The context to this discussion is in setting up an abductive argument for God such as the abductiver version of the Transcendental signifier argument. But it can work for any abductive approach to God argument.
According to Lipton not all induction is probability. He draws the line between deductive and inductive at the point where it is no longer impossible for the premises to be true and the conclusions false; when that's the case its deductive. Inductive is weighing probability not proof. Inductive considerations arise out of indeterminism. It is because outcomes are not necessitated t1hat we can have probability. In assessing the nature of the best explanation, Lipton finds that justification supports explanatory power because with indeterminism we can only go by likelihood. If likelihood were the only guide abduction reduces to induction, or a form of it. Rather he finds that we can't construe best as likeliest alone, but we should view abduction as a guide to inference, not as proof. He urges us to see explanatory factors as guides to illuminating likelihood rather than the other way around.  To use my own examples: suppose someone argues that its not likely that the former friends are jogging together because they made up; the former friends could be jogging together so that they can insult each other. That doesn't seem believable because one hates conflict, the other is too mature. Thus that is a less likely explanation than the theory that they made up. How would likelihood work with the question of God? How to establish probability of an issue such as the reality of God, where there is an inability to produce empirical proof? Such a discussion could not help but be dominated by prior convictions. Yet if we value explanation and we have reasonable parameters for what needs explaining the explanatory power might give a clue to likelihood. This means we are still left with how to establish “best.”
Gabby and Woods offer a rule to determine explanatory power. The rule sets up a criterion of comparison between hypothesis. At least one element must be more plausible in given hypothesis than its counter parts in competing hypotheses.  They develop much more complex statistical theorems. The problem is, even though setting up criteria of comparison is a god idea, we still can't just assert the likelihood of God, or even the unlikelihhod. The individual must decide the values by which to set parameters for comparison. For example if we value explanations that assume a “why” to the universe then God as explanation seems more likely. If we assume flat out there can be no why then we have already eliminated God from consideration. The problem in making a God argument is that God is not given in sense data. Thus God can't be the subject of empirical investigation. What we can do is to specify parameters and criteria that prepare us to make educated decisions about belief. In other words, we can't draw a picture of the hole in a doughnut, but we can draw the doughnut around the hole. In the case of God that means rational warrant justifies belief. Rational warrant means that a given belief is possible and plausible, thus not irrational.
We might be able to say that the best explanation would account for all the data or account for the most crucial data than other explanations. We could also stipulate that the explanation be the most simple as long as we don't confuse conceptual simplicity with absence of data, or simplicity of structure. For example when Dawkins argues that God would have to be more complex than the universe he creates, he's assuming the laws of physics apply to God. He's ignoring conceptual simplicity. Most of the great apologists such as Aquinas saw God as conceptually simple. In other words God is not made up of physical parts. This raises the issue of Occam's razor and parsimony. Parsimony is a principle akin to abductive reasoning used in science where direct empirical data is lacking. It was based upon Occam's razor but the two are not identical. Atheists have, on occasion, taken Occam's razor as a means of ruling God out of the equation. They either assert that God is not necessary, thus Occam's dictum about not multiplying beyond necessity applies to God, or they think Occam said take the simplest of two hypotheses.
They are also confusing Occam's razor with Parsimony. Occam was a priest and he believed in God he didn't think the razor got rid of God. Moreover, what the razor really says is that we should not multiply entities beyond necessity.  Atheists assume that since they don't believe in God then God is not necessary. This is begging the question. They are asserting the lack of a God and using that position to deny the God argument.
To understand what Occam was really talking about we must understand his nominalism.
three senses of nominalism:
(1) Denial of metaphysical universals: applies to Occam.
(2) reduce one's ontology to bare minimum, streamline categories: applies to Occam.
(3) Nix abstract entities, depending upon what one means; here Occam may or may not have been a nominalist in this sense. he did not believe in mathematical entities but he did believe in abstraction such as whiteness, or humanity.
Ockham removes all need for entities in seven of the ten traditional Aristotelian categories; all that remain are entities in the categories of substance and quality, and a few entities in the category of relation, which Ockham thinks are required for theological reasons pertaining to the Trinity, the Incarnation and the Eucharist, even though our natural cognitive powers would see no reason for them at all. As is to be expected, the ultimate success of Ockham's program is a matter of considerable dispute. He was not getting rid of God. Occam's razor never allows us to deny what Spade calls "putative entities" which would definitely include God.  It merely bids us refrain from positing them without good reason. Of course our atheist friends would tell us there is no good reason to assert God, but answering that is the point of making God arguments. In fact for Occam humans can't really know what is necessary. "For Ockham, the only truly necessary entity is God; everything else, the whole of creation, is radically contingent through and through. In short, Ockham does not accept the Principle of Sufficient Reason.This is not a contradiction because all the razor says is refrain form multiplying entities without good reason, not “rub out of existence all concepts that can't be empirically verified.” Note that he includes God as the only truly necessary entity. Thus atheist are violating Occam's razor in trying to use it on God. Of course there is equivocation in the of the term “necessary.” Atheists making the argument applying the razor to God speak of causal necessity while believers rest their ontological arguments upon ontological necessity.
An example of how “best explanation” should be considered:
This example is based upon the multiverse argument. The idea of the multiverse is taken seriously in science, even though it is the stuff of comic books and science fiction. The notion is what it sounds like: reality is divided into an infinite array of parallel universes. The argument is used to answer the fine tuning argument for God. The fine tuning argument says that the attributes of the universe that make life possible are so unlikely the game must be fixed. That's a good reason to believe in a planing intelligence as a creator. Our atheist friends say “not so fast.” There are infinite universes, thus infinite chances for life bearing. With infinite chances the odds of hitting life bearing are not so remote so there is not such a good reason to assert the need of a God. There are good answers to this, the argument is defensible. I wont defend it here because its not relevant. I am not asserting fine tuning to save the TS. My purpose in raising it is to make a point about how to consider best explanation.
The multiverse argument illustrates how the assumptions we make change the kind of explanation we seek. Is the multiverse necessary? It's a matter of empirical investigation and there may be empirical evidence to support it. Claims have been made of hard data proving Multivese, but when investigated they evaporate. Here's a physicist who opposed string theory and multiverse. He argues that his evaluation of the papers finds irresolvable problems.
In recent years there have been many claims made for “evidence” of a multiverse, supposedly found in the CMB data... Such claims often came with the remark that the Planck CMB data would convincingly decide the matter. When the Planck data was released two months ago, I looked through the press coverage and through the Planck papers for any sign of news about what the new data said about these multiverse evidence claims. There was very little there; possibly the Planck scientists found these claims to be so outlandish that it wasn’t worth the time to look into what the new data had to say about them. One exception was this paper, where Planck looked for evidence of “dark flow.” 
If hard evidence turns up for it then we have to deal with that on it's own terms. Until that time Multiverse should be shaved with Occam's razor. We don't need it to explain reality, it's only advanced to keep from having to turn to God. It's naturalistic so it's an arbitrary necessity at best. Arbitrary necessitates are logical impossibilities, contingent things jumped up to the level of necessity to answer a God argument. It's not that we are going to disprove the unnecessary entity (multiverse) but we are going to refrain from advancing it's existence as an assumption until such a time that real evidence makes it empirically undeniable. We can make that kind of ruling about the multiverse because its an empirical matter, even though it may be undetectable; God is not an empirical matter because God is both transcendent and transcendental. Therefore, Multiverse should be taken out of the issues of God arguments, yet we can't make that ruling about God. That's an example of what I meant when I said we can fill in the doughnut around the hole. If we find empirical evidence of multiverse we may have to re-think a couple of God arguments, In the mean time God might be the best explanation for the uniqueness of our world.
In any case parsimony is perhaps the best point of inference for abduction.
Most philosophers believe that, other things being equal, simpler theories are better. But what exactly does theoretical simplicity amount to? Syntactic simplicity, or elegance, measures the number and conciseness of the theory's basic principles. Ontological simplicity, or parsimony, measures the number of kinds of entities postulated by the theory. One issue concerns how these two forms of simplicity relate to one another. There is also an issue concerning the justification of principles, such as Occam's Razor, which favor simple theories. The history of philosophy has seen many approaches to defending Occam's Razor, from the theological justifications of the Early Modern period, to contemporary justifications employing results from probability theory and statistic
Again we have to distinguish between conceptual simplicity as opposed to mere ignorance of the case, or simple structure. In other words Dawkins treats God as a big man who must have more parts than the universe he creates (see above). That is simplicity in terms of structure, the physical structure of God. That is a case we just don't know about. We can't judge that. We can think of God as the simpler concept in terms of the economy of relations. First we can think of God as mind, not brain. We do not know that minds are complex. Brains are complex but we know nothing about mind. On the other hand we might posit that mind is simpler than brain because it's not a set of biological parts, but at least theoretically might be akin to the spirit. In any case God's relation to the whole is simple: one mind which thinks the universe. One mind that in the act of perceiving sets all meaning, creates all that is, and judges all moral value. That is more simple in terms of economical relations between all parts than a multiverse. A multiverse would multiply the problems of fine tuning and something from nothing by every universe.
To spell out the criteria by which we might judge a “best” explanation, not just simplicity alone but conceptual simplicity, we must be able to make comparisons between hypotheses. We can't compare hypotheses if they don't compete for the same results. Belief in God is not a scientific hypothesis, thus it does not compete with science. Thus belief cannot be reduced to the simplicity of “the best science.” For this reason we can call the kind of parsimony of the abductive version as parsimony of elegance. In other words not just take the simplest idea, but take the truly elegant hypothesis. By “elegant” is included conceptually simple in terms of relation to the whole theory, as well as consistant, competitive, and complete (accounts for most data, and most crucial data). To make a list of qualities of an elegant hypothesis. Above I quote Baker as saying elegance is number and conciseness of the theories basic principles. Ontological simplicity is the number of kinds of entities. By that measure God would be both eligant and ontologically simple: one kind and its concise. To that I add the notion of bang for the buck; not just fewer kinds and more concise but accomplishes more for less.
iPeter Lipton, Inference to The Best Explanation. New York: Routledge, International Library of Philosophy, 2nd ed.,2004, 6.
iiiDov M. Gabby and John Woods. A Practical Logic of Cognitive Systems: Vol 2, The Reach of Abduction...Amsterdam, The Neatherlands.:Elsevier B.V., 2005, 160.
ivRicard Dawkins. The God Delusion, Boston: Houghton Mifflin Harcourt; 1st edition, 2006.
vThomas Aquinas, The Summa Theologica of St. Thomas Aquinas Second and Revised Edition, 1920Literally translated by Fathers of the English Dominican ProvinceOnline Edition Copyright © 2008 by Kevin Knight Nihil Obstat. F. Innocentius Apap, O.P., S.T.M., Censor. Theol.Imprimatur. Edus. Canonicus Surmont, Vicarius Generalis. Westmonasterii.New Advent Catholic Encyclopidia, URL:http://www.newadvent.org/summa/1003.htm#article1 accessed 8/28/15.
vi“How to Reason: Section 8, Ocam's Razor,” God Would be An Atheist. URL:
http://www.godwouldbeanatheist.com/0reason/008occam.htmn 8, Occam's Razor,” , accessed 8/6/15
This is a website for atheism, it is not a scholarly site. In fact there is no listing of an author.. I quote it as an example of popular misconception.The site says: “Occam's Razor: in any situation offering two or more explanations, the simpler or simplestexplanationis always best.” Documentation of atheists using Occam to disprove God: Robert T. Carroll, “Occum's Razor,”The Skeptic's Dictionary. Url:http://skepdic.com/occam.html. Accessed 8/6/15
What is known as Occam's razor was a common principle in medieval philosophy and was not originated by William, but because of his frequent usage of the principle, his name has become indelibly attached to it. It is unlikely that William would appreciate what some of us have done in his name. For example, atheists often apply Occam's razor in arguing against the existence of a god on the grounds that any god is an unnecessary hypothesis. We can explain everything without assuming the extra metaphysical baggage of a divine being.
vii C.K. Brampton, "Nominalism and the Law of Parsimony." The Modern School Men, Volume 41, Issue 3, (March 1964), 273-281.
viii Paul Vincent Spade and Claude Panaccio, "William of Ockham", The Stanford Encyclopedia of Philosophy (Fall 2011 Edition), Edward N. Zalta (ed.), Fall 2011 (substantive content change) [new author(s): Spade, Paul Vincent; Panaccio, Claude] on lin resourse
URL: http://starchild.gsfc.nasa.gov/docs/StarChild/questions/question30.html accessed 8/18/15.
ix Spade, et al, Ibid.
xii Alan Baker, "Simplicity", The Stanford Encyclopedia of Philosophy (Fall 2013 Edition), Edward N. Zalta (ed.), URL =