p. 1104

column 1:
BACIP or BACI designs are experimental designs used in situations
where replication is not feasible. Essentially, one takes two plots
and samples both before and after a treatment is imposed on one of
them.  By measuring the difference between the _difference_ between
the two plots before and after the treatment, one can hope (subject to
a variety of caveats) to determine the effect of the treatment.
Samples at multiple times are used to determine the within-block
variance.

column 2:

 effect sizes: cf. Craig's Wednesday lecture

prior distributions: the probability distribution that we believe to
be true before doing the experiment/observation

p. 1105
posterior distribution: the probability distribution that we believe
after doing the experiment/observation

p. 1106
column 1:
dbh: diameter at breast height (a standard measurement of tree size)
"incidental" losses: trees killed, uprooted, etc. during logging but
not harvested

column 2:
paired sites: selected to be as similar as possible (to minimize
interactions between site effects and treatment effects)

p. 1107

column 1:

temporal samples: samples taken at multiple times
transformation: e.g., taking log(1+data)

"demonic intervention": see Hurlbert 1984
Occam's Razor: a philosophical principle of parsimony, accepting the
least complicated hypothesis


column 2:
likelihood fuction: cf. Ben's Weds. lecture

ANOVA: analysis of variance, assuming that measurements in different
treatments (e.g. logged and unlogged) have different means, and
testing whether the variation among the means in different treatments
is large or small relative to the variation within treatments.
Assuming that logarithmic counts have constant error is equivalent to
assuming the same _proportional_ error in different treatments.

N(mu,sigma^2): a normal distribution with mean mu and variance sigma^2

p. 1108

column 1:
equation 2: this is the equation that corresponds to the model
described: independent normally distributed variables, all with
variance sigma^2, where the n measurements in the control treatment
(C_i) have mean eta_i (that's the n-shaped Greek letter), the
measurements in the logged area have mean eta_i+gamma_i=eta_i +
ln(theta) [before logging] and eta_i+ln(theta)+ln(delta) [after
logging].  eta_i is the effect of different times, theta is the
difference between the plots, and delta is the effect of logging.


kernel density plots: a way of estimating the shape of a distribution
(in this case, to see if the distributions of the residual errors are
normal as expected).

normal probability (quantile-quantile) plots: another test for
normally distributed residuals.

Skewness: asymmetry in a probability distribution (implying
non-normality)

column 2:

two-sided test: a test that takes the possibility of deviations in
either direction (control>treatment or control<treatment) into account

noncentral t distribution: the distribution expected from taking
(sample mean/sample std. dev.) when the data are sampled from a normal
distribution with a mean not equal to 0 -- needed for power
calculations

retrospective/post hoc power analyses: power analyses that use the
variance, etc. estimated from the experiment itself

p. 1109

column 1:

subjective probability: probability defined or measured as one's
belief in the likelihood of an outcome

column 2:
fractiles: fractions (often called percentiles or quantiles) of a
distribution: the value below which (e.g.) 10% of the probability
falls

principal components analysis: a multivariate technique for extracting
the combinations of a set of variables that explain most of the
(joint) variation in the variables: a way of summarizing a
multivariate data set

p. 1110

column 1:
lognormal distribution: a distribution whose logarithm is the normal
distribution.  (Runs from 0 to infinity, so it's useful for
characterizing variables that must be positive.)

Nonlinear least squares: a method for finding the (nonlinear)
distribution or curve that fits the data best, with the criterion
being to minimize the sum of squared differences between the data and
the curve

Informative prior: a prior distribution that contains some information
(as opposed to a "flat", "diffuse", "noninformative", "uninformative",
or "weak" prior, which all assume ignorance/contain little or no
information about the parameters or hypotheses in question)

column 2:

elicitation: the method (described on p. 1109) for determining what
prior probability distribution best matches a particular person's
prior beliefs

eq. 3: a mixture of lognormal distributions (the "ln delta" instead of
just delta in the numerator of the fractions makes it log normal)

pi is used to mean "probability" (as well as 3.141592 ...)

location parameters eta_i: parameters indicating the "baseline" value
of captures (not including plot effect and logging effect).

scale parameter: since changing sigma "stretches" the distribution it
is called a scale parameter

marginal priors: the priors of each parameter considered independently
of the other parameters (e.g., there is no correlation between
parameters)

the symbol in the displayed equation means "proportional to"

joint posterior distribution: the distribution of all the parameters
taken together (including the possibility that parameters may
interact/be correlated)

p. 1111
column 1:

Student's t distribution: the old, familiar (?) t distribution used
for comparing sample means when the standard deviations or variances
are also estimated from data

Bayesian credible intervals: symmetric intervals that include 95% of
the probability of a parameter (analogous to the standard frequentist
confidence intervals, but determined in terms of probabilities rather
than tail probabilities)

Gauss Legendre algorithm: don't worry about it

p. 1115 column 1:

mode: the peak of a probability distribution, or most probable
parameter value (with a flat prior, this is the same as the maximum
likelihood estimate)

p. 1120 column 1:

randomization tests: tests based on artificially scrambling data sets
to generate an expectation under a null hypothesis, or to derive
confidence limits