Questions Tagged With probability-modelshttp://www.or-exchange.com/tags/probability-models/?type=rssquestions tagged <span class="tag">probability-models</span>enWed, 22 Jan 2014 03:56:17 -0500How often are sport statistics right?http://www.or-exchange.com/questions/9109/how-often-are-sport-statistics-right<p>There's <a href="http://money.cnn.com/2014/01/21/news/companies/buffett-ncaa-bracket/index.html?iid=Lead">a challenge</a> to correctly predict the entire bracket of the USA basketball teams. This is (mostly) a game of chance. But I wondering how much is it a game of chance?</p>
<p>If we know how often the basketball statistics can predict the correct outcome of a match, we can calculate what are the odds to get it correct. Here are my quick-I-just-got-up-this-morning calculations:</p>
<ul>
<li>Statistics accuracy in predicting the winner: chance to win</li>
<li>100% accuracy: 1</li>
<li>90% accuracy: 1 / 763</li>
<li>80% accuracy: 1 / 1274473</li>
<li>70% accuracy: 1 / 5738831574</li>
<li>60% accuracy: 1 / 94726442140000</li>
<li>50% accuracy (all teams are equally good): 1 / 9223372036854775808</li>
<li>n accuracy: n^63</li>
</ul>
<p>So, how good are statistics in predicting the outcome of a match these days?</p>Geoffrey De SmetWed, 22 Jan 2014 03:56:17 -0500http://www.or-exchange.com/questions/9109/how-often-are-sport-statistics-rightprobability-modelsProgramming for an uncertain envirnomenthttp://www.or-exchange.com/questions/5216/programming-for-an-uncertain-envirnoment<p>Hi,</p>
<p>my work is related <em>to supplier selection</em> in an uncertain environment. For that i am using <a href="http://en.wikipedia.org/wiki/Newsvendor_model">news vendor approach</a>. </p>
<p>While I do coding (MATLAB), I get difficulties as the number of suppliers increases. Specifically in contour plot its not possible to show more than three dimensions.</p>
<p>Is there any other method to solve the problem?</p>PriteeThu, 12 Apr 2012 08:04:24 -0400http://www.or-exchange.com/questions/5216/programming-for-an-uncertain-envirnomentsupplierprobability-modelsselectionnewsvendoruncertainityAllocation probability questionhttp://www.or-exchange.com/questions/5143/allocation-probability-question<p>Hi all,</p>
<p>Let's say you have 10 bins and 25 balls. All the bins and balls are separately labeled and distinct. How do you calculate the probability of a given configuration of the 25 balls stored in the 10 bins? What about if the balls are NOT labeled, so any version of three balls in bin #2 is the same? Finally, what if the bins aren't labeled either?</p>
<p>The context is that I would like to estimate household membership using a maximum entropy objective where balls == people and bins == households.</p>
<p>I would love a simple and general answer, but any pointers to where to look would be appreciated. Maybe the multivariate hypergeometric distribution applies, but I can't make it work (I am not very good at this type of problem though...)</p>
<p>Thanks!</p>forkandwaitTue, 27 Mar 2012 16:29:47 -0400http://www.or-exchange.com/questions/5143/allocation-probability-questionprobability-modelsRemaining Life Markov Chainhttp://www.or-exchange.com/questions/4754/remaining-life-markov-chain<p>I came across a term called Remaining Life Markov Chain while working on randome walks. </p>
<p>What is "remaining life" markov chain?</p>
<p>do we have any references for this application.?</p>
<p>thanks</p>RamSun, 05 Feb 2012 12:31:48 -0500http://www.or-exchange.com/questions/4754/remaining-life-markov-chainapplicationsprobability-modelsor-communityHow does one model probability dependencies?http://www.or-exchange.com/questions/3473/how-does-one-model-probability-dependencies<p>Are there any good resources on probability dependencies?</p>
<p>For example:</p>
<ul>
<li>John Smith has 50% chance to snore.</li>
<li>John has 20% chance to die of long cancer.</li>
<li><em>What is the chance that John snores and will die of long cancer?</em> 10% (snoring and long cancer are unrelated)</li>
<li>John has 50% chance to smoke.</li>
<li><em>What is the chance that John smokes and will die of long cancer?</em> Not 10%, but more (let's presume 15%), because if he smokes, he's more likely to get long cancer.</li>
</ul>
<p>So what's the standard way to model this relationship between smoking and long cancer?</p>Geoffrey De SmetSat, 13 Aug 2011 09:02:51 -0400http://www.or-exchange.com/questions/3473/how-does-one-model-probability-dependenciesprobability-modelsCalling R functions from Javahttp://www.or-exchange.com/questions/3181/calling-r-functions-from-java<p>What is the easiest way to call 'R' functions from inside Java code. Google search indicates several different approaches, it's a bit confusing and i'm no R expert.
Easy = anything that doesn't involve many other dependencies that have to downloaded or learnt, minimal coding/effort, works on Windows, and gets the job done. </p>shivaTue, 12 Jul 2011 13:33:27 -0400http://www.or-exchange.com/questions/3181/calling-r-functions-from-javaprobability-modelssoftwareprogrammingresearchIs there a way to solve an optimization problem where a decision variable shows up in an upper bound (or lower bound) of summation?http://www.or-exchange.com/questions/796/is-there-a-way-to-solve-an-optimization-problem-where-a-decision-variable-shows-up-in-an-upper-bound-or-lower-bound-of-summation<p><strong>minimize/maximize</strong> \(\sum_{i=0}^{f(n)} G(x,n)\)
s.t. \(n \ge 1\) and \(x\) in some feasible region</p>
<p>The decision variables are \(x\) (a vector) and \(x\) (a scalar).</p>
<p>How is this type of optimization problem classified?<br>
Has it been studied? Any references?</p>
<p>Here is an example of how an unconstrained version of the problem arises:</p>
<p><em><strong>"Optimizing capacity of buses, K, on a bus route"</strong></em></p>
<ul>
<li>The bus route is a loop. One point on the loop is designated the “bus station,” the only place passengers can get on the bus.</li>
<li>Passengers can get off the bus at any point on the bus route (other than the bus station).</li>
<li>By the time a bus returns to the bus station, all of its passengers will have gotten off.</li>
<li>Passengers arrive by a Poisson process with rate lambda (per hour).</li>
<li>A bus cannot take off from the bus station until it has K passengers on board.</li>
<li>There are N buses that operate on the one route. When a bus arrives at the bus station, it waits in line behind buses that are already there. It's a FIFO system where the first bus in line gets first K arriving passengers, and so on…</li>
<li>When a passenger arrives at the station, s/he gets on the first bus in line and waits until enough
passengers have gotten on the bus to make a total of K passengers before the bus takes off. Passengers get on the bus in a FIFO manner as well.</li>
<li>The waiting time for a passenger is the length of time from when that passenger arrived at the bus station until a bus with that passenger on board takes off.</li>
<li>The waiting time for a bus is the length of time from when the bus arrives at the station until it has K passengers on board, at which point it takes off.</li>
<li>It is assumed that the “loading” of passengers takes zero time.</li>
<li>Also, it takes C(K) time for buses to travel the length of the bus route. This is a function of K because there is time lost for each passenger that is dropped off.</li>
</ul>
<p><strong>What is the expected waiting time for passengers? For buses?</strong></p>
<p>The <strong>optimization</strong> aspect is as follows. Bus drivers want to make the most amount of money in an hour. The higher K is, the more money a bus driver makes per trip on the bus route, but the number of trips per hour goes down. There is a monetary cost (to bus drivers) for each minute that a passenger waits at the stop for a bus (as in loss of goodwill). So the objective function is dependent on both the expected waiting time of buses (which determines how much money buses make per hour) and the expected waiting time of passengers.</p>
<p>I was able to get an expression for the expected waiting time of buses and it is of the form:</p>
<p><strong>E[Waiting time for a bus]</strong> = \(\sum_{j=0}^{KN} \frac{KN-j}{\lambda}\frac{(\lambda C(K))^j}{j!}e^{-\lambda C(K)}\)</p>
<p><strong>E[Waiting time for a passenger] = ??</strong></p>
<p>I have not been able to get an expression for the waiting time of passengers, but I suspect it will also have the upper bound of summation as some function of K.</p>archbishopmendelTue, 12 Oct 2010 01:30:44 -0400http://www.or-exchange.com/questions/796/is-there-a-way-to-solve-an-optimization-problem-where-a-decision-variable-shows-up-in-an-upper-bound-or-lower-bound-of-summationprobability-modelsoptimizationnonlinear-optimizationHow to determine useful signals for prediction models?http://www.or-exchange.com/questions/131/how-to-determine-useful-signals-for-prediction-models<p>With regards to <a href="http://mat.tepper.cmu.edu/blog/?p=1024" rel="nofollow">this blog post</a>. I have collected a number of datasets for different contributing variables to homicide incidents. I would like to know which of these variables is significantly contributing to the number of homicide in the area. I was planning to use our archaic friend, ANOVA, to see if there is any significant effect from each of these variables and then include the dominating ones in my model.</p>
<p>I just want to know if there is any better (or perhaps more modern) tool to find good signals. perhaps Bayesian Inference? :)</p>MarkWed, 06 Jan 2010 08:14:46 -0500http://www.or-exchange.com/questions/131/how-to-determine-useful-signals-for-prediction-modelsbayesiananovaanalyticsprobability-models