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PPLs often extend from a basic language. For instance, Turing.jl [12] is based on Julia, Infer.NET is based on .NET Framework, [13] while PRISM extends from Prolog. [14] However, some PPLs, such as WinBUGS, offer a self-contained language that maps closely to the mathematical representation of the statistical models, with no obvious origin in another programming language.
Regions in the state space with many particles correspond to a greater probability that the robot will be there—and regions with few particles are unlikely to be where the robot is. The algorithm assumes the Markov property that the current state's probability distribution depends only on the previous state (and not any ones before that), i.e ...
A gambler has $2, she is allowed to play a game of chance 4 times and her goal is to maximize her probability of ending up with a least $6. If the gambler bets $ on a play of the game, then with probability 0.4 she wins the game, recoup the initial bet, and she increases her capital position by $; with probability 0.6, she loses the bet amount $; all plays are pairwise independent.
When the probability distribution of the variable is parameterized, mathematicians often use a Markov chain Monte Carlo (MCMC) sampler. [4] [5] [6] The central idea is to design a judicious Markov chain model with a prescribed stationary probability distribution. That is, in the limit, the samples being generated by the MCMC method will be ...
A discrete probability distribution is applicable to the scenarios where the set of possible outcomes is discrete (e.g. a coin toss, a roll of a die) and the probabilities are encoded by a discrete list of the probabilities of the outcomes; in this case the discrete probability distribution is known as probability mass function.
On average, a beginner with these habits—strength training at least three times per week, eating about one gram of protein per pound of body weight, and maintaining an appropriate caloric ...
The probability of tossing tails is 1 − p (so here p is θ above). Suppose the outcome is 49 heads and 31 tails, and suppose the coin was taken from a box containing three coins: one which gives heads with probability p = 1 ⁄ 3, one which gives heads with probability p = 1 ⁄ 2 and another which gives heads with probability p = 2 ⁄ 3 ...
'Tis the season for spoiling! During a big shopping event like this Black Friday weekend, it's a great time to shop for luxury items you might not always splurge on.