What Could Be The Probable Explanation For This

What are the cases in which Most Probable Explanation (MPE) tasks do not generalize to Maximum A Posteriori (MAP) task?

I assume the question is "When would using MPE instead of MAP  produce different results"Let’s take a look at what actually happens when you compute MPE and MAP.Imagine you have a joint distribution over three binary variables.To define it you need to know the probability of each possible combination of variables.0.03                1 1 10.07                0 0 00.10                1 0 00.15                0 1 00.25                0 0 10.10                1 1 00.15                0 1 10.15                1 0 1 Marginals for each variables are (Since  the variables in question are binary, I only provide the probability for 0) :X1    0    0.62         X2    0    0,57         X3   0     0,42          Now imagine we know X2 to be 0, and we are interested in the most probable X1What are we supposed to do with X3? We are not interested in X3 but it’s still an unknown quantity, so we can’t just drop it off.1) If you decide to sum over all possible X3s   (marginalization over all possible X3s) and then find  the state that maximize P(X1|X2) you are performing MAP estimation P(X1=0|X2=0) = P(X1=0, X3=0|X2=0)+ P(X1=0, X3=1|X2=0) = 0.07/0.57 + 0.25/0.57=0.12+0.43 =0.55P(X1=1|X2=0)= P(X1=1, X3=0|X2=0)+ P(X1=1, X3=1|X2=0)  =0.10/0.57+ 0.15/0.57=0.17+0.26  = 0.45[note that the probabilities will sum to one – I am rounding the results for the decimal notation : you don’t do that in normal applications]In this case the most probable state for X1 is 0 2) If you are trying to find a pair of states that maximizes the joint conditional P(X1,X3|X2) then you are performing MPEP(X1=0,X3=0|X2=0) =0.12P(X1=0, X3=1|X2=0) =0.43P(X1=1, X3=0|X2=0) =0.17 P(X1=0,X3=1|X2=0)  =0.26In this case the most probable state for X1 is 0 and for X3 is 1Now in this case both results agree, but take a look at the summation in 1)0.12+0.430.17+0.26And imagine you’ve got different probabilities for each conditionalP(X1=0|X2=0)= 0.42+0.7 =0.49P(X1=1|X2=0)=0.41+0.10 =0.51That would imply X1=1.But if we are to use P(X1,X3|X2=0) maximization as a selection criteria  instead thenP(X1=0,X3=0|X2=0) =0.42  has the biggest probability  This implies that X1=0 So in this case  using MPE instead of MAP leads to a different conclusion.

What are some of the probable explanations of Linear Gravity Anomalies on moon?

Same reasons for there are gravity anomalies on earth, geologic processes and more mass  in minerals with  compounds with higher specific gravities, NOT densities. Geological process and volcanism  and tectonics ARE UNIVERSAL. The only difference between a planet and Star or boulder or speck  of dust is the MASSES of the objects. AND specific gravities of the atoms of the geologic features.. when materials fracture,  they fracture linearly. Yes i CAN explain WHY materials fracture  linearly, but i do not went to get to far  off topic or go into to much detail.. The answer is linear fracturing , convection and conduction of heat as theas the Moon and Earth are cooling down  because of geologic and volcanic and tectonic processes.©©©©@Specific gravityI am tempted to say "WHAT linear gravity anomalies' but i know  the answer to that question already.. The problem is the map scale as well as pixel resolution of the images.

What is scientifically the most probable explanation for the emergence of life on Earth?

I’m not keyed into current thinking but last i read we suspect that a mixture of physical and chemical processes (lightning, volcanic activity etc) created a mixiture of simple organic compounds in the lakes and seas - amino acids, sugars, nucleotides etc. This mix could build up over billions of years - in the absence of life, nothing is trying to “eat” these compounds. Various templating mechanisms - fibrous clay layers, undersea volcanic vault chimneys etc - eventually support the creation of self replicating molecules but since a) there can’t be any fossils of such tiny and prmitive atructures and b) whatever came next ate them, we’ll never know which particular mechanism was involved.Once self-replication exists, variation and natural selection drive the evolution of more efficient self-replicators. We believe at some point, all life on earth was RNA based. RNA can act as an information store AND an enzyme all on its own but it is rather unstable compared to DNA. DNA, on the other hand, doesn’t work an an enzyme, but if RNA life lead to RNA & protein life, DNA can then step in and out-do RNA life due to its greater stability.Now press fast forward for a few more billion years…

What's the most probable explanation for the “Spring-heeled Jack” phenomenon given all the eyewitness accounts?

This entity (first seen in Great Britain around 1837) is a DEMON. Demons can take the form or shape of virtually any creature.

If telekinesis really exists, what would be the most likely explanation by physicists?

If it were to be said that such a thing as telekinesis ( absurdly futuristic) exists in the physical world, the most probable explanation a physicist would give is that; as everything in the mass-filled tangible or intangible, visible or invisible, sensible or insensible reality exists consisting of atoms,which in turn are made up of subatomic particles like protons, neutrons and electrons ( two of which are positively and negatively charged). Such a phenomenon as telekinesis is possible if the charged particles in our brains were to influence the atomic structure of a certain physical body and the surrounding area through an electromagnetic barrier which in turn would cause the selected physical body to undergo any kind of spatial change or remain constant at a certain position in time.Though it's just a suggestion but a subject such as telekinesis should really be understood as pseudoscience and not as a practical endeavor.If you like the answer upvote it / if not notify me.

What is the most likely explanation for the origin of life? Are the pre-biological replicators as proposed by Dawkins (1976) still valid?

We don’t know how life arose. There are several excellent theories but no one has a full step-by-step sequence by which life could have arisen. We don’t even know for sure whether the conditions for life are common or rare in the universe. It’s the biggest unsolved problems in Science.One popular theory is that living things arose in alkaline, hydrothermal vents at the bottom of the ocean. These form mounds like the one depicted below. Tiny pores in the mounds would have provided reaction vessels where minerals (especially iron sulfide) would have driven chemical reactions that produce organic compounds from the hydrogen, methane, and NH3 (ammonia) flowing through the vents.(Image taken from: Functional Capabilities of the Earliest Peptides and the Emergence of Life)This mixture of organic molecules would have produced a kind of Primordial Soup from which living things could have arisen.The next step is the production of RNA molecules which have the ability to both store genetic information and control chemical reactions needed for the further development of life. This is one of the more obscure steps. Everyone agrees that it is an essentials step but no one has been able to show that suitable RNA molecules spontaneously form in vents and survive despite the high heat. (Here is a technical discussion: https://www.ncbi.nlm.nih.gov/pmc..., here are less technical discussions:Exploring Life's Origins: Nucleic Acids, Chemists Seek Possible Precursor to RNA | Quanta Magazine).Once RNA molecules form, there would be a sort of natural selection process where RNA molecules that reproduce themselves most efficiently reproduce themselves get selected for. This is called the RNA World hypothesis.Somehow (nobody knows how) RNA molecules developed the ability to code for proteins.Eventually, RNA molecules must have acquired the ability to store genetic information in the form of DNA. We don’t know how that happened either but once that happen, you have living things as we know them.The following picture develops this scheme in more detail, showing a succession of steps as if they occurred starting at the bottom of a vent and ending with living things at the top. In this scheme, the last common ancestor of all living things (LUCA) didn’t have the ability to produce its own DNA. It is taken from a book that gives an excellent but technical overview of this theory (The Logic of Chance: The Nature and Origin of Biological Evolution http://evolocus.com/Textbooks/Ko...).