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I have data on average time a real estate property is in the market/time to lease at different price points.

enter image description here

I'd like to calculate the conditional probability for a new property to get leased, given the price.

Additionally, I'd like to include information about the market such as level of supply which affects the avg. time the property is on the market.

How would I frame this as a bayesian probability estimation problem?

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  • $\begingroup$ Your plot is not relevant to your question: you want to swap the axes so that the software estimates average days as a function of price, rather than the other way around. $\endgroup$
    – whuber
    Aug 15, 2020 at 14:22

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A simple way to obtain a conditional probability for your problem is to use a logistic regression.

A logistic regression is a way to model a conditional probability in which we assume that a binary variable $y$ is conditionally distributed over ${\bf x}=(x_1, \ldots, x_M)$ as

$$ t\vert{\bf x} \sim \text{Bern}(\sigma({\bf w}^T {\bf x})) $$

You could obtain the expectation of the conditional distribution via maximum likelihood, a.k.a., minimization of the cross-entropy cost function, or follow a probabilistic approach and find the predictive conditional distribution.

To solve your problem via maximum likelihood you can use a library such as scikit-learn. I am not aware of any libraries that let you find the predictive conditional distirbution, but you can check this notebook for a guide on how to implement it.

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