 50% certain about this unfortunate outcome.
Prior
belief The reader's belief in different values of a parameter
before evaluating the results of a study. In our Bayesian applets,
we call this initial belief.
Sufficient
statistics Arithmetic functions of the data that provide
just the summary needed to perform inference on a parameter of
interest. Many statistics are such second nature, like
the arithmetic mean, that they are thought of as the data themselves.
Likelihood
function A mathematical expression that indicates the likilhood
that the observed data (or sufficient statistic) would have been
observed, given the (unknown) population parameter(s). Note the
difference from the P value.
P
value A frequentist measure: the probability of having observed
the data (or suffidicient statistic or tst statistic) observed
or more extreme, given a paraticular value of the population
parameter, usually the value specified by the null hypothesis.
Likelihood
Principle A theorem, proved by Alan Birnbaum in 1962, that
the likelihood function is the sufficient statistic for linking
a study to a parameter of interest.
Data Results
of a study, encoded as sufficient statistics.
NormalDifferenceSDKnown The
statistical model for a frequentist z-test. Get information on
the Bayesian model and its applet implementation.
Posterior
belief The reader’s belief after seeing the data in the context
of prior belief. In our Bayesian appplets, we call this integrated
belief.
Confidence
interval In frequentist statistics, a 95% confidence interval
represents an interval such that if the experiment werre repeated
100 times, 95% of the resulting confidence intervals (e.g,. average
+/ 1.96 standard error) would contain the true paameter
value. Most statistical clients confuse this with the Bayesian.
Credible
set: an interval in which we have 95% belief that the parameter
value lies therein. If the posterior distribution is symmetric,
then the interval lies between the 2.5 and 97.5 percentile of
the posterior distribution.
Belief
network A graphical reprentation of a joint distribution
over variables, where the absence of an arc between nodes communicates
knowledge of marginal indepdendence or conditional independence.Three
types of nodes are generally distinguished: Chance nodes
(random variables), deterministic nodes (constants or
functions of their parents), and evidence nodes (whose
values have been observed). Chance nodes are generally represented
by ovals, deterministic nodes, as double ovals, and evidence
nodes, as shaded. Chance nodes with no parents are sometimes
called basic nodes, and these ae the variables over which
the user or analyst must specify prior beliefs.
Precision The
certainty in an estimate. In Bayesian terminology, it is calculated
as the reciprocal of variance for a normal distribution. The higher
the
precision, the more certainty there is.
Arm A
group of patients assigned to the same treatment in a randomized clinical
trial.
Control The
treatment against which the experimental treatment is being compared. A
placebo control makes the
study an efficacy study; a control which is standard treatment makes
the study an effectiveness study.
Experimental The
treatment of focus in the study, generally a new treatment.
Standard Deviation
The square root of the variance; a measure of precision.
Variance
The average squared deviance from the mean; a measure of precision.
Units
The units of the scale by which the outcome is measured.
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