Standards of Proof
A criminal case involves shifting obligations between the prosecution and the defendant. In systems where the defendant is given the presumption of innoccence, the prosecution has the burden of proof in demonstrating the crime was committed by the defendant.
Burdens are allocated in shift risk of error from one party to the other.
Types of Burdens
A criminal defense attorney should keep in mind that there are generally two kinds of burdens in a criminal trial: burdens of production and burdens of proof or persuasion.
The burden of proof or persuasion is the burden of convincing a factfinder that a given factual claim is true or false to a given degree of probability.
In contrast, the burden of production, requires the prosecution or defense lawyer to produce some quantum of evidence in order to raise an issue before the fact finder.
Various Standards of Proof
A scintilla is the smallest amount of evidence possible. Rarely used in criminal law, scintilla is the standard used in some courts for denying the plaintiff a restraining order.
Air of Reality
In a criminal trial, a defendant may be required to provide evidence sufficient to raise an issue -- such as the defendant's sanity at the time of alleged offense -- at trial. However, typically courts will require some evidence before they will permit the issue to be raised a trial. Typically, this quantum is more than a scintilla, but something less than reasonable suspicion. Some courts have characterized the evidentiary requirement as the "Air of Reality."
Reasonable suspicion is the standard required before a police officer may stop and question or frisk an individual against their will. In Terry v. Ohio  the court stated that reasonable suspicion meant that the police officer:
...observed unusual conduct which lead him reasonably to conclude in light of his experience that criminal activity may be afoot and that the persons with whom he is dealing with may be armed and dangerous, where in the course of investigating this behavior he identifies himself as a policeman and makes reasonable inquiries and nothing in the initial stages of the encounter serves to dispel his reasonable fear for his own or others' safety, he is entitled (for the protection of himself and others in the area) to conduct a carefully limited search of the outer clothing of such persons in an attempt to discover weapons which might be useful to assault him"
In the United States, probable cause is the standard required to effect a constitutional arrest or issue a valid search warrant.
Probable cause is an objective legal standard that balances effective law enforcement against an individual's freedom from unwarranted invasion into their privacy. Whether or not probable cause exists or not will depend all the facts.
Traditionally probable cause has been determined by a "totality of the circumstances" test. In Illinois v. Gates , a case involving probable cause based on an informant the court phrased the magistrate's task this way:
The task of the issuing magistrate is simply to make a practical, common-sense decision whether, given all the circumstances set forth in the affidavit before him, including the "veracity" and "basis of knowledge" of persons supplying hearsay information, there is a fair probability that contraband or evidence of a crime will be found in a particular place. And the duty of the reviewing court is simply to ensure that the magistrate has a "substantial basis for ... conclud[ing] that probable cause existed.
Preponderance of the Evidence
Preponderance of the evidence, the standard used in civil cases in the United States and in criminal cases in some countries, is the standard of proof that requires the bearer show that the evidence shows a fact is more likely than not to have occurred. The standard is satisfied by a showing that the likelihood of occurrence is more than 50 percent.
Clear and Convincing Evidence
Clear and convincing evidence is a standard employed in both criminal and civil courts. It is higher than the preponderance standard and yet falls short of proof beyond a reasonable doubt. Clear and convincing evidence is the standard used by the United States Supreme Court in Calderon v. Thompson,  where they concluded that a defendant who has been convicted but alleges factual innocence in a habeas motion must demonstrate by clear and convincing evidence that “it is more likely than not that no reasonable juror would have convicted him in light of the new evidence”. Other courts have concluded that the standard requires the proof that a fact is substantially more likely than not to be true.
Proof Beyond a Reasonable Doubt
Proof Beyond a Reasonable Doubt is the standard required in the United States for conviction of a criminal charge. The standard is generally not quantifiable as a percentage probability. The exact formulation of reasonable doubt has never been determined.
Chief Justice Shaw of the Massachusetts Supreme Judicial Court made this observation about the reasonable doubt standard in 1850:
"[W]hat is reasonable doubt? It is a term often used, probably pretty well understood, but not easily defined. It is not mere possible doubt; because every thing relating to human affairs, and depending on moral evidence, is open to some possible or imaginary doubt. It is that state of the case, which, after the entire comparison and consideration of all the evidence, leaves the minds of jurors in that condition that they cannot say they feel an abiding conviction, to a moral certainty, of the truth of the charge. The burden of proof is upon the prosecutor. All the presumptions of law independent of evidence are in favor of innocence; and every person is presumed to be innocent until he is proved guilty. If upon such proof there is reasonable doubt remaining, the accused is entitled to the benefit of it by an acquittal. For it is not sufficient to establish a probability, though a strong one arising from the doctrine of chances, that the fact charged is more likely to be true than the contrary; but the evidence must establish the truth of the fact to a reasonable and moral certainty; a certainty that convinces and directs the understanding, and satisfies the reason and judgment, of those who are bound to act conscientiously upon it. This we take to be proof beyond reasonable doubt." 
In the U.S. Supreme Court case of Victor v. Nebraska , the court held a similar jury instruction on reasonable doubt unconstitutional:
" `[A reasonable doubt] is one that is founded upon a real tangible substantial basis and not upon mere caprice and conjecture. It must be such doubt as would give rise to a grave uncertainty, raised in your mind by reasons of the unsatisfactory character of the evidence or lack thereof. A reasonable doubt is not a mere possible doubt. It is an actual substantial doubt. It is a doubt that a reasonable man can seriously entertain. What is required is not an absolute or mathematical certainty, but a moral certainty.' "
The court held that the portions of the instruction in bold rendered it unconstitutional. The court has never fully approved an instruction.
Proof Beyond a Shadow of a Doubt
Proof Beyond a Shadow of a Doubt is rarely recognized as a legal standard because it presents a standard that may be legally impossible to achieve.