Simple Algorithm Question!?
An algorithm is parsimonious if it never compares the same pair of input values twice. (Assume that all the values being sorted are distinct.) (a) Is insertion sort parsimonious? Why/why not? (b) Is merge sort parsimonious? Why/why not? (c) Is heap sort parsimonious? Why/why not?
What does parsimonious mean?
"Parsimonious" generally means ungenerous or miserly. It's often associated with money matters, though it could be extended to other resources.That's not the entire picture with that word. It carries the sense of being excessively attached to money that the person becomes unwilling to spend it, even on himself. The classic example is the Dickens character Ebeneezer Scrooge.Best summed up by this line: "The retirement committee didn't give me a watch -- they told me the time instead."
What does it mean that a theory is “parsimonious”?
A theory that is not burdened with unnecessary assumptions is parsimonious. See Occam's razor. The rough idea is that, all else being equal, a theory that makes fewer assumptions is to be preferred because it will be more robust. So, we should distill a theory down to the minimum necessary assumptions sufficient to still remain consistent with the empirical data.
What are the laws of parsimony?
A principle according to which an explanation of a thing or event is made with the fewest possible assumptions.The principle that entities should not be multiplied needlessly; the simplest of two competing theories is to be preferred . - Occam's razor
How do you compare two ARIMA models in time series?
[ a good way to ]Say the trends captured in [each] are the same or different?They are on a spectrum of different or the same depending on the coefficients. If you are using an ARIMA model, instead of the more parsimonious flavors like AR MA, etc, then you should have good reason for using one and preprocess the data accordingly. Because with a thing like AR, “tomorrow looks like today or n days ago” is a very reasonable thing to explain to yourself for certain phenomena.Ideally, you would de-trend the data as much as possible and also try to strip out seasonality before using these models. This is why SARIMA and first[etc] differences are a thing.ARIMA isn’t really all that intuitive, so it’s in the class of last resorts if you are a practitioner. People will flame that because they don’t practice actually predicting things(and also needing to explain them). It’s nice to be able to convince yourself why things are happening.As for Akaike and BIC and so forth, I flip flop on which to use and you kinda have to take one as absolute truth to use it implicitly. Those gents were lightyears smarter than I, so I try to believe them if I’m in a corner.But! There are probably as many ways to measure models as there are models. One-step ahead error, mean squared error, APE, MAPE, [and many many super fancy things]and it���s a long and random walk down a windy road.I make the claim: parsimonious models and understanding them is valuable if you’re collecting the variables later and actually using the model. Variables cost money.Preprocessing the data and how to do that are intuitive once you look at the ACF and PACF and others. Then, you can pick a measure of error you believe in for that example.At the end of all that, you imagine a part of the data never happened and you try to predict it! Block sensibly, pick a measure, think, and repeat until satisfied.Chatfield writes a really good book on the stuff. Thank you for joining the time-series club! We are having a new years bash with the actuarial club, should be a doozy.Great Question, Carry on!
What are the six principles of scientific thinking?
1 - Extraordinary Claims Require Extraordinary Evidence – the more a claim contradicts what we already know, the more persuasive the evidence for this claim must be before we should accept it. #2 – Falsifiability – for a claim to be meaningful it must be capable of being disapproved. #3 – Occam's Razor – if two explanations account equally well for a phenomenon, we should generally select the more parsimonious one. #4 – Replicability – A study's findings can be duplicated consistently. #5 – Ruling out Rival Hypotheses – ask ourselves whether we've excluded other plausible explanations for it. #6 – Correlation isn't Causation – error of assuming that because one thing is associated with another, it must cause the other.
Is there a mathematical way to quantify the complexity of a given equation that relates two variables to each other?
Yes, the complexity of a mathematical model is usually referred to as parsimony[1]. This concept is closely related to degree of falsifiability[2], the capacity of a model to be empirically disconfirmed. There is usually a trade-off between parsimony and goodness of fit[3]of a model; the best balance between these two, also called Pareto front, is quantified by parsimony-fit indices[4].How parsimony is measured depends on the model. For an algebraic equation, it is usually the inverse of the number of nodes in its expression tree[5], which means that it goes from 1 (parsimonious model) to 0 (complex model).Here is an example: the equation[math]f(x) = a*sin(x) + c^2[/math]has an expression tree of 8 nodes, i.e. 4 operators [math](*, sin, +, pow)[/math] and 4 terminal nodes [math](a, x, c, 2)[/math], so its parsimony is 0.125.Footnotes[1] http://quantpsy.org/pubs/preache...[2] http://strangebeautiful.com/othe...[3] Occam's razor[4] http://arrow.dit.ie/cgi/viewcont...[5] Expression Trees
What is Wrong with Intelligent Design?
Proponents of Intelligent Design can sometimes ask questions about evolution which make Evolutionary Biologists think about their subject a little differently, or a little deeper: for example, their idea of Irreducible Complexity did indeed lead to biologists thinking about how features like the vertebrate eye, or the bacterial flagellum did evolve. Of course, so far evolution does in fact have an answer to all of the objections raised (especially since it is perfectly OK in science to say "We don't know yet.") The main problem with Intelligent Design is that it is NOT science. For a hypothesis or theory to be scientific, it must meet the following three important criteria: [1] Falsifiability. The hypothesis must, in principle, be able to be disproved by experiment. [2] Predictiveness. The hypothesis must make predictions which can be tested. [3] Parsimony. Also known as "Occam's Razor", the hypothesis must be the simplest explanation which fits all existing data. This means that it must introduce the fewest variables; only if the number of variables cannot fit all the data should more complexity be introduced. ID fails on all three counts: [1] It is not falsifiable, because it invokes a supernatural Designer. Since the supernatural is not open to investigation through science, we cannot verify or refute the existance of such a Designer. [2] It is not predictive, because we know nothing about the nature or motivation of the Designer, so we cannot make any predictions about what to expect from such a Designer. [3] It is not parsimonious, because the Designer must neccessarily be AT LEAST as complicated as the object that has been designed. This therefore at least doubles the complexity of the model. There are other valid scientific objections to ID as a model. The wikipedia entry describes them decently: http://en.wikipedia.org/wiki/Intelligent... Of course, there are many non-scientific subjects which are worthy of study - and you might consider ID one of them. But it should not be confused with science, and it should not be taught in a science curriculum.