It is my understanding from reading various texts that the chief distinction made by “Bayesians” between their practices and those of “frequentists” is that frequentists are referring to the actual probabilities or relative probabilities of events resulting from a test of a predictive hypothesis, while “Bayesians” are referring to “subjective” probabilities encompassing a much broader framework (extending beyond the experimental test).
While there have been attempts to carve out a distinction between “objective” and “subjective” “Bayesian analysis,” these efforts seem, so far, unconvincing. I quote below from the Wikipedia entry on “Bayesian probability”:
“Broadly speaking, there are two interpretations on Bayesian probability. For objectivists, interpreting probability as extension of logic, probability quantifies the reasonable expectation everyone (even a “robot”) sharing the same knowledge should share in accordance with the rules of Bayesian statistics, which can be justified by Cox’s theorem. For subjectivists, probability corresponds to a personal belief. Rationality and coherence allow for substantial variation within the constraints they pose; the constraints are justified by the Dutch book argument or by the decision theory and de Finetti’s theorem. The objective and subjective variants of Bayesian probability differ mainly in their interpretation and construction of the prior probability.”
Thus, we see that even the “objective” version of “Bayesianism” entails subjective cognitive evaluations – “reasonable expectations,” “rationality constraints,” “interpretation of the prior probability.”
Continuing in the Wikipedia entry, we see that, indeed, the “objective” category is the subject of much (subjective) disagreement:
“[Many theorists] have suggested several methods for constructing “objective” priors. (Unfortunately, it is not clear how to assess the relative “objectivity” of the priors proposed under these methods)…The quest for “the universal method for constructing priors” continues to attract statistical theorists.”
Given all the above, given the absence of a “universal method for constructing [objective] priors” I would say that a strong case for “Bayesian probability,” as regards its use in objective science, is still incomplete.
2. Wei Wei (2018) Annual Review of Vision Science
I am puzzled by the author’s unqualified use of the term “receptive field,” a term whose meaning appears to be in flux. The simple notion that there is a circumscribed part of the retina, and a corresponding circumscribed part of perceived space, events in which affect particular neurons, has long been debunked and labelled “classical receptive field.” The understanding that the early concept was problematic came almost from the start, as indicated by the excerpt from Spillma’s (2015/JOV) article, “Beyond the classical receptive field (the two paragraphs are consecutive in the original text):
“Our perception relies on the interaction between proximal and distant points in visual space, requiring short- and long-range neural connections among neurons responding to different regions within the retinotopic map. Evidently, the classical center-surround RF can only accommodate short-range interactions; for long-range interactions, more powerful mechanisms are needed. Accordingly, the hitherto established local RF properties had to be extended to take distant global inputs into account.”
“The idea of an extended (called nonclassical or extraclassical today) RF was not new. Kuffler (1953, p. 45) already wrote, “… not only the areas from which responses can actually be set up by retinal illumination may be included in a definition of the receptive field but also all areas which show a functional connection, by an inhibitory or excitatory effect on a ganglion cell. This may well involve areas which are somewhat remote from a ganglion cell and by themselves do not set up discharges.””
The language of the above text is a bit misleading, implying as it does that the “hitherto established” local RF remained in place and merely needed elaboration. It should be clear that if the firing rate of a neuron “x” can be altered by the conditions of stimulation applying to the whole retina, then it is not possible to experimentally define a local area as in any way special based on the local conditions of stimulation. Or rather, it is artificial, privileging one set of global conditions other an infinite number of alternatives in producing a definition (which even then has not been proven to replicate). Even the verbal expansion of the term to include “non-classical receptive fields” does not rescue the concept from this problem.
The extreme confusion that the concept has produced as researchers have attempted to specify its elusive properties may be appreciated in reading Carandini et al’s (2005) “Do we know what the early visual system does?” The discussion includes reference to a black box “saving device.”
The concept of “direction-selectivity” is closely tied to the receptive field concept. It is difficult for me to understand how Wei can avoid addressing these theoretical problems.
Unqualified use of the term “receptive field” and associated concept is quite common; I’ve highlighted it in several PubPeer comments, including on El Boustani et al (2018)/Science; onBeltramo & Scanziani (2019)/Science; on Olshausen & Field (1996)/Nature
A second stab at Wei Wei also failed:
As noted in the PubPeer comment on Olshausen & Field (1996) as well as other PubPeer comments linked therein, the concept of “receptive field” is currently missing a theoretical definition. Various researchers employ different de facto definitions of the term, strictly tied to the procedures they happen to use. The use of the term by Wei in this review, without qualification or clarification, renders the discussion incomplete.
3. Bakkour, Palombo, Zylberberg, Kang, Reid, Verfaellie , Shadlen , Shohamy (2019) eLife “The hippocampus supports deliberation during value-based decisions.”
(In addition to the comment submitted to PubPeer, I note here that the authors’ use of the term “supports” is an example of Neuroscience Newspeak.)
“Bakkour et al state:
We fit a one-dimensional drift diffusion model to the choice and RT on each decision. The model assumes that choice and RT are linked by a common mechanism of evidence accumulation, which stops when a decision variable reaches one of two bounds.
I’m confused about what the authors are claiming. Experiments are based on two-alternative forced choices and structured so that the data produced may be “modelled” based on the “drift diffusion model.” The fitting procedures allow modellers quite a bit of leeway in adjusting free parameters, and many quantitative choices are unconstrained by theory. The above-stated assumptions of the “drift diffusion model”, i.e. that “choice and RT are linked by a common mechanism of evidence accumulation” are vague; no concrete description (even a vague one) in terms of neural function has ever been proposed. The drift diffusion model is an extension of “signal detection theory;” and the assumptions of this “theory” seem to lack face validity. SDT curves tend to be specific to particular experiments and not to generalize.
In short, under the circumstances I’m not sure that fitting the data acquired to the model under consideration is enough to license inferences about brain function.”
4. Mueller & Weidemann (2008) Psychonomic Bulletin and Review
“SDT assumes that percepts are noisy.”
The term “percept” refers to what is consciously experienced, and generally to what is experienced visually. What we experience visually is not noisy, and does not necessitate any conscious decision-making on the viewer’s part. Conscious decision-making is, both implicitly and explicitly, what we are talking about here. Implicitly, because if the conscious perceptual experience (the percept), is noisy, then the viewer must be called on to make a conscious decision as to how to interpret it. Explicitly, because the associated experiments refer to participants’ decisions, usually binary forced-choice decisions often requiring guesses.
Given all of this, the statement that “SDT assumes percepts are noisy” is hard to interpret. The assumption seems to lack face validity, and no explanation or references, or proposals of how to test it, are offered. On what basis is the assumption considered valid?
5. Oberauer & Lewandowsky (2019) Psychonomic Bulletin and Review.
[It seems particularly unkind of PubPeer moderators to censor my reply to another commenter’s reply to my initial comment, which did post.]
The text you cite seems very confused and waffling to me. Which of Mayo’s arguments have you found compelling with respect to making the fruits of post hoc correlation-fishing reliable – something that, as mentioned, is virtually never the case? Has she proposed and tested a method of post hoc statistical inference that produces replicable outcomes?
6. Chen, Yeh & Tyler (2019) Journal of Vision
I’d like to discuss the authors’ dichotomization of the images used in their procedures into “target” and “noise.” It seems to me that this dichotomy is not a valid one, for fairly obvious reasons.
In this comment, I’ll be using the term “image” to refer to a surface reflecting light into the eyes of a seeing human.
By target, the authors are referring to certain more-or-less smoothly-changing bands of light and dark which they call “Gabors.” These patterns are typically perceived either as alternating bars or, if the transitions are fairly gradual, as partly-shaded cylinders. By “noise,” they mean a different type of pattern, consisting of variously-arranged dots.
Collections of dots always tend to be grouped spontaneously by both human and species of non-human viewers to produce various perceived shapes or patterns, among the simplest examples being the simple “rows” or “columns” of dots typically used to demonstrate principles of organization. We may see the same tendency in the grouping of stars into constellations, and the perception of objects in clouds.
Here, we have two types of patterns; one rather orderly both physically and perceptually, the other less so – but both requiring and eliciting perceptual/neural organizing processes in order for perceived structures, stable or unstable, to arise in consciousness.
When two patterns are super-imposed in an image, the structures that will emerge in consciousness are not necessarily the sum of these two. They may be – it depends on the combined pattern, and how it is interpreted by the perceptual organizing processes. The combination of the two may destroy the structural coherence of one or the other or both; and new structures may be perceived. A classic series of experiments by Gottschaldt demonstrated, many decades ago, that “targets” may not be perceived in certain contexts, even when observers expect and are actively watching for them.
It seems to me the above facts are relevant and should be addressed in the authors’ theoretical discussion.