The decision-theory tag has no wiki summary.
2
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0answers
54 views
Lower bound on uncertainty reduction
Let $T$ be a set of tuples such that each score tuple $s(t_i)$, $t_i \in T$ is uncertain (i.e., not known deterministically). The score $s(t_i)$ can be represented as a uniform probability density ...
3
votes
0answers
66 views
Inadmissibility of Simpson's rule
Let $B_t$, $t\ge0$ be a standard Brownian motion and suppose $0<x_1<x_2<\cdots<x_n<1$. Then the conditional expectation
$$
\mathbb E\left(\int_0^1 B_t\,dt \,\middle\vert\, B_0, ...
0
votes
1answer
60 views
Lower Expectation
Let $X$ be, for simplicity, a finite set (with the discrete topology).
Denote with $M(X)$ the set of probability measures on $X$ endowed with the weak topology.
For $\mu\in M(X)$ and a (necessarily ...
1
vote
2answers
40 views
What is the most common decision making math model?
I have been told that there are psychological math model to make decision. I want to know what is it and how it work.
2
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1answer
76 views
Coin Game, Probability and Fairness
The following game is being played :
Player $\mathrm{B}$ pays to Player $\mathrm{A}$ an amount $\mathrm{X}$ and throws a coin at most $20$ times. If at the toss $k\space (k \leq 20)$ tail is thrown, ...
0
votes
1answer
81 views
question related to Bayes' rule and Bays' risk.
Let $X_1, X_2, X_3, \ldots, X_n$ be a random sample for $N(e,1)$. Let the prior p.d.f. of $e$ be $N(0,\sigma^2)$ under the square error loss function $L(e,d)={(d-e)}^2$. Find the Bayes' decision rule ...
0
votes
0answers
50 views
Decision boundary gauss classifier
If I have 2 class and training data then I calculate the parameters from the training data example class 1: $\mu = 0.26$ $\sigma = 0.1221$ class 2: $\mu = 0.8625$ $\sigma = 0.096$.
My data is one ...
0
votes
1answer
63 views
Deducing probability of an event, when opponent's type is uncertain
Suppose, two players I and II, given a state space of three states$\{a,b,c\}$ with a common prior, $p(a) = p(b) =p(c) =1/3$, are endowed with two partitions of state space, $\mathscr{P}_\text{I} = ...
1
vote
2answers
300 views
Sum of two stopping times is a stopping time?
Let $\sigma$ and $\tau$ be two stopping times in $\mathscr{F}_t$ and let this filtration satisfy all the usual conditions.
Question: Is $\sigma + \tau$ a stopping time?
Attempt at a solution:
I ...
-1
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0answers
23 views
A intersects B complements [closed]
How should I drive the A intersects B complements decision tree? I am confused when I was trying to solve. Is there any missing data?
1
vote
1answer
257 views
Mathematical Analysis of the Electoral College
Let us consider the electoral college voting system used to elect the American president. I have a few questions from the point of view of decision-making/gaming theory. My ultimate goal is to vote in ...
0
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0answers
19 views
Solving for bayesian decision surfaces-quadric vector equation
I have three discriminant functions g1(x) , g2(x) and g3(x), each denoting one of the three classes under which an input is to be specified. The class conditional densities are gaussian.
The ...
0
votes
1answer
74 views
How to formulate the probability of being correct?
Suppose we have the following Bayesian net (or a probabilistic graphical model):
$L \rightarrow X \leftarrow F$, i.e. $P(L,X,F) = P(X|L,F)P(L)P(F)$ and all of these probabilities are known.
Let ...
0
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0answers
53 views
Controlling auto-correlated 1D Brownian motion
I have 1D Brownian motion process $x(t)$, and ability to control it.
The control allows to shift the $x$ by $D$ at any time.
I need the controlled process to be zero-mean, and to use the control ...
0
votes
1answer
72 views
Solution for assigning independent tasks to independent individuals
I have $n$ tasks that I wish to delegate to $m$ independent individuals, where $m$ is a factor or divisor of $n$. Each of the tasks $T_{1} ... T_{n}$ is independent. From the following two extremes, ...
1
vote
2answers
84 views
Efficient method for testing membership
Suppose I have a finite set $S$ of real numbers, and let $F(S)$ be the set of real numbers which can be obtained by applying additions and multiplications to elements of $S$ and their additive and ...
1
vote
1answer
126 views
Maximum Likelihood optimal threshold
I have a decision (detection) problem trying to decide between symbols ${0,2}$. I have the two probability density functions: $$
f(z|s=0) =
\begin{cases}
0.25z + 0.5, & -2\le\ z <0 \\
...
4
votes
1answer
468 views
What is the relationship of $\mathcal{L}_1$ (total variation) distance to hypothesis testing?
Kullback-Leibler divergence (a.k.a. relative entropy) has a nice property in hypothesis testing: given some observed measurement $m\in \mathcal{Q}$, and two probability distributions $P_0$ and $P_1$ ...
0
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0answers
57 views
Best estimator when prior distribution is random
Maximum a posteriori estimator is a Bayes estimator under the 0-1 loss function and some given prior distribution. I was wondering how to give an estimation that is best in some sense if the prior ...
