History of uninformative prior theory I am writing a short theoretical essay for a Bayesian Statistics course (in an Economics M.Sc.) on uninformative priors and I am trying to understand which are the steps in the development of this theory.
By now, my timeline is made three main steps: Laplace's indifference principle (1812), Non-Invariant priors (Jeffreys (1946)), Bernardo reference prior (1979).
From my literature review, I've understood that indifference principle (Laplace) was the first tool used to represent lack of prior information but the missing requirement of invariance has led to its abandonment until the 40s, when Jeffreys introduced his method, which has the desired property of invariance. The arise of paradoxes of marginalization due to the careless use of improper prior in the 70s pushed Bernardo to elaborate his reference prior theory to deal with this issue. 
Reading the literature, every author cites different contributes: Jaynes' maximum entropy, Box and Tiao's data-translated likelihood, Zellner, ... 
In your opinion, what are the crucial steps I am missing? 
EDIT: I add my (main) references, if someone needs:
1) The selection of prior by formal rules, Kass, Wasserman
2) A catalogue of non informative priors, Yang, Berger
3) Noninformative Bayesians Priors Interpretation and Problems with Construction and Applications
EDIT 2: Sorry for the 2 year delay but here you can find my essay here
 A: A few comments about flaws of noninformative priors (uninformative priors) are probably a good idea since the investigation of such flaws helped development of the concept of noninformative prior in history. 
You may want to add some comments about the drawbacks/flaws of adopting noninformative priors. Among many criticisms I point out two.
(1) Generally the adoption of noninformative priors has consistency problems especially when the model distribution has multi-modal behavior. 
This problem is not unique to noninformative priors but is shared by many other Bayesian procedures as pointed out in the following  paper along with its discussions.
Diaconis, Persi, and David Freedman. "On the consistency of Bayes estimates." The Annals of Statistics (1986): 1-26.
Nowadays the noninformative prior is no longer a research focus. It seems that there is more interest in more flexible choices of prior in nonparametric settings. Examples are the Gaussian process prior in nonparametric Bayes procedure or a flexible model like a mixture of Dirichlet priors, as in
Antoniak, Charles E. "Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems." The annals of statistics (1974): 1152-1174.
But again such a prior has its own consistency problems.
(2) Most so-called "noninformative priors" are not well-defined. 
This is probably the most evident problem associated with noninformative priors during their development.
One example is that the limit definition of noninformative prior as a limit of a sequence of proper priors will lead to a marginalization paradox. As you mentioned, Bernardo's reference prior also has the problem that Berger never proved that its formal definition is independent from its construction/partition. See the discussion in
Berger, James O., José M. Bernardo, and Dongchu Sun. "The formal definition of reference priors." The Annals of Statistics (2009): 905-938.
One best definition about Jeffreys' prior that is well-defined is that it is chosen to be a prior such that it is invariant under certain parallel translation over the Riemannian manifold equipped with Fisher information metric, but even that does not solve the first problem.
Also you may want to read my explanation about marginalization paradox.
A: I would have posted in the comments, but I guess I do not have the reputation yet.  The only missing thing, not in the comments already marked, is a special case of noninformative priors whose origins that I have tried to hunt down and have not found.  It may precede Jeffreys paper.
For the normal distribution, I have seen the Cauchy distribution used as a noninformative prior for data with a normal likelihood.  The reason is that the precision of the Cauchy distribution is zero, where precision is one divided by the variance.  It creates a rather peculiar set of contradictory concepts.  
The formula for the Cauchy is $$\frac{1}{\pi}\frac{\Gamma}{\Gamma^2+(x-\mu)^2}.$$
Depending on how you define the integral there is either no defined variance or it goes to infinity about the median, which implies the precision goes to zero.  In conjugate updating, which wouldn't apply here, you add the weighted precisions.  I think this is why this idea of a proper prior with a perfectly imprecise density formed.  It is also equivalent to Student's t with one degree of freedom, which could also be the source.
This is a strange idea in the sense that the Cauchy distribution has a well defined center of location and inter-quartile range, which is $2\Gamma$.
The two earliest references to the Cauchy distribution are as likelihood functions.  The first in a letter from Poisson to Laplace as an exception to the Central Limit Theorem.  The second was in 1851 journal articles in a battle between Bienayme' and Cauchy over the validity of ordinary least squares.
I have found references to its use as a noninformative prior back into the 1980's but I cannot find a first article or book.  I also have not found a proof that it is noninformative.  I did find a citation to Jeffreys' 1961 book on probability theory, but I have never requested the book via interlibrary loan.
It may be simply weakly informative.  The 99.99% highest density region is 1272 semi-interquartile ranges wide.
I hope it helps.  It is a weird special case, but you see it come up in a number of regression papers.  It satisfies the requirements for a Bayes action by being a proper prior, while minimally influencing location and scale.
A: What you seem to be missing is the early history. You can check the paper by Fienberg (2006) When Did Bayesian Inference Become "Bayesian"?. First, he notices that Thomas Bayes was the first one who suggested using a uniform prior:

In current statistical language, Bayes' paper introduces a uniform
  prior distribution on the binomial parameter, $\theta$, reasoning by
  analogy with a "billiard table" and drawing on the form of the
  marginal distribution of the binomial random variable, and not on the
  principle of "insufficient reason," as many others have claimed.

Pierre Simon Laplace was the next person to discuss it:

Laplace also articulated, more clearly than Bayes, his argument for
  the choice of a uniform prior distribution, arguing that the posterior
  distribution of the parameter $\theta$ should be proportional to what
  we now call the likelihood of the data, i.e.,
$$ f(\theta\mid x_1,x_2,\dots,x_n) \propto f(x_1,x_2,\dots,x_n\mid\theta) $$
We now understand that this implies that the prior distribution for
  $\theta$ is uniform, although in general, of course, the prior may not
  exist.

Moreover Carl Friedrich Gauss also referred to using an uninformative prior, as noted by David and Edwards (2001) in their book Annotated Readings in the History of Statistics:

Gauss uses an ad hoc Bayesian-type argument to show that the posterior
  density of $h$ is proportional to the likelihood (in modern
  terminology):
$$ f(h|x) \propto f(x|h) $$
where he has assumed $h$ to be uniformly distributed over $[0,
 \infty)$. Gauss mentions neither Bayes nor Laplace, although the
  latter had popularized this approach since Laplace (1774).

and as Fienberg (2006) notices, "inverse probability" (and what follows, using uniform priors) was popular at the turn of the 19th century

[...] Thus, in retrospect, it shouldn't be surprising to see inverse
  probability as the method of choice of the great English statisticians
  of the turn of the century, such as Edgeworth and Pearson. For
  example, Edgeworth (49) gave one of the earliest derivations of what
  we now know as Student's $t$-distribution, the posterior distribution
  of the mean $\mu$ of a normal distribution given uniform prior
  distributions on $\mu$ and $h =\sigma^{-1}$ [...]

The early history of the Bayesian approach is also reviewed by Stigler (1986) in his book The history of statistics: The measurement of uncertainty before 1900.
In your short review you also do not seem to mention Ronald Aylmer Fisher (again quoted after Fienberg, 2006):

Fisher moved away from the inverse methods and towards his own
  approach to inference he called the "likelihood," a concept he claimed
  was distinct from probability. But Fisher's progression in this regard
  was slow. Stigler (164) has pointed out that, in an unpublished
  manuscript dating from 1916, Fisher didn't distinguish between
  likelihood and inverse probability with a flat prior, even though when
  he later made the distinction he claimed to have understood it at this
  time.

Jaynes (1986) provided his own short review paper Bayesian Methods: General Background. An Introductory Tutorial that you could check, but it does not focus on uninformative priors. Moreover, as noted by AdamO, you should definitely read The Epic Story of Maximum Likelihood by Stigler (2007).
It is also worth mentioning that there is no such thing as an "uninformative prior", so many authors prefer talking about "vague priors", or "weekly informative priors".
A theoretical review is provided by Kass and Wasserman (1996) in The selection of prior distributions by formal rules, who go into greater detail about choosing priors, with extended discussion of usage of uninformative priors.
