Probability Archives - GaussianWaves

Implementing Markov Chain in Python

Mathuranathan — Sun, 20 Mar 2022 15:30:00 +0000

Keywords: Markov Chain, Python, probability, data analysis, data science Markov Chain Markov chain is a probabilistic models that describe a sequence of observations whose occurrence are statistically dependent only on the previous ones. This article is about implementing Markov chain in Python Markov chain is described in one of the earlier posts. For better understanding ... Read more

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Bayes’ theorem

Mathuranathan — Sat, 17 Apr 2021 13:48:29 +0000

Key focus: Bayes’ theorem is a method for revising the prior probability for specific event, taking into account the evidence available about the event. Introduction In statistics, the process of drawing conclusions from data subject to random variations – is called “statistical inference”. Usually, in any random experiment, the observations are recorded and conclusions have ... Read more

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Hidden Markov Models (HMM) – Simplified !!!

Mathuranathan — Tue, 17 Mar 2020 05:08:35 +0000

Markov chains are useful in computing the probability of events that are observable. However, in many real world applications, the events that we are interested in are usually hidden, that is we don’t observe them directly. These hidden events need to be inferred. For example, given a sentence in a natural language we only observe the ... Read more

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Markov Chains – Simplified !!

Mathuranathan — Fri, 06 Mar 2020 07:11:37 +0000

Key focus: Markov chains are a probabilistic models that describe a sequence of observations whose occurrence are statistically dependent only on the previous ones. ● Time-series data like speech, stock price movements.● Words in a sentence.● Base pairs on the rung of a DNA ladder. States and transitions Assume that we want to model the ... Read more

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Plot histogram and estimated PDF in Matlab

Mathuranathan — Thu, 06 Oct 2016 07:40:37 +0000

Key focus: With examples, let’s estimate and plot the probability density function of a random variable using Matlab histogram function. Generation of random variables with required probability distribution characteristic is of paramount importance in simulating a communication system. Let’s see how we can generate a simple random variable, estimate and plot the probability density function ... Read more

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Derive BPSK BER – optimum receiver in AWGN channel

Mathuranathan — Wed, 25 Jul 2012 09:05:15 +0000

Key focus: Derive BPSK BER (bit error rate) for optimum receiver in AWGN channel. Explained intuitively step by step. BPSK modulation is the simplest of all the M-PSK techniques. An insight into the derivation of error rate performance of an optimum BPSK receiver is essential as it serves as a stepping stone to understand the ... Read more

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