A probability provides a quantitative description of the likely occurrence of a particular event.
3
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2answers
31 views
Trying to understand formula for the Survival Function (survival analysis)
I'm trying to learn the Cox Proportional Hazards Model on my own, and found this link that describes it in clear terms. But when I get to formula (5) (S(t) = exp(−H(t))) I can't figure out where ...
1
vote
0answers
12 views
How can I calculate the relative probability of each move resulting in a win, given historic win/loss data for the possible moves?
We are at a position in a game where there is a decision to be made. As there are relatively few game positions and possible moves, we have collected statistics from previous occasions the game was ...
6
votes
1answer
103 views
Kernel density estimation on asymmetric distributions
Let $\{s_1,\ldots,s_N\}$ be a set of samples drawn from an unknown (but certainly asymmetric) probability distribution.
I would like to find the probability distribution by using the KDE approach:
$$
...
3
votes
1answer
39 views
Probability of reaching a threshold after several trials
I was wondering if there wasn't some better way to get to the bottom of this question I had regarding the chances of reaching a certain threshold of guessing numbers correctly over a series of trials. ...
5
votes
1answer
50 views
Probability of a subsequence occurring simultaneously in two longer sequences
Suppose I have two sequences of characters of length L and M respectively, with the characters chosen i.i.d. from an alphabet of A through H, each with probability p=1/8. I want to find the ...
2
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0answers
26 views
+100
Importance sampling of finite path of stochastic difference equation
Before passing to question, let me briefly recap what's importance sampling of random variables is about. Suppose $\xi$ is a real-valued random variable with density $f$, and let $g:\Bbb R\to \Bbb R$ ...
0
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0answers
41 views
Identifying argmax result in information theory
I'm reading through a thesis at the moment which uses a "well known result from information theory", namely
$\mathrm{argmax}_\mathbf{g}\,\mathbf{f}\,\mathrm{log}\,\mathbf{g} = \mathbf{f}$,
for two ...
0
votes
0answers
21 views
Logit: what does irrelevance of the benchmark mean?
In McFadden - Analysis of Qualitative Choice Behavior, Axiom 3 (Irrelevance of Alternative Set Effect) states:
The function $V(s,x,z)$ determining the selection probabilities in
$P(x|s,B) =\ ...
1
vote
1answer
17 views
Weighted sampling from objects with costs
I have a set of models which I have fit using nonlinear regression to some data, and hence for each has an associated squared error, or cost. I want to sample an models in a manner which favours ...
0
votes
1answer
37 views
Probability distributions
What is the probability that a random number [0,1) will lie in [0.5,0.6]?
As far as I know, there are 3 probability distributions in physics we usually use, but I am not sure when we can use ...
2
votes
1answer
51 views
Finding conditions on unspecified CDF that permit a solution to an equation
[A duplicate thread can also be found at http://mathoverflow.net/questions/131142/finding-conditions-on-unspecified-cdf-that-permit-a-solution-to-an-equation ]
Let $F(\alpha) := ...
0
votes
0answers
37 views
How to calculate probability with sigmoid output in feedforward neural network?
first of all I'm sorry for my not very skilled English, but I will do my best to explain my problem.
I'm trying to create a feedforward neural network with one hidden layer (with probably arctan ...
3
votes
1answer
62 views
Probability over $50$-day ranges to predict results on one day
The title is a bit complex, so I'll just post the question. This is in preparation for a final I'm going to take.
Consider the total number of cars that a car dealership might sell over $50$ ...
0
votes
2answers
66 views
Finding the probability of given model
I'm trying to model a system given as a project, any help or advice is useful for now.
Here our assumptions for a part of it:
If I study for the finals and do assignments, I have $80\%$ chance to ...
1
vote
2answers
260 views
Decomposition of the sum of two random variables
We observe the input samples as $Z = X+Y$, where distribution of $Z$ could be estimated by histogram of samples and $X,Y$ are two independent random variables. One of the variable was known following ...
8
votes
0answers
110 views
Product of two independent random variables
I have a sample of about 1000 values. These data are obtained from the product of two independent random variables $\xi \ast \psi $. The first random variable has a uniform distribution $\xi \sim ...
1
vote
1answer
125 views
Are first passage times in a Brownian motion the same as the ARL in a CUSUM?
I am investigating a link between a random walk with drift (call it Brownian process or difusion with drift) and the CUSUM statistic.
The CUSUM procedure accumulates deviations from the process mean ...
0
votes
3answers
54 views
When the selection depends on a prior experience, what statistical test is appropriate?
We have raised a batch of frogs on one species A fly. We then present the frogs with species A and a second species B fly. Will the frogs pick species A or B? Lets say 40% choose A and 60% choose B. ...
3
votes
1answer
110 views
How can I predict the odds that a dodgeball team is going to win based on the winning history of its players?
Imagine there are 80 dodgeball players in the world. Each of them has played thousands of dodgeball games with the other 79 players in more-or-less random order. This is a world without teams (e.g., ...
1
vote
0answers
22 views
Partials of PDF with no closed form solution
I need to estimate partial derivatives for all N parameters denoted $\theta_{N}$ of a probability density function(PDF) $\mathcal{f}$.
This PDF $\mathcal{f}$ has no closed form solution and is ...
0
votes
1answer
139 views
How to rewrite a sum of probabilities formula as multiplications?
I have an equation like that:
$p(r|s)= \frac{p(s,r)}{p(s)}=\frac{ \sum_{w,c} p(c,s,r,w)}{\sum_{w,c,r} p(c,s,r,w)} $
I am new to probability and I want to learn that how can I write sum formula as ...
0
votes
0answers
20 views
Random variables resulting due to single or multiple experiments
Assume there are ‘n’ entities that collect some data after each ‘t’ time instances. Generally their collected data is within an “expected” range. However, occasionally the data exceeds the “expected” ...
4
votes
1answer
129 views
Confusion related to semisupervised learning in random walk
I am trying to understand the semi supervised learning in random walk. Lets say I have 10 classes and I have some labelled and unlabelled points. Now, I need to find the labels for the unlabelled ...
1
vote
1answer
37 views
Expected peak to trough calculation
I am having trouble coding up in R equation 3.1 in the following paper: http://www.intelligenthedgefundinvesting.com/pubs/rb-cb.pdf
My function:
...
1
vote
2answers
93 views
Function with variable having gaussian distribution
If I have a variable $X$ whose Gaussian distribution is known and let $f$ be a known function, is there a way to compute $f(X)$ i.e. the resulting Gaussian distribution from this? Is the result ...
1
vote
1answer
27 views
Assigning a sample set to one of several populations based on composition
I have a problem that seems tractable, which I will attempt to describe with classic balls and buckets probability nomenclature.
Imagine someone brings you a bag of colored balls. This sample was ...
1
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0answers
38 views
Question about proof for luce choice axiom w.r.t. conditional probability
In Luce (1959) the choice axiom is definied, that for a finite subset $T$ of $U$ such that, for every $S\subset T, P_S$ is defined.
If $P(x,y)\ne 0,1$ for all $x,y\in T$, then for $R\subset S\subset ...
5
votes
0answers
118 views
Luce Choice Axiom, question about conditional probability
I'm reading Luce (1959). Then I found this statement:
When a person chooses among alternatives, very often their responses
appear to be governed by probabilities that are conditioned on the
...
2
votes
0answers
43 views
A question regarding the central limit theorem
I would appreciate if you could please take a look at the following attempt. I am preparing for an upcoming exam, and this is taken from a past exam paper. I would like to know if it is correct. Thank ...
4
votes
0answers
36 views
Estimating repeat shoppers from an incomplete sampling
I'm trying to estimate how many people visited the farmers market once, twice, thrice, etc. in a given time period, using sampled data. We have interview data from approximately 50% of visitors as ...
0
votes
1answer
55 views
Determining butterfly weight distribution
I'm a researcher studying a specific butterfly species. I've conducted an experiment where I measure the weight of this species at different locations on the earth. The data is cateogorical and ...
0
votes
1answer
34 views
Working out probability with alpha and beta
Working out probability with alpha and beta?
Let's say in an experiment, the Null hypothesis is patients having Condition A. Alpha (type I error) is 0.05 and beta (type II error) is 0.15.
If i have ...
3
votes
1answer
220 views
How to interpret the divergence of Fisher information expectation?
Consider translated Weibull distribution with probability density function:
$$
f(x ; k, \lambda, \theta) = \frac{k}{\lambda} \left( \frac{x-\theta}{\lambda} \right)^{k-1} \exp\left( - ...
2
votes
0answers
42 views
How to interpret the divergence of Fisher information expectation [duplicate]
Possible Duplicate:
How to interpret the divergence of Fisher information expectation?
Consider translated Weibull distribution with probability density function:
$$
f(x ; k, \lambda, ...
0
votes
1answer
32 views
Probability of a specific element in different sets having the same attribute value
Assume we have n number of sets with varying number of elements, some of which appear in more than one set. Each element can have zero or more attributes.
If we ...
0
votes
1answer
138 views
Total probability problem
I currently have log files all off different sizes, and I am trying to calculate the total probability of an event that occurs being an error.
For example:
Log file #1: Has a total of 1000 ...
0
votes
1answer
33 views
Calculating chance of event over time from sample data
I am doing the following experiment:
I have slots which I monitor, the slot can either be occupied / free. The study is per slot, so we are discussing one slot here.
Every now and then I receive the ...
4
votes
3answers
121 views
Problem with p-values from A/B testing
I'm pretty confused right now and the more I look at it, the more confused I get. Overthinking!
I'm doing some A/B tests for my website. I'm using the significance calculator that's in this article:
...
2
votes
2answers
167 views
Is the probability of a unique DNA match the same, irrespective of the size of the dataset?
One can argue that the evidential value of a database hit increases when the database gets larger. Indeed, having a unique hit in a database simply means that all the other persons in the database are ...
2
votes
1answer
33 views
Detect bias in subset of Bernoulli processes
I'm looking for advice on the best method to use to answer this question.
General scenario:
We have multiple testing machines A,B,C,D etc. each tests a identical randomly selected part and provides ...
0
votes
1answer
130 views
Marginalizing a conditional distribution
Suppose I have a conditional discrete distribution $P_{M|A}(m,a)$. If I take sum over $m$, i.e. $\sum_{m}P_{M|A}(m,a)$, do I get $f_A(a)$, where $f_A(a)$ is the pmf of the random variable A?
0
votes
0answers
24 views
How to calculate probability contingent on multiple events?
This isn't a homework problem, but something I just thought of when watching a crime show.
If I am trying to determine the probability of [insert Conclusion] or C, and I know C is comprised of A ...
3
votes
2answers
151 views
How to define a posterior probability of y given x when the model is not probabilistic?
Suppose we have a very simple online k-means where each new data-point is assigned to its nearest center (the mean is updated incrementally). Each center (cluster) is labelled with the most common ...
0
votes
0answers
52 views
Distribution of independent binomial variables conditional upon the sum
Suppose that we have independent binomial variates with differing sizes and probabilities $X_i \sim Binomial(n_i,p_i)$, and $Z = \sum_iX_i$ is the sum. I understand that $Z$ is distributed ...
1
vote
1answer
44 views
Consistency of the marginals
I have random variables $U,V_1,V_2,V_3$, and I want to specify the following distributions (the "sum notation" means a mixture):
$$ U\sim\mathrm{Gamma}(2,3) $$
$$ V_1 \mid U=u,V_2=v_2,V_3=v_3 \sim ...
-1
votes
0answers
51 views
satellite radios has a 3% defective rate. A random sample of 1000 radios is drawn. What is probability the defective rate is greater than 5%?
The assembly line that produces satellite radios has historically resulted in a 3% defective rate. A random sample of 1000 radios is drawn. What is the probability that the defective rate is ...
1
vote
0answers
29 views
Hilbert curves: bounds / probabilities of preserving neighbors
Hilbert Curves (Wikipedia) are space-filling curves said to "fairly well preserve locality".
Do you know any theoretical results here, such as bounds that neighbors within a radius of $\varepsilon$ ...
1
vote
1answer
57 views
Z test of coefficients of output?
I have fitted a certain ARMA model and got the following output:
As you can see, some coeff were set to zero and the focus is on the ma5 coeff and the intercept. To be exactly, the ma5 coeff is ...
1
vote
1answer
38 views
Probability of $C_n^k$ elements which contains at least K elements
I'm trying to do a simple problem.
I have a set of integers:
$$N={1, 2, 3, 4, 5, 6} $$
I want to combine this elements in a set of combinations of size $k=3$ from this set, i.e. $C_6^3$, where ...
2
votes
1answer
81 views
Determining conserved features using a Bayesian approach
I would like to perform some sort of binary classification, and my data set consists of 100 examples (for each class), which are vectors with 2500 elements. Ideally, I would like to determine which ...
